Sequencer | StrangerCoug's turn

Plotinus · Post Post #469 (isolation #200) » Mon Mar 30, 2020 8:07 am

Yeah, that's why I said he'd have to still provide some other rule that the rest of us could use, like maybe all green numbers happen to be the ones with straight lines in them when you draw them, then we could allow "drawn with a straight line"

Plotinus · Post Post #472 (isolation #201) » Mon Mar 30, 2020 7:16 pm

Spoiler: Completed sequences

[1, 2, 3, 4, 5, 10, 39, 55] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
} numbers that are divisible by their first digit
[6, 21, 27, 42, 69, 72, 78, 165, 576] {
3n
} numbers whose sum is a multiple of 3
[4, 8, 9, 15, 20, 32, 66, 80] {
n = 2ⁱ ± 2^j
} numbers that can be written as the sum or difference of two powers of two
[20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 2^k; a_i ≥ 0; d > 0; k ∈ ℤ
} sum of the digits is a power of 2 }
[16, 20, 25, 32, 94, 120, 200] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is prime
[1, 3, 4, 5, 6, 7, 9] {
n < 10
} single digit numbers }
[3, 5, 16, 17, 25, 64, 128, 729] {
p^k, p is prime, k ≥ 1
} powers of primes (1st and higher)
[12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
[10, 88, 90, 97, 100, 225, 441] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
} digit sum is a perfect square
[1, 2, 3, 7, 9 11, 77]{
str(n)[::-1] == str(n)
} Palindromic numbers
[84, 56, 3, 29, 93, 5, 70] {
n % 9 ∈ {2, 3, 5, 7}
Numbers who digital root is prime
[22, 3, 8, 65, 51, 64, 12] {
i % (i % 10) == 0 }
Numbers divisible by their last digit
[12, 20, 21, 27, 512, 52, 24] {
n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
} Numbers where at least one digit is 2
[15, 50, 75, 100, 50, 35, 250] {
5n
} numbers that are evenly divisible by 5
[13, 28, 35, 300, 98 343, 63, 289] contains a treble letter when written in Roman numerals
[6, 15, 44, 1, 36, 55, 4] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
} Numbers divisible by each of its digits
[18, 99, 324, 500, 8, 45, 81, 700] {
k² | n; k > 1
} numbers with a factor that is a square number
[25, 49, 100, 256, 400, 529, 841] {
n²
} square numbers
[1, 15, 17, 18, 1000, 11, 16, 19] {
n = 1 * 10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with one
[10, 40, 600, 60, 20, 800, 1000] {
n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that end with zero
[83, 89, 400, 1, 41, 45, 484] {
n = 2^x*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d, x ≥ 0
} first digit is a power of 2
[5, 10, 18, 43, 30, 59, 81, 27, 45] {
n is odd (mod 9)
numbers whose digital root is odd
[29, 61, 71, 89, 3, 7, 11, 13] {
n is prime
} primes
[16, 56, 76, 196, 676, 6, 36] {
n ≡ 6 (mod 10)
} numbers that end in 6
[30, 58, 87, 31, 47, 21, 34, 63] 2 digit numbers where one digit is prime and the other is not
[4, 21, 30, 2, 84, 1, 3] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i | 12
} sum of the digits is a factor of 12
[7, 8, 42, 1000, 5, 6, 121, 750] { {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_d <= a₀
} last digit is less than or equal to the first digit

Analysis (Not_Mafia, Micc) has 116 points and:

[91, 900, 961] {
n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with nine
[1, 125, 216] at least one digit is 1

Algebra (StrangerCoug, skitter30) has 82 points and:

[19, 46, 64, 361] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[1, 17, 33, 73, 729] {
n ≡ 1 (mod 8)
} numbers that are congruent to 1 mod 8
[10, 23, 36, 49] {
n ≡ 10 (mod 13)
} numbers congruent to 10 mod 13
[15, 57, 21] {
3 * p, p is prime
} numbers that are 3 times a prime number

Cards left in deck: 17

It is

Micc's

turn

When we run out of cards, the game will continue until 4 people pass in a row.

Plotinus · Post Post #475 (isolation #202) » Tue Mar 31, 2020 5:54 pm

Spoiler: Completed sequences

[1, 2, 3, 4, 5, 10, 39, 55] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
} numbers that are divisible by their first digit
[6, 21, 27, 42, 69, 72, 78, 165, 576] {
3n
} numbers whose sum is a multiple of 3
[4, 8, 9, 15, 20, 32, 66, 80] {
n = 2ⁱ ± 2^j
} numbers that can be written as the sum or difference of two powers of two
[20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 2^k; a_i ≥ 0; d > 0; k ∈ ℤ
} sum of the digits is a power of 2 }
[16, 20, 25, 32, 94, 120, 200] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is prime
[1, 3, 4, 5, 6, 7, 9] {
n < 10
} single digit numbers }
[3, 5, 16, 17, 25, 64, 128, 729] {
p^k, p is prime, k ≥ 1
} powers of primes (1st and higher)
[12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
[10, 88, 90, 97, 100, 225, 441] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
} digit sum is a perfect square
[1, 2, 3, 7, 9 11, 77]{
str(n)[::-1] == str(n)
} Palindromic numbers
[84, 56, 3, 29, 93, 5, 70] {
n % 9 ∈ {2, 3, 5, 7}
Numbers who digital root is prime
[22, 3, 8, 65, 51, 64, 12] {
i % (i % 10) == 0 }
Numbers divisible by their last digit
[12, 20, 21, 27, 512, 52, 24] {
n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
} Numbers where at least one digit is 2
[15, 50, 75, 100, 50, 35, 250] {
5n
} numbers that are evenly divisible by 5
[13, 28, 35, 300, 98 343, 63, 289] contains a treble letter when written in Roman numerals
[6, 15, 44, 1, 36, 55, 4] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
} Numbers divisible by each of its digits
[18, 99, 324, 500, 8, 45, 81, 700] {
k² | n; k > 1
} numbers with a factor that is a square number
[25, 49, 100, 256, 400, 529, 841] {
n²
} square numbers
[1, 15, 17, 18, 1000, 11, 16, 19] {
n = 1 * 10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with one
[10, 40, 600, 60, 20, 800, 1000] {
n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that end with zero
[83, 89, 400, 1, 41, 45, 484] {
n = 2^x*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d, x ≥ 0
} first digit is a power of 2
[5, 10, 18, 43, 30, 59, 81, 27, 45] {
n is odd (mod 9)
numbers whose digital root is odd
[29, 61, 71, 89, 3, 7, 11, 13] {
n is prime
} primes
[16, 56, 76, 196, 676, 6, 36] {
n ≡ 6 (mod 10)
} numbers that end in 6
[30, 58, 87, 31, 47, 21, 34, 63] 2 digit numbers where one digit is prime and the other is not
[4, 21, 30, 2, 84, 1, 3] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i | 12
} sum of the digits is a factor of 12
[7, 8, 42, 1000, 5, 6, 121, 750] { {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_d <= a₀
} last digit is less than or equal to the first digit

Analysis (Not_Mafia, Micc) has 116 points and:

[91, 900, 961] {
n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with nine
[1, 125, 216] at least one digit is 1
[14, 62, 256] {
(2 | n) ∧ (3 | n ↓ 5 | n)
} divisible by 2 but not by 3 or 5

Algebra (StrangerCoug, skitter30) has 82 points and:

[19, 46, 64, 361] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[1, 17, 33, 73, 729] {
n ≡ 1 (mod 8)
} numbers that are congruent to 1 mod 8
[10, 23, 36, 49] {
n ≡ 10 (mod 13)
} numbers congruent to 10 mod 13
[15, 57, 21] {
3 * p, p is prime
} numbers that are 3 times a prime number

Cards left in deck: 14

It is

skitter30's

turn

When we run out of cards, the game will continue until 4 people pass in a row.

Welcome, Jake the Wolfie! We'll be starting a new game soon. I'll put you in the replacements queue for now.

Plotinus · Post Post #477 (isolation #203) » Wed Apr 01, 2020 2:54 am

Spoiler: Completed sequences

[1, 2, 3, 4, 5, 10, 39, 55] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
} numbers that are divisible by their first digit
[6, 21, 27, 42, 69, 72, 78, 165, 576] {
3n
} numbers whose sum is a multiple of 3
[4, 8, 9, 15, 20, 32, 66, 80] {
n = 2ⁱ ± 2^j
} numbers that can be written as the sum or difference of two powers of two
[20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 2^k; a_i ≥ 0; d > 0; k ∈ ℤ
} sum of the digits is a power of 2 }
[16, 20, 25, 32, 94, 120, 200] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is prime
[1, 3, 4, 5, 6, 7, 9] {
n < 10
} single digit numbers }
[3, 5, 16, 17, 25, 64, 128, 729] {
p^k, p is prime, k ≥ 1
} powers of primes (1st and higher)
[12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
[10, 88, 90, 97, 100, 225, 441] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
} digit sum is a perfect square
[1, 2, 3, 7, 9 11, 77]{
str(n)[::-1] == str(n)
} Palindromic numbers
[84, 56, 3, 29, 93, 5, 70] {
n % 9 ∈ {2, 3, 5, 7}
Numbers who digital root is prime
[22, 3, 8, 65, 51, 64, 12] {
i % (i % 10) == 0 }
Numbers divisible by their last digit
[12, 20, 21, 27, 512, 52, 24] {
n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
} Numbers where at least one digit is 2
[15, 50, 75, 100, 50, 35, 250] {
5n
} numbers that are evenly divisible by 5
[13, 28, 35, 300, 98 343, 63, 289] contains a treble letter when written in Roman numerals
[6, 15, 44, 1, 36, 55, 4] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
} Numbers divisible by each of its digits
[18, 99, 324, 500, 8, 45, 81, 700] {
k² | n; k > 1
} numbers with a factor that is a square number
[25, 49, 100, 256, 400, 529, 841] {
n²
} square numbers
[1, 15, 17, 18, 1000, 11, 16, 19] {
n = 1 * 10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with one
[10, 40, 600, 60, 20, 800, 1000] {
n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that end with zero
[83, 89, 400, 1, 41, 45, 484] {
n = 2^x*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d, x ≥ 0
} first digit is a power of 2
[5, 10, 18, 43, 30, 59, 81, 27, 45] {
n is odd (mod 9)
numbers whose digital root is odd
[29, 61, 71, 89, 3, 7, 11, 13] {
n is prime
} primes
[16, 56, 76, 196, 676, 6, 36] {
n ≡ 6 (mod 10)
} numbers that end in 6
[30, 58, 87, 31, 47, 21, 34, 63] 2 digit numbers where one digit is prime and the other is not
[4, 21, 30, 2, 84, 1, 3] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i | 12
} sum of the digits is a factor of 12
[7, 8, 42, 1000, 5, 6, 121, 750] { {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_d <= a₀
} last digit is less than or equal to the first digit
[14, 62, 256, 2, 4, 8, 56] {
(2 | n) ∧ (3 | n ↓ 5 | n)
} divisible by 2 but not by 3 or 5

Analysis (Not_Mafia, Micc) has 116 points and:

[91, 900, 961] {
n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with nine
[1, 125, 216] at least one digit is 1

Algebra (StrangerCoug, skitter30) has 89 points and:

[19, 46, 64, 361] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[1, 17, 33, 73, 729] {
n ≡ 1 (mod 8)
} numbers that are congruent to 1 mod 8
[10, 23, 36, 49] {
n ≡ 10 (mod 13)
} numbers congruent to 10 mod 13
[15, 57, 21] {
3 * p, p is prime
} numbers that are 3 times a prime number

Cards left in deck: 11

It is

Not_Mafia's

turn

When we run out of cards, the game will continue until 4 people pass in a row.

Plotinus · Post Post #481 (isolation #204) » Wed Apr 01, 2020 7:20 pm

Spoiler: Completed sequences

[1, 2, 3, 4, 5, 10, 39, 55] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
} numbers that are divisible by their first digit
[6, 21, 27, 42, 69, 72, 78, 165, 576] {
3n
} numbers whose sum is a multiple of 3
[4, 8, 9, 15, 20, 32, 66, 80] {
n = 2ⁱ ± 2^j
} numbers that can be written as the sum or difference of two powers of two
[20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 2^k; a_i ≥ 0; d > 0; k ∈ ℤ
} sum of the digits is a power of 2 }
[16, 20, 25, 32, 94, 120, 200] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is prime
[1, 3, 4, 5, 6, 7, 9] {
n < 10
} single digit numbers }
[3, 5, 16, 17, 25, 64, 128, 729] {
p^k, p is prime, k ≥ 1
} powers of primes (1st and higher)
[12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
[10, 88, 90, 97, 100, 225, 441] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
} digit sum is a perfect square
[1, 2, 3, 7, 9 11, 77]{
str(n)[::-1] == str(n)
} Palindromic numbers
[84, 56, 3, 29, 93, 5, 70] {
n % 9 ∈ {2, 3, 5, 7}
Numbers who digital root is prime
[22, 3, 8, 65, 51, 64, 12] {
i % (i % 10) == 0 }
Numbers divisible by their last digit
[12, 20, 21, 27, 512, 52, 24] {
n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
} Numbers where at least one digit is 2
[15, 50, 75, 100, 50, 35, 250] {
5n
} numbers that are evenly divisible by 5
[13, 28, 35, 300, 98 343, 63, 289] contains a treble letter when written in Roman numerals
[6, 15, 44, 1, 36, 55, 4] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
} Numbers divisible by each of its digits
[18, 99, 324, 500, 8, 45, 81, 700] {
k² | n; k > 1
} numbers with a factor that is a square number
[25, 49, 100, 256, 400, 529, 841] {
n²
} square numbers
[1, 15, 17, 18, 1000, 11, 16, 19] {
n = 1 * 10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with one
[10, 40, 600, 60, 20, 800, 1000] {
n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that end with zero
[83, 89, 400, 1, 41, 45, 484] {
n = 2^x*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d, x ≥ 0
} first digit is a power of 2
[5, 10, 18, 43, 30, 59, 81, 27, 45] {
n is odd (mod 9)
numbers whose digital root is odd
[29, 61, 71, 89, 3, 7, 11, 13] {
n is prime
} primes
[16, 56, 76, 196, 676, 6, 36] {
n ≡ 6 (mod 10)
} numbers that end in 6
[30, 58, 87, 31, 47, 21, 34, 63] 2 digit numbers where one digit is prime and the other is not
[4, 21, 30, 2, 84, 1, 3] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i | 12
} sum of the digits is a factor of 12
[7, 8, 42, 1000, 5, 6, 121, 750] { {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_d <= a₀
} last digit is less than or equal to the first digit
[14, 62, 256, 2, 4, 8, 56] {
(2 | n) ∧ (3 | n ↓ 5 | n)
} divisible by 2 but not by 3 or 5
[38, 55, 2, 27, 54, 70, 512] {
k | n with k ≡ n (mod 9)
} numbers divisible by their digital root

Analysis (Not_Mafia, Micc) has 116 points and:

[91, 900, 961] {
n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with nine
[1, 125, 216] at least one digit is 1

Algebra (StrangerCoug, skitter30) has 96 points and:

[19, 46, 64, 361] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[1, 17, 33, 73, 729] {
n ≡ 1 (mod 8)
} numbers that are congruent to 1 mod 8
[10, 23, 36, 49] {
n ≡ 10 (mod 13)
} numbers congruent to 10 mod 13
[15, 57, 21] {
3 * p, p is prime
} numbers that are 3 times a prime number

Cards left in deck: 4

It is

Micc's

turn

When we run out of cards, the game will continue until 4 people pass in a row.

Plotinus · Post Post #483 (isolation #205) » Thu Apr 02, 2020 8:37 pm

Spoiler: Completed sequences

[1, 2, 3, 4, 5, 10, 39, 55] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
} numbers that are divisible by their first digit
[6, 21, 27, 42, 69, 72, 78, 165, 576] {
3n
} numbers whose sum is a multiple of 3
[4, 8, 9, 15, 20, 32, 66, 80] {
n = 2ⁱ ± 2^j
} numbers that can be written as the sum or difference of two powers of two
[20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 2^k; a_i ≥ 0; d > 0; k ∈ ℤ
} sum of the digits is a power of 2 }
[16, 20, 25, 32, 94, 120, 200] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is prime
[1, 3, 4, 5, 6, 7, 9] {
n < 10
} single digit numbers }
[3, 5, 16, 17, 25, 64, 128, 729] {
p^k, p is prime, k ≥ 1
} powers of primes (1st and higher)
[12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
[10, 88, 90, 97, 100, 225, 441] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
} digit sum is a perfect square
[1, 2, 3, 7, 9 11, 77]{
str(n)[::-1] == str(n)
} Palindromic numbers
[84, 56, 3, 29, 93, 5, 70] {
n % 9 ∈ {2, 3, 5, 7}
Numbers who digital root is prime
[22, 3, 8, 65, 51, 64, 12] {
i % (i % 10) == 0 }
Numbers divisible by their last digit
[12, 20, 21, 27, 512, 52, 24] {
n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
} Numbers where at least one digit is 2
[15, 50, 75, 100, 50, 35, 250] {
5n
} numbers that are evenly divisible by 5
[13, 28, 35, 300, 98 343, 63, 289] contains a treble letter when written in Roman numerals
[6, 15, 44, 1, 36, 55, 4] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
} Numbers divisible by each of its digits
[18, 99, 324, 500, 8, 45, 81, 700] {
k² | n; k > 1
} numbers with a factor that is a square number
[25, 49, 100, 256, 400, 529, 841] {
n²
} square numbers
[1, 15, 17, 18, 1000, 11, 16, 19] {
n = 1 * 10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with one
[10, 40, 600, 60, 20, 800, 1000] {
n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that end with zero
[83, 89, 400, 1, 41, 45, 484] {
n = 2^x*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d, x ≥ 0
} first digit is a power of 2
[5, 10, 18, 43, 30, 59, 81, 27, 45] {
n is odd (mod 9)
numbers whose digital root is odd
[29, 61, 71, 89, 3, 7, 11, 13] {
n is prime
} primes
[16, 56, 76, 196, 676, 6, 36] {
n ≡ 6 (mod 10)
} numbers that end in 6
[30, 58, 87, 31, 47, 21, 34, 63] 2 digit numbers where one digit is prime and the other is not
[4, 21, 30, 2, 84, 1, 3] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i | 12
} sum of the digits is a factor of 12
[7, 8, 42, 1000, 5, 6, 121, 750] { {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_d <= a₀
} last digit is less than or equal to the first digit
[14, 62, 256, 2, 4, 8, 56] {
(2 | n) ∧ (3 | n ↓ 5 | n)
} divisible by 2 but not by 3 or 5
[38, 55, 2, 27, 54, 70, 512] {
k | n with k ≡ n (mod 9)
} numbers divisible by their digital root

Analysis (Not_Mafia, Micc) has 116 points and:

[91, 900, 961] {
n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with nine
[1, 125, 216] at least one digit is 1
[1, 19, 67] {
n ≡ 1 (mod 6)
} congruent to 1 mod 6

Algebra (StrangerCoug, skitter30) has 96 points and:

[19, 46, 64, 361] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[1, 17, 33, 73, 729] {
n ≡ 1 (mod 8)
} numbers that are congruent to 1 mod 8
[10, 23, 36, 49] {
n ≡ 10 (mod 13)
} numbers congruent to 10 mod 13
[15, 57, 21] {
3 * p, p is prime
} numbers that are 3 times a prime number

Cards left in deck: 1

It is

skitter30's

turn

When we run out of cards, the game will continue until 4 people pass in a row.

Plotinus · Post Post #485 (isolation #206) » Fri Apr 03, 2020 4:40 am

Glad to have you, vincentw. The next game should start fairly soon, this one probably has less than 10 turns left.

Plotinus · Post Post #487 (isolation #207) » Fri Apr 03, 2020 4:47 am

Spoiler: Completed sequences

[1, 2, 3, 4, 5, 10, 39, 55] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
} numbers that are divisible by their first digit
[6, 21, 27, 42, 69, 72, 78, 165, 576] {
3n
} numbers whose sum is a multiple of 3
[4, 8, 9, 15, 20, 32, 66, 80] {
n = 2ⁱ ± 2^j
} numbers that can be written as the sum or difference of two powers of two
[20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 2^k; a_i ≥ 0; d > 0; k ∈ ℤ
} sum of the digits is a power of 2 }
[16, 20, 25, 32, 94, 120, 200] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is prime
[1, 3, 4, 5, 6, 7, 9] {
n < 10
} single digit numbers }
[3, 5, 16, 17, 25, 64, 128, 729] {
p^k, p is prime, k ≥ 1
} powers of primes (1st and higher)
[12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
[10, 88, 90, 97, 100, 225, 441] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
} digit sum is a perfect square
[1, 2, 3, 7, 9 11, 77]{
str(n)[::-1] == str(n)
} Palindromic numbers
[84, 56, 3, 29, 93, 5, 70] {
n % 9 ∈ {2, 3, 5, 7}
Numbers who digital root is prime
[22, 3, 8, 65, 51, 64, 12] {
i % (i % 10) == 0 }
Numbers divisible by their last digit
[12, 20, 21, 27, 512, 52, 24] {
n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
} Numbers where at least one digit is 2
[15, 50, 75, 100, 50, 35, 250] {
5n
} numbers that are evenly divisible by 5
[13, 28, 35, 300, 98 343, 63, 289] contains a treble letter when written in Roman numerals
[6, 15, 44, 1, 36, 55, 4] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
} Numbers divisible by each of its digits
[18, 99, 324, 500, 8, 45, 81, 700] {
k² | n; k > 1
} numbers with a factor that is a square number
[25, 49, 100, 256, 400, 529, 841] {
n²
} square numbers
[1, 15, 17, 18, 1000, 11, 16, 19] {
n = 1 * 10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with one
[10, 40, 600, 60, 20, 800, 1000] {
n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that end with zero
[83, 89, 400, 1, 41, 45, 484] {
n = 2^x*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d, x ≥ 0
} first digit is a power of 2
[5, 10, 18, 43, 30, 59, 81, 27, 45] {
n is odd (mod 9)
numbers whose digital root is odd
[29, 61, 71, 89, 3, 7, 11, 13] {
n is prime
} primes
[16, 56, 76, 196, 676, 6, 36] {
n ≡ 6 (mod 10)
} numbers that end in 6
[30, 58, 87, 31, 47, 21, 34, 63] 2 digit numbers where one digit is prime and the other is not
[4, 21, 30, 2, 84, 1, 3] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i | 12
} sum of the digits is a factor of 12
[7, 8, 42, 1000, 5, 6, 121, 750] { {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_d <= a₀
} last digit is less than or equal to the first digit
[14, 62, 256, 2, 4, 8, 56] {
(2 | n) ∧ (3 | n ↓ 5 | n)
} divisible by 2 but not by 3 or 5
[38, 55, 2, 27, 54, 70, 512] {
k | n with k ≡ n (mod 9)
} numbers divisible by their digital root

Analysis (Not_Mafia, Micc) has 116 points and:

[91, 900, 961] {
n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with nine
[1, 125, 216] at least one digit is 1
[1, 19, 67] {
n ≡ 1 (mod 6)
} congruent to 1 mod 6

Algebra (StrangerCoug, skitter30) has 96 points and:

[19, 46, 64, 361, 82] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[1, 17, 33, 73, 729] {
n ≡ 1 (mod 8)
} numbers that are congruent to 1 mod 8
[10, 23, 36, 49] {
n ≡ 10 (mod 13)
} numbers congruent to 10 mod 13
[15, 57, 21] {
3 * p, p is prime
} numbers that are 3 times a prime number

Cards left in deck: 0

It is

Not_Mafia's

turn

The game will continue until 4 people pass in a row.

Plotinus · Post Post #490 (isolation #208) » Sat Apr 04, 2020 4:30 am

Micc has submitted his turn by PM

Micc wrote:If available my next play will be to finish starts with 9 by playing 92, 95, 9 and 96.

Spoiler: Completed sequences

[1, 2, 3, 4, 5, 10, 39, 55] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
} numbers that are divisible by their first digit
[6, 21, 27, 42, 69, 72, 78, 165, 576] {
3n
} numbers whose sum is a multiple of 3
[4, 8, 9, 15, 20, 32, 66, 80] {
n = 2ⁱ ± 2^j
} numbers that can be written as the sum or difference of two powers of two
[20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 2^k; a_i ≥ 0; d > 0; k ∈ ℤ
} sum of the digits is a power of 2 }
[16, 20, 25, 32, 94, 120, 200] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is prime
[1, 3, 4, 5, 6, 7, 9] {
n < 10
} single digit numbers }
[3, 5, 16, 17, 25, 64, 128, 729] {
p^k, p is prime, k ≥ 1
} powers of primes (1st and higher)
[12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
[10, 88, 90, 97, 100, 225, 441] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
} digit sum is a perfect square
[1, 2, 3, 7, 9 11, 77]{
str(n)[::-1] == str(n)
} Palindromic numbers
[84, 56, 3, 29, 93, 5, 70] {
n % 9 ∈ {2, 3, 5, 7}
Numbers who digital root is prime
[22, 3, 8, 65, 51, 64, 12] {
i % (i % 10) == 0 }
Numbers divisible by their last digit
[12, 20, 21, 27, 512, 52, 24] {
n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
} Numbers where at least one digit is 2
[15, 50, 75, 100, 50, 35, 250] {
5n
} numbers that are evenly divisible by 5
[13, 28, 35, 300, 98 343, 63, 289] contains a treble letter when written in Roman numerals
[6, 15, 44, 1, 36, 55, 4] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
} Numbers divisible by each of its digits
[18, 99, 324, 500, 8, 45, 81, 700] {
k² | n; k > 1
} numbers with a factor that is a square number
[25, 49, 100, 256, 400, 529, 841] {
n²
} square numbers
[1, 15, 17, 18, 1000, 11, 16, 19] {
n = 1 * 10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with one
[10, 40, 600, 60, 20, 800, 1000] {
n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that end with zero
[83, 89, 400, 1, 41, 45, 484] {
n = 2^x*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d, x ≥ 0
} first digit is a power of 2
[5, 10, 18, 43, 30, 59, 81, 27, 45] {
n is odd (mod 9)
numbers whose digital root is odd
[29, 61, 71, 89, 3, 7, 11, 13] {
n is prime
} primes
[16, 56, 76, 196, 676, 6, 36] {
n ≡ 6 (mod 10)
} numbers that end in 6
[30, 58, 87, 31, 47, 21, 34, 63] 2 digit numbers where one digit is prime and the other is not
[4, 21, 30, 2, 84, 1, 3] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i | 12
} sum of the digits is a factor of 12
[7, 8, 42, 1000, 5, 6, 121, 750] { {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_d <= a₀
} last digit is less than or equal to the first digit
[14, 62, 256, 2, 4, 8, 56] {
(2 | n) ∧ (3 | n ↓ 5 | n)
} divisible by 2 but not by 3 or 5
[38, 55, 2, 27, 54, 70, 512] {
k | n with k ≡ n (mod 9)
} numbers divisible by their digital root
[1, 17, 33, 73, 729, 49, 625] {
n ≡ 1 (mod 8)
} numbers that are congruent to 1 mod 8
[91, 900, 961, 92, 95, 9 96.] {
n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with nine

Analysis (Not_Mafia, Micc) has 123 points and:

[1, 125, 216] at least one digit is 1
[1, 19, 67] {
n ≡ 1 (mod 6)
} congruent to 1 mod 6

Algebra (StrangerCoug, skitter30) has 103 points and:

[19, 46, 64, 361, 82] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[10, 23, 36, 49] {
n ≡ 10 (mod 13)
} numbers congruent to 10 mod 13
[15, 57, 21] {
3 * p, p is prime
} numbers that are 3 times a prime number

Cards left in deck: 0

It is

skitter30's

turn

The game will continue until 4 people pass in a row.

Plotinus · Post Post #492 (isolation #209) » Sat Apr 04, 2020 7:46 pm

Spoiler: Completed sequences

[1, 2, 3, 4, 5, 10, 39, 55] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
} numbers that are divisible by their first digit
[6, 21, 27, 42, 69, 72, 78, 165, 576] {
3n
} numbers whose sum is a multiple of 3
[4, 8, 9, 15, 20, 32, 66, 80] {
n = 2ⁱ ± 2^j
} numbers that can be written as the sum or difference of two powers of two
[20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 2^k; a_i ≥ 0; d > 0; k ∈ ℤ
} sum of the digits is a power of 2 }
[16, 20, 25, 32, 94, 120, 200] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is prime
[1, 3, 4, 5, 6, 7, 9] {
n < 10
} single digit numbers }
[3, 5, 16, 17, 25, 64, 128, 729] {
p^k, p is prime, k ≥ 1
} powers of primes (1st and higher)
[12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
[10, 88, 90, 97, 100, 225, 441] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
} digit sum is a perfect square
[1, 2, 3, 7, 9 11, 77]{
str(n)[::-1] == str(n)
} Palindromic numbers
[84, 56, 3, 29, 93, 5, 70] {
n % 9 ∈ {2, 3, 5, 7}
Numbers who digital root is prime
[22, 3, 8, 65, 51, 64, 12] {
i % (i % 10) == 0 }
Numbers divisible by their last digit
[12, 20, 21, 27, 512, 52, 24] {
n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
} Numbers where at least one digit is 2
[15, 50, 75, 100, 50, 35, 250] {
5n
} numbers that are evenly divisible by 5
[13, 28, 35, 300, 98 343, 63, 289] contains a treble letter when written in Roman numerals
[6, 15, 44, 1, 36, 55, 4] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
} Numbers divisible by each of its digits
[18, 99, 324, 500, 8, 45, 81, 700] {
k² | n; k > 1
} numbers with a factor that is a square number
[25, 49, 100, 256, 400, 529, 841] {
n²
} square numbers
[1, 15, 17, 18, 1000, 11, 16, 19] {
n = 1 * 10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with one
[10, 40, 600, 60, 20, 800, 1000] {
n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that end with zero
[83, 89, 400, 1, 41, 45, 484] {
n = 2^x*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d, x ≥ 0
} first digit is a power of 2
[5, 10, 18, 43, 30, 59, 81, 27, 45] {
n is odd (mod 9)
numbers whose digital root is odd
[29, 61, 71, 89, 3, 7, 11, 13] {
n is prime
} primes
[16, 56, 76, 196, 676, 6, 36] {
n ≡ 6 (mod 10)
} numbers that end in 6
[30, 58, 87, 31, 47, 21, 34, 63] 2 digit numbers where one digit is prime and the other is not
[4, 21, 30, 2, 84, 1, 3] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i | 12
} sum of the digits is a factor of 12
[7, 8, 42, 1000, 5, 6, 121, 750] { {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_d <= a₀
} last digit is less than or equal to the first digit
[14, 62, 256, 2, 4, 8, 56] {
(2 | n) ∧ (3 | n ↓ 5 | n)
} divisible by 2 but not by 3 or 5
[38, 55, 2, 27, 54, 70, 512] {
k | n with k ≡ n (mod 9)
} numbers divisible by their digital root
[1, 17, 33, 73, 729, 49, 625] {
n ≡ 1 (mod 8)
} numbers that are congruent to 1 mod 8
[91, 900, 961, 92, 95, 9 96.] {
n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with nine

Analysis (Not_Mafia, Micc) has 123 points and:

[1, 125, 216, 144] at least one digit is 1
[1, 19, 67] {
n ≡ 1 (mod 6)
} congruent to 1 mod 6

Algebra (StrangerCoug, skitter30) has 103 points and:

[19, 46, 64, 361, 82] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[10, 23, 36, 49] {
n ≡ 10 (mod 13)
} numbers congruent to 10 mod 13
[15, 57, 21] {
3 * p, p is prime
} numbers that are 3 times a prime number

Cards left in deck: 0

It is

Not_Mafia's

turn

The game will continue until 4 people pass in a row.

Plotinus · Post Post #496 (isolation #210) » Sun Apr 05, 2020 5:49 am

Spoiler: Completed sequences

[1, 2, 3, 4, 5, 10, 39, 55] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
} numbers that are divisible by their first digit
[6, 21, 27, 42, 69, 72, 78, 165, 576] {
3n
} numbers whose sum is a multiple of 3
[4, 8, 9, 15, 20, 32, 66, 80] {
n = 2ⁱ ± 2^j
} numbers that can be written as the sum or difference of two powers of two
[20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 2^k; a_i ≥ 0; d > 0; k ∈ ℤ
} sum of the digits is a power of 2 }
[16, 20, 25, 32, 94, 120, 200] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is prime
[1, 3, 4, 5, 6, 7, 9] {
n < 10
} single digit numbers }
[3, 5, 16, 17, 25, 64, 128, 729] {
p^k, p is prime, k ≥ 1
} powers of primes (1st and higher)
[12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
[10, 88, 90, 97, 100, 225, 441] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
} digit sum is a perfect square
[1, 2, 3, 7, 9 11, 77]{
str(n)[::-1] == str(n)
} Palindromic numbers
[84, 56, 3, 29, 93, 5, 70] {
n % 9 ∈ {2, 3, 5, 7}
Numbers who digital root is prime
[22, 3, 8, 65, 51, 64, 12] {
i % (i % 10) == 0 }
Numbers divisible by their last digit
[12, 20, 21, 27, 512, 52, 24] {
n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
} Numbers where at least one digit is 2
[15, 50, 75, 100, 50, 35, 250] {
5n
} numbers that are evenly divisible by 5
[13, 28, 35, 300, 98 343, 63, 289] contains a treble letter when written in Roman numerals
[6, 15, 44, 1, 36, 55, 4] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
} Numbers divisible by each of its digits
[18, 99, 324, 500, 8, 45, 81, 700] {
k² | n; k > 1
} numbers with a factor that is a square number
[25, 49, 100, 256, 400, 529, 841] {
n²
} square numbers
[1, 15, 17, 18, 1000, 11, 16, 19] {
n = 1 * 10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with one
[10, 40, 600, 60, 20, 800, 1000] {
n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that end with zero
[83, 89, 400, 1, 41, 45, 484] {
n = 2^x*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d, x ≥ 0
} first digit is a power of 2
[5, 10, 18, 43, 30, 59, 81, 27, 45] {
n is odd (mod 9)
numbers whose digital root is odd
[29, 61, 71, 89, 3, 7, 11, 13] {
n is prime
} primes
[16, 56, 76, 196, 676, 6, 36] {
n ≡ 6 (mod 10)
} numbers that end in 6
[30, 58, 87, 31, 47, 21, 34, 63] 2 digit numbers where one digit is prime and the other is not
[4, 21, 30, 2, 84, 1, 3] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i | 12
} sum of the digits is a factor of 12
[7, 8, 42, 1000, 5, 6, 121, 750] { {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_d <= a₀
} last digit is less than or equal to the first digit
[14, 62, 256, 2, 4, 8, 56] {
(2 | n) ∧ (3 | n ↓ 5 | n)
} divisible by 2 but not by 3 or 5
[38, 55, 2, 27, 54, 70, 512] {
k | n with k ≡ n (mod 9)
} numbers divisible by their digital root
[1, 17, 33, 73, 729, 49, 625] {
n ≡ 1 (mod 8)
} numbers that are congruent to 1 mod 8
[91, 900, 961, 92, 95, 9 96.] {
n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with nine

Analysis (Not_Mafia, Micc) has 123 points and:

[1, 125, 216, 144] at least one digit is 1
[1, 19, 67] {
n ≡ 1 (mod 6)
} congruent to 1 mod 6

Algebra (StrangerCoug, skitter30) has 103 points and:

[19, 46, 64, 361, 82] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[10, 23, 36, 49] {
n ≡ 10 (mod 13)
} numbers congruent to 10 mod 13
[15, 57, 21, 9] {
3 * p, p is prime
} numbers that are 3 times a prime number

Cards left in deck: 0

It is

skitter30's

turn

The game will continue until 4 people pass in a row.

Plotinus · Post Post #502 (isolation #211) » Mon Apr 06, 2020 7:04 pm

Spoiler: Completed sequences

[1, 2, 3, 4, 5, 10, 39, 55] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
} numbers that are divisible by their first digit
[6, 21, 27, 42, 69, 72, 78, 165, 576] {
3n
} numbers whose sum is a multiple of 3
[4, 8, 9, 15, 20, 32, 66, 80] {
n = 2ⁱ ± 2^j
} numbers that can be written as the sum or difference of two powers of two
[20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 2^k; a_i ≥ 0; d > 0; k ∈ ℤ
} sum of the digits is a power of 2 }
[16, 20, 25, 32, 94, 120, 200] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is prime
[1, 3, 4, 5, 6, 7, 9] {
n < 10
} single digit numbers }
[3, 5, 16, 17, 25, 64, 128, 729] {
p^k, p is prime, k ≥ 1
} powers of primes (1st and higher)
[12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
[10, 88, 90, 97, 100, 225, 441] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
} digit sum is a perfect square
[1, 2, 3, 7, 9 11, 77]{
str(n)[::-1] == str(n)
} Palindromic numbers
[84, 56, 3, 29, 93, 5, 70] {
n % 9 ∈ {2, 3, 5, 7}
Numbers who digital root is prime
[22, 3, 8, 65, 51, 64, 12] {
i % (i % 10) == 0 }
Numbers divisible by their last digit
[12, 20, 21, 27, 512, 52, 24] {
n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
} Numbers where at least one digit is 2
[15, 50, 75, 100, 50, 35, 250] {
5n
} numbers that are evenly divisible by 5
[13, 28, 35, 300, 98 343, 63, 289] contains a treble letter when written in Roman numerals
[6, 15, 44, 1, 36, 55, 4] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
} Numbers divisible by each of its digits
[18, 99, 324, 500, 8, 45, 81, 700] {
k² | n; k > 1
} numbers with a factor that is a square number
[25, 49, 100, 256, 400, 529, 841] {
n²
} square numbers
[1, 15, 17, 18, 1000, 11, 16, 19] {
n = 1 * 10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with one
[10, 40, 600, 60, 20, 800, 1000] {
n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that end with zero
[83, 89, 400, 1, 41, 45, 484] {
n = 2^x*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d, x ≥ 0
} first digit is a power of 2
[5, 10, 18, 43, 30, 59, 81, 27, 45] {
n is odd (mod 9)
numbers whose digital root is odd
[29, 61, 71, 89, 3, 7, 11, 13] {
n is prime
} primes
[16, 56, 76, 196, 676, 6, 36] {
n ≡ 6 (mod 10)
} numbers that end in 6
[30, 58, 87, 31, 47, 21, 34, 63] 2 digit numbers where one digit is prime and the other is not
[4, 21, 30, 2, 84, 1, 3] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i | 12
} sum of the digits is a factor of 12
[7, 8, 42, 1000, 5, 6, 121, 750] { {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_d <= a₀
} last digit is less than or equal to the first digit
[14, 62, 256, 2, 4, 8, 56] {
(2 | n) ∧ (3 | n ↓ 5 | n)
} divisible by 2 but not by 3 or 5
[38, 55, 2, 27, 54, 70, 512] {
k | n with k ≡ n (mod 9)
} numbers divisible by their digital root
[1, 17, 33, 73, 729, 49, 625] {
n ≡ 1 (mod 8)
} numbers that are congruent to 1 mod 8
[91, 900, 961, 92, 95, 9 96.] {
n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
} numbers that start with nine

Analysis (Not_Mafia, Micc) has 123 points and:

[1, 125, 216, 144, 14, ] at least one digit is 1
[1, 19, 67, 13] {
n ≡ 1 (mod 6)
} congruent to 1 mod 6

Algebra (StrangerCoug, skitter30) has 103 points and:

[19, 46, 64, 361, 82] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[10, 23, 36, 49] {
n ≡ 10 (mod 13)
} numbers congruent to 10 mod 13
[15, 57, 21, 9] {
3 * p, p is prime
} numbers that are 3 times a prime number

Cards left in deck: 0

It is

skitter30's

turn

The game will continue until 4 people pass in a row.

Plotinus · Post Post #503 (isolation #212) » Tue Apr 07, 2020 7:31 pm

Prodded skitter, who has (expired on 2020-04-09 08:31:00) to go, or I'll count it as a Pass.

Plotinus · Wed Apr 08, 2020 10:45 pm

Congrats Not_Mafia and Micc!

Plotinus · Wed Apr 08, 2020 10:48 pm

Do we want to make any changes to the deck between rounds?

Is 2 teams of 4 a good number of players for the next round? Depending on interest, should we try for 2 teams of 3, or 3 teams of 2 instead, or should we keep any extra interested people in the wings for replacements?

Plotinus · Wed Apr 08, 2020 10:51 pm

Are there any rule changes we want to make before the next game starts?

Plotinus · Post Post #513 (isolation #216) » Thu Apr 09, 2020 2:33 am

Both of those sound reasonable to me.

Another thing I noticed but didn't want to bring up while the game was going on, was that since StrangerCoug was submitting his moves by PM most of the time, you and Micc could (or could have) guessed that he was unlikely to complete a sequence Not_Mafia started since his move would likely have been submitted before you even went.

I don't want to disallow submitting moves by PM because I think it's a good idea if you have a regular V/LA on weekends, but I noticed that it might not be the best strategy to do it all the time.

Plotinus · Thu Apr 09, 2020 10:21 am

In post 518, Jake The Wolfie wrote:I also have some question:

Could you make a "subjective sequence" (eg. Numbers that Jake likes)
Could you make a nonsense sequence (eg. Numbers in Jake's hand)

sequences do have to be something other people can contribute to, so if numbers that Jake likes happen to be of the form x^y*y^x, x, y > 1, then that's okay (though you won't find 7 unique such numbers in the deck we're using), or if Jake likes all numbers that are only made of straight lines, or numbers that are written without the letter i in Turkish

The numbers in the sequence need to have something meaningful in common with each other, and we've historically vetoed "x < 27" as being too boring. Being currently in your hand is not an interesting numerical property.

If you want to play all 7 of your cards at once, the rules are stricter, look for the word "bingo" in the opening post.

StrangerCoug wrote:
In post 513, Plotinus wrote:Another thing I noticed but didn't want to bring up while the game was going on, was that since StrangerCoug was submitting his moves by PM most of the time, you and Micc could (or could have) guessed that he was unlikely to complete a sequence Not_Mafia started since his move would likely have been submitted before you even went.

I don't want to disallow submitting moves by PM because I think it's a good idea if you have a regular V/LA on weekends, but I noticed that it might not be the best strategy to do it all the time.
Fair, and I'd still like being allowed to submit by PM.

I'll still accept moves by PM

Plotinus · Thu Apr 09, 2020 11:05 am

That'd be a good one. Exactly one digit or at least one digit?

Plotinus · Post Post #530 (isolation #219) » Sat Apr 11, 2020 6:29 pm

Good to have you again! So there's another ~7 hours for a sixth player or Not_Mafia will be in too.

Which deck do we want to use? We talked some earlier about making a deck to accommodate days of the year, should we just put every number between 1 and 366 once?

The first game lasted 54 days, and the deck had 230 cards, so we used ~4.3 cards/day. This second game, not counting the couple months in the middle when we were waiting for replacements, lasted 57 days and the deck had 272 cards. We used ~4.7 cards/day.

So a 366 card game would last 77-87 days, about 3 months. If we added a repeats of the first 100 numbers that'd be about 99-110 days, almost 4 months.

Plotinus · Post Post #532 (isolation #220) » Thu Apr 16, 2020 7:40 pm

All right, lets get started, deck is the numbers between 1 and 366 inclusive, each number is unique.

players = ["Not Mafia", "skitter30", "Jake the Wolfie", "StrangerCoug", "Jackal711", "vincentw"]
random.shuffle(players)
print(players)
['Jackal711', 'StrangerCoug', 'Jake the Wolfie', 'Not Mafia', 'vincentw', 'skitter30']

Topology: Jackal711, Not Mafia

Measure: StrangerCoug, vincentw

Dynamics: Jake the Wolfie, skitter30

You can change your team name if both partners agree

It is

Jackal711

's turn

Plotinus · Post Post #533 (isolation #221) » Sat Apr 18, 2020 3:53 am

Jackal711 has been prodded and has (expired on 2020-04-19 10:53:32) to move before I start looking for a replacement

Plotinus · Post Post #535 (isolation #222) » Mon Apr 20, 2020 8:48 am

It's all right, I was late starting it, too. I'm glad you're here now.

Topology: Jackal711, Not Mafia

[55, 226, 253] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10

Measure: StrangerCoug, vincentw

Dynamics: Jake the Wolfie, skitter30

It is

Strangercoug's

's turn

Plotinus · Post Post #537 (isolation #223) » Mon Apr 20, 2020 5:43 pm

Topology: Jackal711, Not Mafia

[55, 226, 253] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10

Measure: StrangerCoug, vincentw

[3, 7, 229] primes

Dynamics: Jake the Wolfie, skitter30

It is

Jake the Wolfies

's turn

Plotinus · Post Post #539 (isolation #224) » Tue Apr 21, 2020 4:55 am

Topology: Jackal711, Not Mafia

[55, 226, 253] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10

Measure: StrangerCoug, vincentw

[3, 7, 229] primes

Dynamics: Jake the Wolfie, skitter30

[54, 183, 272, 313] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4

It is

Not_Mafia's

's turn

Plotinus · Post Post #541 (isolation #225) » Tue Apr 21, 2020 8:20 am

Spoiler: completed sequences

Topology: Jackal711, Not Mafia 8 points

[55, 226, 253] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10

Measure: StrangerCoug, vincentw

[3, 7, 229] primes

Dynamics: Jake the Wolfie, skitter30

It is

vincentw's

's turn

Plotinus · Post Post #543 (isolation #226) » Tue Apr 21, 2020 6:10 pm

Spoiler: completed sequences

Topology: Jackal711, Not Mafia 8 points

[55, 226, 253] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10

Measure: StrangerCoug, vincentw

[3, 7, 229] primes
[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order

Dynamics: Jake the Wolfie, skitter30

It is

skitter30's

's turn

Plotinus · Post Post #545 (isolation #227) » Wed Apr 22, 2020 6:15 pm

Spoiler: completed sequences

Topology: Jackal711, Not Mafia 8 points

[55, 226, 253] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10

Measure: StrangerCoug, vincentw

[3, 7, 229] primes
[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order

Dynamics: Jake the Wolfie, skitter30

[166, 337, 333] Numbers with at least one immediately repeating digit

It is

Jackal711's

's turn

Plotinus · Post Post #547 (isolation #228) » Thu Apr 23, 2020 5:05 pm

Spoiler: completed sequences

Topology: Jackal711, Not Mafia 8 points

[55, 226, 253, 190] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10

Measure: StrangerCoug, vincentw

[3, 7, 229] primes
[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order

Dynamics: Jake the Wolfie, skitter30

[166, 337, 333] Numbers with at least one immediately repeating digit

It is

Strangercoug's

's turn

Plotinus · Post Post #549 (isolation #229) » Fri Apr 24, 2020 7:40 am

Spoiler: completed sequences

Topology: Jackal711, Not Mafia 8 points

[55, 226, 253, 190] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10

Measure: StrangerCoug, vincentw

[3, 7, 229] primes
[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[78, 126, 336, 348] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite

Dynamics: Jake the Wolfie, skitter30

[166, 337, 333] Numbers with at least one immediately repeating digit

It is

Jake the Wolfie's

's turn

Plotinus · Post Post #551 (isolation #230) » Fri Apr 24, 2020 8:07 pm

Spoiler: completed sequences

Topology: Jackal711, Not Mafia 8 points

[55, 226, 253, 190] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10

Measure: StrangerCoug, vincentw

[3, 7, 229, 5, 179] primes
[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[78, 126, 336, 348] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite

Dynamics: Jake the Wolfie, skitter30

[166, 337, 333] Numbers with at least one immediately repeating digit

It is

Not_Mafia's

's turn

Plotinus · Post Post #554 (isolation #231) » Sat Apr 25, 2020 7:03 am

Spoiler: completed sequences

Topology: Jackal711, Not Mafia: 15 points

Measure: StrangerCoug, vincentw: 7 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order

Dynamics: Jake the Wolfie, skitter30

[166, 337, 333] Numbers with at least one immediately repeating digit
[3, 7, 229, 5, 179] primes

It is

skitter30's

's turn

Plotinus · Post Post #556 (isolation #232) » Sat Apr 25, 2020 9:02 am

fixed, thanks

Plotinus · Post Post #558 (isolation #233) » Sat Apr 25, 2020 5:52 pm

Spoiler: completed sequences

Topology: Jackal711, Not Mafia: 15 points

Measure: StrangerCoug, vincentw: 7 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order

Dynamics: Jake the Wolfie, skitter30: 7 points

[166, 337, 333] Numbers with at least one immediately repeating digit

It is

Jackal711's

's turn

Plotinus · Post Post #559 (isolation #234) » Mon Apr 27, 2020 8:01 am

Prodding Jackal711, who has (expired on 2020-04-28 15:01:19) to post before I start looking for a replacement

Plotinus · Post Post #560 (isolation #235) » Mon Apr 27, 2020 8:42 pm

Jackal has submitted his turn by PM:

Jackal711 wrote:Submitting here since I keep getting errors trying to load the game thread.

Gonna use a sequence idea I really liked from game 2.

Play 25, 44, 63, 365 as {
i % (i % 10) == 0
} Numbers divisible by their last digit

Spoiler: completed sequences

Topology: Jackal711, Not Mafia: 15 points

[25, 44, 63, 365] {
i % (i % 10) == 0
} Numbers divisible by their last digit

Measure: StrangerCoug, vincentw: 7 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order

Dynamics: Jake the Wolfie, skitter30: 7 points

[166, 337, 333] Numbers with at least one immediately repeating digit

It is

StrangerCoug's

's turn

Plotinus · Post Post #562 (isolation #236) » Tue Apr 28, 2020 6:49 am

Spoiler: completed sequences

Topology: Jackal711, Not Mafia: 15 points

Measure: StrangerCoug, vincentw: 15 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order

Dynamics: Jake the Wolfie, skitter30: 7 points

[166, 337, 333] Numbers with at least one immediately repeating digit

It is

Jake the Wolfie's

's turn

Plotinus · Post Post #564 (isolation #237) » Tue Apr 28, 2020 8:17 pm

Spoiler: completed sequences

Topology: Jackal711, Not Mafia: 15 points

Measure: StrangerCoug, vincentw: 15 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order

Dynamics: Jake the Wolfie, skitter30: 7 points

[166, 337, 333, 112] Numbers with at least one immediately repeating digit

It is

Not Mafia's

's turn

Plotinus · Post Post #565 (isolation #238) » Thu Apr 30, 2020 8:37 pm

Prodding Not Mafia, who has (expired on 2020-05-02 03:37:00) to go before I start looking for a replacement

Plotinus · Post Post #567 (isolation #239) » Fri May 01, 2020 6:52 pm

Spoiler: completed sequences

Topology: Jackal711, Not Mafia: 15 points

[166, 337, 333, 112, 311] Numbers with at least one immediately repeating digit

Measure: StrangerCoug, vincentw: 15 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order

Dynamics: Jake the Wolfie, skitter30: 7 points

It is

vincentw's

's turn

Plotinus · Post Post #569 (isolation #240) » Sat May 02, 2020 2:49 am

Spoiler: completed sequences

Topology: Jackal711, Not Mafia: 15 points

Measure: StrangerCoug, vincentw: 23 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order

Dynamics: Jake the Wolfie, skitter30: 7 points

It is

skitter30's

's turn

Plotinus · Post Post #570 (isolation #241) » Sun May 03, 2020 6:53 am

Prodded skitter. She has another (expired on 2020-05-04 13:53:28) to move before I start looking for a replacement.

Plotinus · Post Post #573 (isolation #242) » Mon May 04, 2020 7:47 am

To start a sequence, you need 3 cards, but you can go again

Plotinus · Post Post #575 (isolation #243) » Mon May 04, 2020 6:11 pm

Spoiler: completed sequences

Topology: Jackal711, Not Mafia: 15 points

Measure: StrangerCoug, vincentw: 23 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order

Dynamics: Jake the Wolfie, skitter30: 7 points

[234, 342, 356] {
n = 100*a + 10*b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits

It is

Jackal711's

's turn

Plotinus · Post Post #576 (isolation #244) » Tue May 05, 2020 9:11 pm

Jackal711 has been prodded and has (expired on 2020-05-07 04:11:15) to go before I start looking for a replacement.

Plotinus · Post Post #577 (isolation #245) » Sat May 09, 2020 5:16 pm

Micc is replacing Jackal

Plotinus · Sat May 09, 2020 10:30 pm

Spoiler: completed sequences

Topology: Micc, Not Mafia: 15 points

[1, 43, 341] have four or fewer factors

Measure: StrangerCoug, vincentw: 23 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order

Dynamics: Jake the Wolfie, skitter30: 7 points

[234, 342, 356] {
n = 100*a + 10*b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits

It is

StrangerCoug's

's turn

Plotinus · Post Post #582 (isolation #247) » Sun May 10, 2020 5:29 pm

Spoiler: completed sequences

Topology: Micc, Not Mafia: 15 points

[1, 43, 341] have four or fewer factors

Measure: StrangerCoug, vincentw: 23 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers

Dynamics: Jake the Wolfie, skitter30: 7 points

[234, 342, 356] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits

It is

Jake the Wolfie's

's turn

Plotinus · Post Post #584 (isolation #248) » Mon May 11, 2020 6:21 pm

Okay, I'll start looking for a replacement.

I was thinking of some options to keep the game moving while we wait.

1) I could play the left-most card from their hand into the top-most sequence it fit into, if there are any such cards, and pass otherwise.
2) We could just skip them until a replacement is found.
3) Their partner could play during their turn

Plotinus · Post Post #586 (isolation #249) » Mon May 11, 2020 7:33 pm

For 3, I was thinking that skitter would play from her own hand, not that she'd see her partner's. It'd still be the most advantageous option for her because she'd be playing more frequently and could plan ahead, but she'd only have her 7 cards to work with, not the 14 the other teams have.

But I'd like everyone to weigh in before I make a decision.

Plotinus · Post Post #587 (isolation #250) » Mon May 11, 2020 7:57 pm

lilith2013 is replacing Jake the Wolfie! Yay!

We should keep discussing how to keep the game moving when there are replacements in case it comes up in the future but it's no longer urgent

Plotinus · Post Post #589 (isolation #251) » Mon May 11, 2020 8:33 pm

Spoiler: completed sequences

Topology: Micc, Not Mafia: 15 points

Measure: StrangerCoug, vincentw: 23 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers

Dynamics: lilith2013, skitter30: 14 points

[234, 342, 356] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits

It is

Not Mafia's

's turn

Plotinus · Mon May 11, 2020 11:21 pm

I think that might be more than half the deck:
90 cards between 100 and 199
80 cards between 200 and 299
46 cards between 300 and 366

216/366 = 64%

You can go again

Plotinus · Post Post #596 (isolation #253) » Tue May 12, 2020 7:00 am

Spoiler: completed sequences

Topology: Micc, Not Mafia: 15 points

[174, 118, 274] {
2 | n∧n ≥ 100
} 3 digit even numbers

Measure: StrangerCoug, vincentw: 23 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers

Dynamics: lilith2013, skitter30: 14 points

[234, 342, 356] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits

It is

vincentws

's turn

2 votes for option 1
1 vote for option 3

Plotinus · Post Post #599 (isolation #254) » Tue May 12, 2020 6:37 pm

Spoiler: completed sequences

Topology: Micc, Not Mafia: 15 points

[174, 118, 274] {
2 | n∧n ≥ 100
} 3 digit even numbers

Measure: StrangerCoug, vincentw: 23 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[39, 86, 261] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero

Dynamics: lilith2013, skitter30: 14 points

[234, 342, 356] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits

It is

skitter30

's turn

3 votes for option 1
1 vote for option 3

Plotinus · Post Post #600 (isolation #255) » Wed May 13, 2020 7:04 pm

Spoiler: completed sequences

Topology: Micc, Not Mafia: 15 points

[174, 118, 274] {
2 | n∧n ≥ 100
} 3 digit even numbers

Measure: StrangerCoug, vincentw: 23 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[39, 86, 261] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero

Dynamics: lilith2013, skitter30: 14 points

[234, 342, 356] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits

It is

skitter30

's turn

3 votes for option 1
1 vote for option 3

quoted this to get it on the top of the new page. I went to prod skitter just now, which I usually do by quoting the last copy of the person's hand that I sent them, and it looks like I forgot to send her her new hand after her last turn, so I've fixed that now and I'll prod her in 24 hours if needed.

It's okay to poke me if I mess up -- If you haven't received new cards within a few minutes of me updating the game after your turn, something's wrong.

Plotinus · Post Post #604 (isolation #256) » Thu May 14, 2020 4:56 am

Spoiler: completed sequences

Topology: Micc, Not Mafia: 25 points

[174, 118, 274] {
2 | n∧n ≥ 100
} 3 digit even numbers

Measure: StrangerCoug, vincentw: 31 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[39, 86, 261] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero

Dynamics: lilith2013, skitter30: 14 points

It is

lilith2013

's turn

3 votes for option 1
1 vote for option 3

Everyone has gone since we started talking about this so unless there's further discussion, the next time there's a replacement, I'll play the left-most card to the top-most sequence it fits in, if there are any such cards and pass otherwise.

Plotinus · Post Post #608 (isolation #257) » Thu May 14, 2020 8:25 pm

Spoiler: completed sequences

Topology: Micc, Not Mafia: 25 points

[174, 118, 274] {
2 | n∧n ≥ 100
} 3 digit even numbers

Measure: StrangerCoug, vincentw: 31 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[39, 86, 261] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero

Dynamics: lilith2013, skitter30: 14 points

[48, 135, 306] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one

It is

Not_Mafia

's turn

Plotinus · Post Post #609 (isolation #258) » Fri May 15, 2020 6:44 pm

Prodded Not_Mafia. He has another (expired on 2020-05-17 01:44:44) to go before I start looking for a replacement

Plotinus · Fri May 15, 2020 10:51 pm

Spoiler: completed sequences

Topology: Micc, Not Mafia: 25 points

[174, 118, 274] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[191, 359, 305] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers

Measure: StrangerCoug, vincentw: 31 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[39, 86, 261] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero

Dynamics: lilith2013, skitter30: 14 points

[48, 135, 306] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one

It is

vincentw

's turn

Plotinus · Post Post #613 (isolation #260) » Sat May 16, 2020 6:28 am

Spoiler: completed sequences

Topology: Micc, Not Mafia: 25 points

[174, 118, 274] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[191, 359, 305] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers

Measure: StrangerCoug, vincentw: 31 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320, 30] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[39, 86, 261] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero

Dynamics: lilith2013, skitter30: 14 points

[48, 135, 306] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one

It is

skitter30

's turn

Plotinus · Post Post #615 (isolation #261) » Sat May 16, 2020 6:15 pm

Spoiler: completed sequences

Topology: Micc, Not Mafia: 25 points

[174, 118, 274] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[191, 359, 305] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers

Measure: StrangerCoug, vincentw: 31 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320, 30] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers

Dynamics: lilith2013, skitter30: 21 points

[48, 135, 306] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one

It is

Micc

's turn

Plotinus · Post Post #618 (isolation #262) » Sun May 17, 2020 5:52 pm

Spoiler: completed sequences

Topology: Micc, Not Mafia: 32 points

[191, 359, 305] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers

Measure: StrangerCoug, vincentw: 31 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320, 30] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers

Dynamics: lilith2013, skitter30: 21 points

[48, 135, 306] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one

It is

StrangerCoug

's turn

Plotinus · Post Post #620 (isolation #263) » Mon May 18, 2020 5:48 pm

Spoiler: completed sequences

Topology: Micc, Not Mafia: 32 points

[191, 359, 305] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers

Measure: StrangerCoug, vincentw: 31 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320, 30] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[116, 217, 219] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero

Dynamics: lilith2013, skitter30: 21 points

[48, 135, 306] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one

It is

lilith2013

's turn

cool!

Plotinus · Post Post #622 (isolation #264) » Mon May 18, 2020 7:17 pm

Spoiler: completed sequences

Topology: Micc, Not Mafia: 32 points

[191, 359, 305] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers

Measure: StrangerCoug, vincentw: 31 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320, 30] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[116, 217, 219] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero

Dynamics: lilith2013, skitter30: 28 points

It is

Not_Mafia

's turn

Plotinus · Post Post #623 (isolation #265) » Tue May 19, 2020 7:09 pm

Prodded Not_Mafia, who has another (expired on 2020-05-21 02:09:34) to go before I start looking for a replacement.

Plotinus · Tue May 19, 2020 10:45 pm

The dates need to work in both mm/dd and dd/mm format, so 215 can be 2/15 or 21/5 but the others don't work:

176 can be 17th June but it can't be January 76th or 17th month 6th day
271 can be 27th January but it can't be February 71st or 27th month 1st day
199 can be 19th September but it can't be January 99th or 19th month 9th day

Do you want to play 215 to the date thing or do you want to do something else?

Plotinus · Post Post #627 (isolation #267) » Wed May 20, 2020 1:05 am

Spoiler: completed sequences

Topology: Micc, Not Mafia: 32 points

[191, 359, 305] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers

Measure: StrangerCoug, vincentw: 31 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320, 30] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[116, 217, 219, 215] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero

Dynamics: lilith2013, skitter30: 28 points

It is

vincentw

's turn

Plotinus · Post Post #629 (isolation #268) » Wed May 20, 2020 6:17 pm

Spoiler: completed sequences

Topology: Micc, Not Mafia: 32 points

[191, 359, 305] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers

Measure: StrangerCoug, vincentw: 31 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320, 30] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[116, 217, 219, 215] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[120, 143, 194] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square

Dynamics: lilith2013, skitter30: 28 points

It is

skitter30

's turn

Plotinus · Post Post #631 (isolation #269) » Thu May 21, 2020 8:42 am

Spoiler: completed sequences

Topology: Micc, Not Mafia: 32 points

[191, 359, 305] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers

Measure: StrangerCoug, vincentw: 31 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[125, 270, 320, 30] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[116, 217, 219, 215] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[120, 143, 194] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square

Dynamics: lilith2013, skitter30: 28 points

[235, 242, 268] numbers with a 2-digit prime factor

It is

Micc

's turn

Plotinus · Post Post #636 (isolation #270) » Thu May 21, 2020 8:49 pm

Spoiler: completed sequences

Topology: Micc, Not Mafia: 40 points

[191, 359, 305] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers

Measure: StrangerCoug, vincentw: 38 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[116, 217, 219, 215] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[120, 143, 194] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square

Dynamics: lilith2013, skitter30: 28 points

It is

lilith2013

's turn

Plotinus · Post Post #639 (isolation #271) » Fri May 22, 2020 7:34 am

We've had primes already this round, but you can go again

Plotinus · Post Post #641 (isolation #272) » Fri May 22, 2020 7:45 am

Spoiler: completed sequences

Topology: Micc, Not_Mafia: 40 points

[191, 359, 305] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers

Measure: StrangerCoug, vincentw: 38 points

[134, 146, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[116, 217, 219, 215] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[120, 143, 194] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square

Dynamics: lilith2013, skitter30: 28 points

[37, 53, 75 ] all digits are odd

It is

Not_Mafia

's turn

Plotinus · Post Post #646 (isolation #273) » Fri May 22, 2020 7:36 pm

Spoiler: completed sequences

Topology: Micc, Not_Mafia: 40 points

[191, 359, 305] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[20, 56, 60] {
9 < n < 100
2 digit numbers

Measure: StrangerCoug, vincentw: 38 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[116, 217, 219, 215] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[120, 143, 194] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square

Dynamics: lilith2013, skitter30: 28 points

[37, 53, 75 ] all digits are odd
[81, 189, 324] {
27 | n
} multiples of 27

It is

Micc

's turn

Micc is V/LA until the 25th, that's not too long so I think we can wait.

Though we could discuss whether, if someone is V/LA and doesn't move for 48 (or 72?) hours, do we want me to play the leftmost card to the topmost sequence or should that only be for replacements.

Plotinus · Post Post #647 (isolation #274) » Fri May 22, 2020 7:44 pm

I think 72 hours would be better for auto-moving during V/LAs because I know skitter has a weekly V/LA for the Sabbath. I wouldn't want a V/LA rule to affect her disproportionately. I have a similar rule of giving people extra (but not unlimited) time while V/LA in my mafia games that works fairly well.

Plotinus · Post Post #651 (isolation #275) » Sun May 24, 2020 5:34 pm

Spoiler: completed sequences

Topology: Micc, Not_Mafia: 40 points

[191, 359, 305] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[20, 56, 60] {
9 < n < 100
2 digit numbers
[202, 351, 204] have a three digit factor other than itself

Measure: StrangerCoug, vincentw: 38 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[116, 217, 219, 215] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[120, 143, 194] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square

Dynamics: lilith2013, skitter30: 28 points

[37, 53, 75 ] all digits are odd
[81, 189, 324] {
27 | n
} multiples of 27

It is

StrangerCoug

's turn

Plotinus · Post Post #654 (isolation #276) » Mon May 25, 2020 5:51 pm

Spoiler: completed sequences

Topology: Micc, Not_Mafia: 40 points

[191, 359, 305] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[20, 56, 60] {
9 < n < 100
2 digit numbers

Measure: StrangerCoug, vincentw: 45 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[116, 217, 219, 215] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero

Dynamics: lilith2013, skitter30: 35 points

[37, 53, 75 ] all digits are odd
[81, 189, 324] {
27 | n
} multiples of 27

It is

Not_Mafia

's turn

Plotinus · Post Post #656 (isolation #277) » Tue May 26, 2020 7:27 pm

Prodded Not_Mafia; he has another (expired on 2020-05-28 02:27:43) to go before I start looking for a replacement.

Plotinus · Post Post #658 (isolation #278) » Wed May 27, 2020 2:07 am

To an existing sequence or a new one?

Plotinus · Post Post #660 (isolation #279) » Wed May 27, 2020 6:50 am

Spoiler: completed sequences

Topology: Micc, Not_Mafia: 47 points

[20, 56, 60] {
9 < n < 100
2 digit numbers

Measure: StrangerCoug, vincentw: 45 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[116, 217, 219, 215] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero

Dynamics: lilith2013, skitter30: 35 points

[37, 53, 75 ] all digits are odd
[81, 189, 324] {
27 | n
} multiples of 27

It is

vincentw

's turn

Plotinus · Post Post #662 (isolation #280) » Wed May 27, 2020 6:09 pm

Spoiler: completed sequences

Topology: Micc, Not_Mafia: 47 points

[20, 56, 60] {
9 < n < 100
2 digit numbers

Measure: StrangerCoug, vincentw: 45 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[116, 217, 219, 215] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero

Dynamics: lilith2013, skitter30: 35 points

[37, 53, 75, 339] all digits are odd
[81, 189, 324] {
27 | n
} multiples of 27

It is

skitter30

's turn

Plotinus · Post Post #667 (isolation #281) » Thu May 28, 2020 6:13 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)

Topology: Micc, Not_Mafia: 54 points

[20, 56, 60] {
9 < n < 100
2 digit numbers

Measure: StrangerCoug, vincentw: 45 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[116, 217, 219, 215] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[95, 138, 246] squarefree composite numbers

Dynamics: lilith2013, skitter30: 35 points

[37, 53, 75, 339] all digits are odd
[81, 189, 324] {
27 | n
} multiples of 27

It is

lilith2013

's turn

skitter is V/LA until Sunday

Plotinus · Post Post #669 (isolation #282) » Thu May 28, 2020 7:54 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero

Topology: Micc, Not_Mafia: 54 points

[20, 56, 60] {
9 < n < 100
2 digit numbers

Measure: StrangerCoug, vincentw: 45 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[95, 138, 246] squarefree composite numbers

Dynamics: lilith2013, skitter30: 42 points

[37, 53, 75, 339] all digits are odd
[81, 189, 324] {
27 | n
} multiples of 27

It is

Not_Mafia

's turn

skitter is V/LA until Sunday

Plotinus · Post Post #671 (isolation #283) » Fri May 29, 2020 5:48 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero

Topology: Micc, Not_Mafia: 54 points

[20, 56, 60] {
9 < n < 100
2 digit numbers
[176, 298, 295,] {
n = 100*a + 10*b + c, b is odd
3 digit numbers where the middle digit is odd

Measure: StrangerCoug, vincentw: 45 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[95, 138, 246] squarefree composite numbers

Dynamics: lilith2013, skitter30: 42 points

[37, 53, 75, 339] all digits are odd
[81, 189, 324] {
27 | n
} multiples of 27

It is

vincentw

's turn

skitter is V/LA until Sunday

Plotinus · Fri May 29, 2020 11:47 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck

Topology: Micc, Not_Mafia: 54 points

[20, 56, 60] {
9 < n < 100
2 digit numbers
[176, 298, 295,] {
n = 100*a + 10*b + c, b is odd
3 digit numbers where the middle digit is odd

Measure: StrangerCoug, vincentw: 52 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[95, 138, 246] squarefree composite numbers

Dynamics: lilith2013, skitter30: 42 points

[37, 53, 75, 339] all digits are odd
[81, 189, 324] {
27 | n
} multiples of 27

It is

skitter30

's turn.

skitter is V/LA until Sunday, so she has until early Tuesday to go.

wow, nice one, vincent!

Plotinus · Post Post #675 (isolation #285) » Sat May 30, 2020 5:06 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers

Topology: Micc, Not_Mafia: 54 points

[20, 56, 60] {
9 < n < 100
2 digit numbers
[176, 298, 295,] {
n = 100*a + 10*b + c, b is odd
3 digit numbers where the middle digit is odd

Measure: StrangerCoug, vincentw: 52 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order

Dynamics: lilith2013, skitter30: 49 points

[37, 53, 75, 339] all digits are odd
[81, 189, 324] {
27 | n
} multiples of 27

It is

Micc

's turn.

Plotinus · Post Post #676 (isolation #286) » Sun May 31, 2020 6:02 pm

Prodded Micc. He has another (expired on 2020-06-02 01:02:00) to go before I start looking for a replacement.

Plotinus · Post Post #679 (isolation #287) » Mon Jun 01, 2020 7:15 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers

Topology: Micc, Not_Mafia: 54 points

[20, 56, 60] {
9 < n < 100
2 digit numbers
[176, 298, 295,] {
n = 100*a + 10*b + c, b is odd
3 digit numbers where the middle digit is odd
[171, 323, 77] palindromes

Measure: StrangerCoug, vincentw: 52 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[81, 189, 324, 27] {
27 | n
} multiples of 27

Dynamics: lilith2013, skitter30: 49 points

[37, 53, 75, 339] all digits are odd

It is

lilith2013

's turn.

Plotinus · Post Post #681 (isolation #288) » Tue Jun 02, 2020 6:15 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd

Topology: Micc, Not_Mafia: 54 points

[20, 56, 60] {
9 < n < 100
2 digit numbers
[176, 298, 295,] {
n = 100*a + 10*b + c, b is odd
3 digit numbers where the middle digit is odd
[171, 323, 77] palindromes

Measure: StrangerCoug, vincentw: 52 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[81, 189, 324, 27] {
27 | n
} multiples of 27

Dynamics: lilith2013, skitter30: 56 points

It is

Not_Mafia

's turn.

The remaining cards in the deck take up 4 lines on my screen. (I'll switch to a more precise number when we're closer to running out of cards; this is over 100)

Plotinus · Post Post #682 (isolation #289) » Tue Jun 02, 2020 7:49 pm

Prodded Not_Mafia. He has another (expired on 2020-06-04 02:49:24) to go before I start looking for a replacement

Plotinus · Post Post #684 (isolation #290) » Wed Jun 03, 2020 6:03 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd

Topology: Micc, Not_Mafia: 54 points

[20, 56, 60] {
9 < n < 100
2 digit numbers
[176, 298, 295,] {
n = 100*a + 10*b + c, b is odd
3 digit numbers where the middle digit is odd
[171, 323, 77] palindromes
[220, 162, 18]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit

Measure: StrangerCoug, vincentw: 52 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[81, 189, 324, 27] {
27 | n
} multiples of 27

Dynamics: lilith2013, skitter30: 56 points

It is

vincentw

's turn.

The remaining cards in the deck take up 4 lines on my screen.

Plotinus · Post Post #687 (isolation #291) » Thu Jun 04, 2020 7:18 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd

Topology: Micc, Not_Mafia: 54 points

[20, 56, 60] {
9 < n < 100
2 digit numbers
[176, 298, 295] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[171, 323, 77] palindromes
[220, 162, 18]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit

Measure: StrangerCoug, vincentw: 52 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[81, 189, 324, 27] {
27 | n
} multiples of 27
[121, 209, 252 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number

Dynamics: lilith2013, skitter30: 56 points

[328, 28, 276, 275] numbers that contain a 27 or 28

It is

Micc

's turn.

The remaining cards in the deck take up 6 lines on my screen because I've zoomed in to read it better. About 25 numbers / line at this zoom level and the last line isn't full.

Plotinus · Post Post #689 (isolation #292) » Fri Jun 05, 2020 7:15 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd

Topology: Micc, Not_Mafia: 54 points

[20, 56, 60] {
9 < n < 100
2 digit numbers
[176, 298, 295] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[171, 323, 77] palindromes
[220, 162, 18]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[65, 345 285] {
5 | n
} multiples of 5

Measure: StrangerCoug, vincentw: 52 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[81, 189, 324, 27] {
27 | n
} multiples of 27
[121, 209, 252 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number

Dynamics: lilith2013, skitter30: 56 points

[328, 28, 276, 275] numbers that contain a 27 or 28

It is

StrangerCoug

's turn.

The remaining cards in the deck take up 6 lines on my screen.

Plotinus · Post Post #691 (isolation #293) » Sat Jun 06, 2020 7:06 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit

Topology: Micc, Not_Mafia: 54 points

[20, 56, 60] {
9 < n < 100
2 digit numbers
[176, 298, 295] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[171, 323, 77] palindromes
[65, 345 285] {
5 | n
} multiples of 5

Measure: StrangerCoug, vincentw: 60 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[81, 189, 324, 27] {
27 | n
} multiples of 27
[121, 209, 252 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number

Dynamics: lilith2013, skitter30: 56 points

[328, 28, 276, 275] numbers that contain a 27 or 28

It is

lilith2013

's turn.

The remaining cards in the deck take up 5 lines on my screen (same zoom level as last time)

Plotinus · Post Post #693 (isolation #294) » Sun Jun 07, 2020 7:10 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number

Topology: Micc, Not_Mafia: 54 points

[20, 56, 60] {
9 < n < 100
2 digit numbers
[176, 298, 295] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[171, 323, 77] palindromes
[65, 345 285] {
5 | n
} multiples of 5

Measure: StrangerCoug, vincentw: 60 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[81, 189, 324, 27] {
27 | n
} multiples of 27

Dynamics: lilith2013, skitter30: 63 points

[328, 28, 276, 275] numbers that contain a 27 or 28

It is

Not_Mafia

's turn.

The remaining cards in the deck take up 5 lines on my screen

Plotinus · Post Post #696 (isolation #295) » Mon Jun 08, 2020 6:25 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number

Topology: Micc, Not_Mafia: 54 points

[20, 56, 60, 85] {
9 < n < 100
2 digit numbers
[176, 298, 295, 251] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[171, 323, 77] palindromes
[65, 345 285] {
5 | n
} multiples of 5

Measure: StrangerCoug, vincentw: 60 points

[134, 146, 238, 248] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[81, 189, 324, 27] {
27 | n
} multiples of 27

Dynamics: lilith2013, skitter30: 63 points

[328, 28, 276, 275] numbers that contain a 27 or 28

It is

skitter30

's turn.

The remaining cards in the deck take up 5 lines on my screen

Plotinus · Post Post #699 (isolation #296) » Mon Jun 08, 2020 7:01 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd

Topology: Micc, Not_Mafia: 61 points

[20, 56, 60, 85] {
9 < n < 100
2 digit numbers
[171, 323, 77] palindromes
[65, 345 285] {
5 | n
} multiples of 5

Measure: StrangerCoug, vincentw: 60 points

[81, 189, 324, 27] {
27 | n
} multiples of 27

Dynamics: lilith2013, skitter30: 70 points

[328, 28, 276, 275] numbers that contain a 27 or 28

It is

StrangerCoug

's turn.

The remaining cards in the deck take up 5 lines on my screen

Plotinus · Post Post #701 (isolation #297) » Mon Jun 08, 2020 8:48 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers

Topology: Micc, Not_Mafia: 61 points

[171, 323, 77] palindromes
[65, 345 285] {
5 | n
} multiples of 5

Measure: StrangerCoug, vincentw: 69 points

[81, 189, 324, 27] {
27 | n
} multiples of 27

Dynamics: lilith2013, skitter30: 70 points

[328, 28, 276, 275] numbers that contain a 27 or 28

It is

lilith2013

's turn.

The remaining cards in the deck take up 5 lines on my screen

Plotinus · Post Post #703 (isolation #298) » Mon Jun 08, 2020 7:35 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers

Topology: Micc, Not_Mafia: 61 points

[171, 323, 77] palindromes
[65, 345 285] {
5 | n
} multiples of 5

Measure: StrangerCoug, vincentw: 69 points

[81, 189, 324, 27] {
27 | n
} multiples of 27

Dynamics: lilith2013, skitter30: 70 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[361, 283, 343] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1

It is

Not_Mafia

's turn.

The remaining cards in the deck take up 3 lines on my screen at normal zoom (about 42 numbers per line)

Plotinus · Post Post #705 (isolation #299) » Wed Jun 10, 2020 6:44 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers

Topology: Micc, Not_Mafia: 61 points

[171, 323, 77] palindromes
[65, 345 285] {
5 | n
} multiples of 5

Measure: StrangerCoug, vincentw: 69 points

[81, 189, 324, 27] {
27 | n
} multiples of 27

Dynamics: lilith2013, skitter30: 70 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[361, 283, 343, 223] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1

It is

vincentw

's turn.

The remaining cards in the deck take up 3 lines on my screen at normal zoom (about 42 numbers per line)

prodding vincent

Plotinus · Post Post #707 (isolation #300) » Wed Jun 10, 2020 9:03 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers

Topology: Micc, Not_Mafia: 61 points

[171, 323, 77] palindromes
[65, 345 285, 240] {
5 | n
} multiples of 5

Measure: StrangerCoug, vincentw: 69 points

[81, 189, 324, 27] {
27 | n
} multiples of 27

Dynamics: lilith2013, skitter30: 70 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[361, 283, 343, 223] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1

It is

skitter30's

's turn.

The remaining cards in the deck take up 3 lines on my screen at normal zoom (about 42 numbers per line)

Plotinus · Post Post #708 (isolation #301) » Fri Jun 12, 2020 4:19 am

prodding skitter

Plotinus · Post Post #710 (isolation #302) » Fri Jun 12, 2020 4:51 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1

Topology: Micc, Not_Mafia: 61 points

[171, 323, 77] palindromes
[65, 345 285, 240] {
5 | n
} multiples of 5

Measure: StrangerCoug, vincentw: 69 points

[81, 189, 324, 27] {
27 | n
} multiples of 27

Dynamics: lilith2013, skitter30: 78 points

[328, 28, 276, 275] numbers that contain a 27 or 28

It is

Micc's

's turn.

The remaining cards in the deck take up 3 lines on my screen at normal zoom (about 42 numbers per line)

Plotinus · Post Post #711 (isolation #303) » Fri Jun 12, 2020 8:29 pm

Micc wrote:Is this an acceptable bingo? It works for 171/366 numbers (46.7%), but I want to run it by you for meta rules before I post.

Numbers that have at least one digit being 2 or at least one digit being 0, but not both.

I am pretty sure this is an allowable bingo and that it meets the meta rule of <= 1% of randomly selected hands will meet the criteria "at least one digit is x or at least one digit is y, but not both". But I can't do the math today myself.

If anyone in the next 24 hours can prove that it doesn't meet the criteria for a bingo, then Micc can do something else with his turn, otherwise, the cards will be revealed and Topology will get 7 points

Plotinus · Post Post #714 (isolation #304) » Sun Jun 14, 2020 5:00 am

Sorry, the part of my brain that knows what numbers is went missing. The 1% thing means: of all possible hands you could draw from the deck, the algorithm you're using to check if you have a bingo or not should produce a bingo about 1% of them time (though "all cards are even" is explicitly allowed so maybe I should make it 1/64 or 2% instead. Either way I guess this one's out after all. Thanks for putting in the work for us, vincentw.

I noticed that summing row 371 didn't give the same answer as multiplying row 372 and I'm curious about why summing those isn't another way of arriving at the answer. (Summing them is also well over 1% so it doesn't matter for the question of whether it's a bingo)

Plotinus · Post Post #715 (isolation #305) » Sun Jun 14, 2020 5:03 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1

Topology: Micc, Not_Mafia: 61 points

[171, 323, 77] palindromes
[65, 345 285, 240] {
5 | n
} multiples of 5
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 69 points

[81, 189, 324, 27] {
27 | n
} multiples of 27

Dynamics: lilith2013, skitter30: 78 points

[328, 28, 276, 275] numbers that contain a 27 or 28

It is

StrangerCoug's

's turn.

The remaining cards in the deck take up 3 lines on my screen at normal zoom (about 42 numbers per line)

Plotinus · Post Post #718 (isolation #306) » Sun Jun 14, 2020 7:42 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1

Topology: Micc, Not_Mafia: 61 points

[171, 323, 77] palindromes
[65, 345 285, 240] {
5 | n
} multiples of 5
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 69 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[105, 122, 239, 287] digit sum is squarefree (1 counts as squarefree)

Dynamics: lilith2013, skitter30: 78 points

[328, 28, 276, 275] numbers that contain a 27 or 28

It is

lilith2013

's turn.

The remaining cards in the deck take up 3 lines on my screen at normal zoom (about 42 numbers per line)

Plotinus · Post Post #721 (isolation #307) » Sun Jun 14, 2020 8:31 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)

Topology: Micc, Not_Mafia: 61 points

[171, 323, 77] palindromes
[65, 345 285, 240] {
5 | n
} multiples of 5
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 69 points

[81, 189, 324, 27] {
27 | n
} multiples of 27

Dynamics: lilith2013, skitter30: 85 points

[328, 28, 276, 275] numbers that contain a 27 or 28

It is

Not_Mafia

's turn.

The remaining cards in the deck take up 3 lines on my screen at normal zoom (about 42 numbers per line)

Plotinus · Post Post #722 (isolation #308) » Sun Jun 14, 2020 8:32 pm

Thanks, vincent, that makes sense.

Plotinus · Post Post #725 (isolation #309) » Tue Jun 16, 2020 6:05 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)

Topology: Micc, Not_Mafia: 61 points

[171, 323, 77] palindromes
[65, 345 285, 240] {
5 | n
} multiples of 5
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.
[244, 267, 212, 221] numbers where the amount of digits that are "2" is an infinitely recurring percentage

Measure: StrangerCoug, vincentw: 69 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15

Dynamics: lilith2013, skitter30: 85 points

[328, 28, 276, 275] numbers that contain a 27 or 28

It is

skitter30

's turn.

There are 84 cards remaining

Plotinus · Post Post #726 (isolation #310) » Wed Jun 17, 2020 2:03 am

prodded skitter

Plotinus · Post Post #728 (isolation #311) » Wed Jun 17, 2020 6:05 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)

Topology: Micc, Not_Mafia: 61 points

[171, 323, 77] palindromes
[65, 345 285, 240] {
5 | n
} multiples of 5
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.
[244, 267, 212, 221] numbers where the amount of digits that are "2" is an infinitely recurring percentage

Measure: StrangerCoug, vincentw: 69 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15

Dynamics: lilith2013, skitter30: 85 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[47, 74, 131, 245] remove each digit that is a power of 2 (including 1) and you're left with a prime

It is

Micc

's turn.

There are 80 cards remaining

Plotinus · Post Post #730 (isolation #312) » Wed Jun 17, 2020 6:56 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0; k ∈ ℤ
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage

Topology: Micc, Not_Mafia: 68 points

[171, 323, 77] palindromes
[65, 345 285, 240] {
5 | n
} multiples of 5
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 69 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15

Dynamics: lilith2013, skitter30: 85 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[47, 74, 131, 245] remove each digit that is a power of 2 (including 1) and you're left with a prime

It is

StrangerCoug

's turn.

There are 77 cards remaining

Plotinus · Post Post #732 (isolation #313) » Thu Jun 18, 2020 8:06 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage

Topology: Micc, Not_Mafia: 68 points

[171, 323, 77] palindromes
[65, 345 285, 240] {
5 | n
} multiples of 5
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 69 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

Dynamics: lilith2013, skitter30: 85 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[47, 74, 131, 245] remove each digit that is a power of 2 (including 1) and you're left with a prime

It is

lilith2013

's turn.

There are 74 cards remaining

Plotinus · Post Post #734 (isolation #314) » Fri Jun 19, 2020 7:27 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage

Topology: Micc, Not_Mafia: 68 points

[171, 323, 77] palindromes
[65, 345 285, 240] {
5 | n
} multiples of 5
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 69 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

Dynamics: lilith2013, skitter30: 85 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[47, 74, 131, 245] remove each digit that is a power of 2 (including 1) and you're left with a prime
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

It is

Not_Mafia

's turn.

There are 71 cards remaining

Plotinus · Post Post #736 (isolation #315) » Fri Jun 19, 2020 9:33 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage

Topology: Micc, Not_Mafia: 68 points

[171, 323, 77] palindromes
[65, 345 285, 240] {
5 | n
} multiples of 5
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.
[347, 130, 357, 233] numbers where the amount of digits that are "3" is an infinitely recurring percentage.

Measure: StrangerCoug, vincentw: 69 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

Dynamics: lilith2013, skitter30: 85 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[47, 74, 131, 245] remove each digit that is a power of 2 (including 1) and you're left with a prime
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

It is

vincentw

's turn.

There are 67 cards remaining

Plotinus · Post Post #738 (isolation #316) » Sat Jun 20, 2020 1:37 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.

Topology: Micc, Not_Mafia: 68 points

[171, 323, 77] palindromes
[65, 345 285, 240] {
5 | n
} multiples of 5
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 77 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

Dynamics: lilith2013, skitter30: 85 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[47, 74, 131, 245] remove each digit that is a power of 2 (including 1) and you're left with a prime
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

It is

skitter30

's turn. Today's the sabbath so if she needs a prod then it'll happen when I wake up on Monday, at least 24 hours after sabbath ends in her timezone.

There are 63 cards remaining

Plotinus · Post Post #741 (isolation #317) » Sat Jun 20, 2020 8:06 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5

Topology: Micc, Not_Mafia: 75 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 77 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

Dynamics: lilith2013, skitter30: 85 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[47, 74, 131, 245] remove each digit that is a power of 2 (including 1) and you're left with a prime
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

It is

StrangerCoug

's turn.

There are 60 cards remaining

Plotinus · Post Post #747 (isolation #318) » Mon Jun 22, 2020 2:35 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5

Topology: Micc, Not_Mafia: 75 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 77 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[73, 157, 231] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite

Dynamics: lilith2013, skitter30: 85 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[47, 74, 131, 245] remove each digit that is a power of 2 (including 1) and you're left with a prime
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

It is

lilith2013

's turn.

There are 57 cards remaining

Plotinus · Post Post #749 (isolation #319) » Mon Jun 22, 2020 4:44 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime

Topology: Micc, Not_Mafia: 75 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 77 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[73, 157, 231] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite

Dynamics: lilith2013, skitter30: 92 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

It is

Not_Mafia

's turn.

There are 54 cards remaining

Plotinus · Post Post #751 (isolation #320) » Mon Jun 22, 2020 7:22 am

89 isn't a perfect square, but you can go again

Plotinus · Post Post #753 (isolation #321) » Mon Jun 22, 2020 7:51 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime

Topology: Micc, Not_Mafia: 75 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.
[80, 187, 345] numbers that contain an L when written in roman numerals

Measure: StrangerCoug, vincentw: 77 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[73, 157, 231] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite

Dynamics: lilith2013, skitter30: 92 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

It is

vincentw

's turn.

There are 51 cards remaining

it could happen to any of us, a few of the current sequences let you remove powers of two but this one only lets you remove two itself.

Plotinus · Post Post #756 (isolation #322) » Tue Jun 23, 2020 5:04 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals

Topology: Micc, Not_Mafia: 75 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[73, 157, 231] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite

Dynamics: lilith2013, skitter30: 92 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

It is

skitter30

's turn.

There are 47 cards remaining

Plotinus · Post Post #758 (isolation #323) » Wed Jun 24, 2020 6:48 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals

Topology: Micc, Not_Mafia: 75 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[73, 157, 231] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite

Dynamics: lilith2013, skitter30: 92 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[102, 366, 87] {
3 | n
} multiplies of 3

It is

Micc

's turn.

There are 44 cards remaining

Plotinus · Post Post #760 (isolation #324) » Wed Jun 24, 2020 6:56 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3

Topology: Micc, Not_Mafia: 82 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[73, 157, 231] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite

Dynamics: lilith2013, skitter30: 92 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

It is

StrangerCoug

's turn.

There are 40 cards remaining

Plotinus · Post Post #763 (isolation #325) » Thu Jun 25, 2020 8:12 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3

Topology: Micc, Not_Mafia: 82 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[73, 157, 231] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even

Dynamics: lilith2013, skitter30: 92 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

It is

lilith2013

's turn.

There are 37 cards remaining

Lilith, I think you're looking at an older version of your hand. You only have 2 of those cards still -- the last hand I sent you was titlted "Re: Sequencer | lilith2013's Turn" not "Sequencer Hand" because I forgot to change the subject line. You can go again.

Plotinus · Post Post #765 (isolation #326) » Fri Jun 26, 2020 1:17 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite

Topology: Micc, Not_Mafia: 82 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[318, 266, 208] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even

Dynamics: lilith2013, skitter30: 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

It is

Not_Mafia

's turn.

There are 33 cards remaining

Plotinus · Post Post #767 (isolation #327) » Fri Jun 26, 2020 7:15 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite

Topology: Micc, Not_Mafia: 82 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[318, 266, 208, 154] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even

Dynamics: lilith2013, skitter30: 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

It is

vincentw

's turn.

There are 32 cards remaining

Plotinus · Post Post #768 (isolation #328) » Sat Jun 27, 2020 7:14 am

Prodding vincentw

Plotinus · Sat Jun 27, 2020 10:28 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite

Topology: Micc, Not_Mafia: 82 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

[81, 189, 324, 27] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[318, 266, 208, 154] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[23, 293, 161] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6

Dynamics: lilith2013, skitter30: 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

It is

skitter30

's turn.

There are 29 cards remaining

Plotinus · Post Post #772 (isolation #330) » Mon Jun 29, 2020 6:10 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite

Topology: Micc, Not_Mafia: 82 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[318, 266, 208, 154] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[23, 293, 161] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6

Dynamics: lilith2013, skitter30: 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

It is

Micc

's turn.

There are 28 cards remaining

Plotinus · Post Post #774 (isolation #331) » Mon Jun 29, 2020 6:57 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even

Topology: Micc, Not_Mafia: 89 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[23, 293, 161] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6

Dynamics: lilith2013, skitter30: 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[81, 189, 324, 27, 297] {
27 | n
} multiples of 27

It is

StrangerCoug

's turn.

There are 25 cards remaining

Plotinus · Post Post #776 (isolation #332) » Tue Jun 30, 2020 5:17 am

I have only just now sent StrangerCoug his hand, so his 48 hours start now.

Plotinus · Post Post #778 (isolation #333) » Tue Jun 30, 2020 7:23 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even

Topology: Micc, Not_Mafia: 89 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[23, 293, 161] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69. 99, 269] numbers that contain a 9

Dynamics: lilith2013, skitter30: 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[81, 189, 324, 27, 297] {
27 | n
} multiples of 27

It is

ilith2013

's turn.

There are 22 cards remaining

Plotinus · Post Post #780 (isolation #334) » Tue Jun 30, 2020 7:47 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even

Topology: Micc, Not_Mafia: 89 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[23, 293, 161] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69. 99, 269] numbers that contain a 9

Dynamics: lilith2013, skitter30: 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[360, 152, 265] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit

It is

Not_Mafia

's turn.

There are 19 cards remaining

It looks fine to me. Are ties okay, like 332? Or should it be strictly larger than the other digits?

Plotinus · Post Post #782 (isolation #335) » Tue Jun 30, 2020 8:10 pm

Thanks for clarifying it

Plotinus · Post Post #785 (isolation #336) » Wed Jul 01, 2020 3:42 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even

Topology: Micc, Not_Mafia: 89 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.
[277, 51, 165] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit

Measure: StrangerCoug, vincentw: 84 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[23, 293, 161] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294] numbers that contain a 9

Dynamics: lilith2013, skitter30: 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[360, 152, 265] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit

It is

skitter30

's turn.

There are 15 cards remaining

Plotinus · Post Post #790 (isolation #337) » Wed Jul 01, 2020 6:22 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even

Topology: Micc, Not_Mafia: 89 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.
[277, 51, 165] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit

Measure: StrangerCoug, vincentw: 84 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[23, 293, 161] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294] numbers that contain a 9

Dynamics: lilith2013, skitter30: 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[124, 214, 282] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[360, 152, 265] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13

It is

Micc

's turn.

There are 12 cards remaining

Plotinus · Post Post #792 (isolation #338) » Wed Jul 01, 2020 7:41 pm

StrangerCoug has submitted his turn by PM:

StrangerCoug wrote:Reinstate my out-of-turn play of adding 14 to the numbers whose digits are powers of two when it's my turn, please.

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit

Topology: Micc, Not_Mafia: 97 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[23, 293, 161] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294] numbers that contain a 9
[124, 214, 282, 14] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

Dynamics: lilith2013, skitter30: 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[360, 152, 265] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13

It is

lilith2013

's turn.

There are 6 cards remaining

Plotinus · Post Post #794 (isolation #339) » Thu Jul 02, 2020 2:05 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit

Topology: Micc, Not_Mafia: 97 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[23, 293, 161] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294] numbers that contain a 9
[124, 214, 282, 14] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

Dynamics: lilith2013, skitter30: 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[360, 152, 265, 262] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13

It is

Not_Mafia

's turn.

There are 5 cards remaining

Plotinus · Post Post #798 (isolation #340) » Thu Jul 02, 2020 6:21 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)

Topology: Micc, Not_Mafia: 104 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[23, 293, 161] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294] numbers that contain a 9

Dynamics: lilith2013, skitter30: 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[360, 152, 265, 262] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13

It is

vincentw

's turn.

There are 2 cards remaining. When we run out of cards we'll keep playing until

4

6

people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Post Post #800 (isolation #341) » Thu Jul 02, 2020 7:08 pm

6 players, yes.

Sounds like a good bingo to me.

Plotinus · Post Post #801 (isolation #342) » Thu Jul 02, 2020 7:12 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month

Topology: Micc (7), Not_Mafia (7): 104 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug (7), vincentw (2): 91 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[23, 293, 161] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294] numbers that contain a 9

Dynamics: lilith2013 (7), skitter30 (7): 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[360, 152, 265, 262] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13

It is

skitter30'

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card. I've added how many cards you each have in parentheses after your names.

Plotinus · Post Post #804 (isolation #343) » Fri Jul 03, 2020 6:41 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit

Topology: Micc (4), Not_Mafia (7): 111 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug (7), vincentw (2): 91 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[69, 99, 269, 294] numbers that contain a 9

Dynamics: lilith2013 (7), skitter30 (6): 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13
[23, 293, 161, 147] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6

It is

StrangerCoug

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Post Post #806 (isolation #344) » Sat Jul 04, 2020 8:01 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit

Topology: Micc (4), Not_Mafia (7): 111 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug (6), vincentw (2): 91 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[286, 207, 349] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[69, 99, 269, 294] numbers that contain a 9
[23, 293, 161, 147, 203] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6

Dynamics: lilith2013 (7), skitter30 (6): 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13

It is

lilith2013

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Post Post #808 (isolation #345) » Sat Jul 04, 2020 8:05 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit

Topology: Micc (4), Not_Mafia (7): 111 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug (6), vincentw (2): 91 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[69, 99, 269, 294] numbers that contain a 9
[23, 293, 161, 147, 203] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6

Dynamics: lilith2013 (6), skitter30 (6): 99 points

[328, 28, 276, 275] numbers that contain a 27 or 28
[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13
[286, 207, 349, 103] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

It is

Not_Mafia

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Post Post #811 (isolation #346) » Sat Jul 04, 2020 6:33 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit

Topology: Micc (4), Not_Mafia (6): 111 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.
[328, 28, 276, 275, 273] numbers that contain a 27 or 28

Measure: StrangerCoug (6), vincentw (1): 91 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[69, 99, 269, 294] numbers that contain a 9
[23, 293, 161, 147, 203, 11] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6

Dynamics: lilith2013 (6), skitter30 (6): 99 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13
[286, 207, 349, 103] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

It is

skitter30

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Post Post #813 (isolation #347) » Sun Jul 05, 2020 7:37 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit

Topology: Micc (4), Not_Mafia (6): 111 points

[171, 323, 77] palindromes
[249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.
[328, 28, 276, 275, 273] numbers that contain a 27 or 28

Measure: StrangerCoug (6), vincentw (1): 91 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[23, 293, 161, 147, 203, 11] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6

Dynamics: lilith2013 (6), skitter30 (5): 99 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13
[286, 207, 349, 103] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[69, 99, 269, 294, 96] numbers that contain a 9

It is

Micc

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.[/quote]

Plotinus · Post Post #815 (isolation #348) » Mon Jul 06, 2020 6:33 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit

Topology: Micc (3), Not_Mafia (6): 111 points

[171, 323, 77] palindromes
[249, 224, 292, 326] Remove each digit that is a 2 and you are left with a perfect square.
[328, 28, 276, 275, 273] numbers that contain a 27 or 28

Measure: StrangerCoug (6), vincentw (1): 91 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15
[23, 293, 161, 147, 203, 11] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6

Dynamics: lilith2013 (6), skitter30 (5): 99 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13
[286, 207, 349, 103] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[69, 99, 269, 294, 96] numbers that contain a 9

It is

StrangerCoug

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Post Post #817 (isolation #349) » Tue Jul 07, 2020 6:36 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[23, 293, 161, 147, 203, 11, 317] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6

Topology: Micc (3), Not_Mafia (6): 111 points

[171, 323, 77] palindromes
[249, 224, 292, 326] Remove each digit that is a 2 and you are left with a perfect square.
[328, 28, 276, 275, 273] numbers that contain a 27 or 28

Measure: StrangerCoug (5), vincentw (1): 98 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15

Dynamics: lilith2013 (6), skitter30 (5): 99 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13
[286, 207, 349, 103] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square
[69, 99, 269, 294, 96] numbers that contain a 9

It is

lilith2013

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Post Post #819 (isolation #350) » Tue Jul 07, 2020 7:16 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[23, 293, 161, 147, 203, 11, 317] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294, 96, 290, 129] numbers that contain a 9

Topology: Micc (3), Not_Mafia (6): 111 points

[171, 323, 77] palindromes
[249, 224, 292, 326] Remove each digit that is a 2 and you are left with a perfect square.
[328, 28, 276, 275, 273] numbers that contain a 27 or 28

Measure: StrangerCoug (5), vincentw (1): 98 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15

Dynamics: lilith2013 (4), skitter30 (5): 106 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13
[286, 207, 349, 103] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

It is

Not_Mafia

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Post Post #821 (isolation #351) » Tue Jul 07, 2020 7:58 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[23, 293, 161, 147, 203, 11, 317] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294, 96, 290, 129] numbers that contain a 9

Topology: Micc (3), Not_Mafia (3): 111 points

[171, 323, 77] palindromes
[249, 224, 292, 326] Remove each digit that is a 2 and you are left with a perfect square.
[328, 28, 276, 275, 273] numbers that contain a 27 or 28
[237, 205, 332] numbers that start or end with 2

Measure: StrangerCoug (5), vincentw (1): 98 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15

Dynamics: lilith2013 (4), skitter30 (5): 106 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13
[286, 207, 349, 103] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

It is

vincentw

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Post Post #824 (isolation #352) » Tue Jul 07, 2020 7:58 pm

Yeah, you're right. Okay, you'll be passed until/unless a new sequence appears on the board.

it's skitter30's turn

Plotinus · Post Post #826 (isolation #353) » Wed Jul 08, 2020 3:10 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[23, 293, 161, 147, 203, 11, 317] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294, 96, 290, 129] numbers that contain a 9

Topology: Micc (3), Not_Mafia (3): 111 points

[171, 323, 77] palindromes
[249, 224, 292, 326] Remove each digit that is a 2 and you are left with a perfect square.
[328, 28, 276, 275, 273] numbers that contain a 27 or 28
[237, 205, 332] numbers that start or end with 2

Measure: StrangerCoug (5), vincentw (1, skip): 98 points

[46, 59, 164] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15

Dynamics: lilith2013 (4), skitter30 (5): 106 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13
[286, 207, 349, 103] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

It is

Micc

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Post Post #829 (isolation #354) » Wed Jul 08, 2020 7:15 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[23, 293, 161, 147, 203, 11, 317] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294, 96, 290, 129] numbers that contain a 9

Topology: Micc (2), Not_Mafia (3): 111 points

[171, 323, 77] palindromes
[249, 224, 292, 326] Remove each digit that is a 2 and you are left with a perfect square.
[328, 28, 276, 275, 273] numbers that contain a 27 or 28
[237, 205, 332] numbers that start or end with 2
[46, 59, 164, 89] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15

Measure: StrangerCoug (4), vincentw (1, skip): 98 points

[286, 207, 349, 103, 31] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

Dynamics: lilith2013 (4), skitter30 (5): 106 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13

It is

lilith2013

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Post Post #830 (isolation #355) » Thu Jul 09, 2020 8:24 pm

Prodded lilith2013

Plotinus · Post Post #832 (isolation #356) » Thu Jul 09, 2020 9:09 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[23, 293, 161, 147, 203, 11, 317] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294, 96, 290, 129] numbers that contain a 9

Topology: Micc (2), Not_Mafia (3): 111 points

[171, 323, 77] palindromes
[249, 224, 292, 326] Remove each digit that is a 2 and you are left with a perfect square.
[328, 28, 276, 275, 273] numbers that contain a 27 or 28
[46, 59, 164, 89] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15

Measure: StrangerCoug (4), vincentw (1, skip): 98 points

[286, 207, 349, 103, 31] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

Dynamics: lilith2013 (4), skitter30 (5): 106 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13
[237, 205, 332, 257] numbers that start or end with 2

It is

Not_Mafia

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Thu Jul 09, 2020 10:49 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[23, 293, 161, 147, 203, 11, 317] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294, 96, 290, 129] numbers that contain a 9

Topology: Micc (2), Not_Mafia (2): 111 points

[171, 323, 77] palindromes
[249, 224, 292, 326] Remove each digit that is a 2 and you are left with a perfect square.
[328, 28, 276, 275, 273] numbers that contain a 27 or 28
[46, 59, 164, 89] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15

Measure: StrangerCoug (4), vincentw (1, skip): 98 points

[286, 207, 349, 103, 31] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

Dynamics: lilith2013 (3), skitter30 (5): 106 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13
[237, 205, 332, 257, 142] numbers that start or end with 2

It is

skitter30

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

vincentw is skipped because he only has 1 card and there haven't been any new sequences since he last skipped.

Not skipping skitter in case she wants to start a new sequence but she isn't required to start one.

Plotinus · Post Post #842 (isolation #358) » Fri Jul 10, 2020 7:16 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[23, 293, 161, 147, 203, 11, 317] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294, 96, 290, 129] numbers that contain a 9
[237, 205, 332, 257, 142, 26, 250, 254] numbers that start or end with 2
[46, 59, 164, 89, 61, 104, 106] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15

Topology: Micc (1), Not_Mafia (2): 111 points

[171, 323, 77] palindromes
[249, 224, 292, 326] Remove each digit that is a 2 and you are left with a perfect square.
[328, 28, 276, 275, 273] numbers that contain a 27 or 28

Measure: StrangerCoug (1), vincentw (1, skip): 106 points

[286, 207, 349, 103, 31] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

Dynamics: lilith2013 (1), skitter30 (5): 113 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13

It is

Not_Mafia

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Sat Jul 11, 2020 12:26 am

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[23, 293, 161, 147, 203, 11, 317] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294, 96, 290, 129] numbers that contain a 9
[237, 205, 332, 257, 142, 26, 250, 254] numbers that start or end with 2
[46, 59, 164, 89, 61, 104, 106] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15

Topology: Micc (1), Not_Mafia (1): 111 points

[171, 323, 77] palindromes
[249, 224, 292, 326] Remove each digit that is a 2 and you are left with a perfect square.
[328, 28, 276, 275, 273, 289] numbers that contain a 27 or 28

Measure: StrangerCoug (1), vincentw (1, skip): 106 points

[286, 207, 349, 103, 31] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

Dynamics: lilith2013 (1), skitter30 (5): 113 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27
[49, 94, 148] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13

It is

skitter30

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Post Post #847 (isolation #360) » Sun Jul 12, 2020 7:13 pm

StrangerCoug has submitted his turn by PM

StrangerCoug wrote:Pass unless skitter plays a sequence to which I can legally play my last card, in which case play it to that.

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[23, 293, 161, 147, 203, 11, 317] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294, 96, 290, 129] numbers that contain a 9
[237, 205, 332, 257, 142, 26, 250, 254] numbers that start or end with 2
[46, 59, 164, 89, 61, 104, 106] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15

Topology: Micc (0, skip), Not_Mafia (1): 111 points

[171, 323, 77] palindromes
[249, 224, 292, 326] Remove each digit that is a 2 and you are left with a perfect square.
[328, 28, 276, 275, 273, 289] numbers that contain a 27 or 28
[49, 94, 148, 256] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13

Measure: StrangerCoug (1, skip), vincentw (1, skip): 106 points

[286, 207, 349, 103, 31] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

Dynamics: lilith2013 (1), skitter30 (5): 113 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27

It is

lilith2013

's turn.

We'll keep playing until 6 people pass in a row. You can pass only if there are no sequences to which you can add a card.

Plotinus · Post Post #849 (isolation #361) » Sun Jul 12, 2020 7:20 pm

It is

Not_Mafia

's

turn

Plotinus · Post Post #851 (isolation #362) » Sun Jul 12, 2020 9:12 pm

Spoiler: completed sequences

[54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
[78, 126, 336, 348, 192, 315, 123] {
n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
} composite numbers whose digit sum is composite
[55, 226, 253, 190, 19, 352, 334] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
} numbers whose digit sum equals 10
[3, 7, 229, 5, 179, 17, 137] primes
[25, 44, 63, 365, 52, 62, 88, 175] {
i % (i % 10) == 0
} Numbers divisible by their last digit
[166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
[1, 4, 43, 141, 301, 302, 341] have four or fewer factors
[90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
[234, 342, 356, 140, 173, 200, 280, 299] {
n = 100×a + 10×b + c with c < a + b
} 3 digit numbers where the last digit is less than the sum of the first two digits
[39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
[174, 118, 274, 232, 316, 180, 358 ] {
2 | n ∧ n ≥ 100
} 3 digit even numbers
[48, 135, 306, 40, 84, 132, 243] {
k² | n, k > 1
} numbers that are divisible by a perfect square greater than one
[235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
[125, 270, 320, 30, 45, 100, 150] {
2ⁱ×3^j×5^k with i, j, k ≥ 0
} 5-smooth numbers
[202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
[120, 143, 194, 8, 15, 98, 170] {
n ∈ [k² - 2, k² + 2], k ∈ ℤ
numbers within 2 of a perfect square
[191, 359, 305, 271, 199, 163, 109] {
n > 100 ∧ n % 2 = 1
} 3 digit odd numbers
[128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
[116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
[16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
[95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
[37, 53, 75, 339, 9, 57, 197] all digits are odd
[220, 162, 18, 42, 107, 201, 213, 230]
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers where the sum of the digits is a single digit
[121, 209, 252, 29, 67, 92, 119 ] {
(n(n+1)/2 + 1) or (n(n+1)/2 - 1)
} numbers that are exactly one away from a triangular number
[134, 146, 238, 248, 145, 139, 236] {
n = 100*a + 10*b + c with 0 < a < b < c < 10
} 3 digit numbers whose digits are in strictly ascending order
[176, 298, 295, 251, 330, 258, and 211] {
n = 100*a + 10*b + c, b is odd
} 3 digit numbers where the middle digit is odd
[20, 56, 60, 85, 36, 41, 66, 79, 82] {
9 < n < 100
2 digit numbers
[361, 283, 343, 223, 241, 355, 331, 91] {
n ≡ 1 (mod 6)
} (multiples of 6) + 1
[105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
[244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
[347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
[65, 345 285, 240, 160, 70, 225] {
5 | n
} multiples of 5
[47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
[80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
[102, 366, 87, 108, 198, 264, 159] {
3 | n
} multiplies of 3
[73, 157, 231, 35, 111, 72, 101] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
} Numbers none of whose digits are composite
[318, 266, 208, 154, 64, 6, 350] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
} Even numbers whose digit sum is also even
[277, 51, 165, 181, 13, 327, 291, and 169] {
n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} Odd numbers that also contain an odd digit that isn’t the last digit
[124, 214, 282, 14, 24, 12, 21] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
} numbers that consist only of digits that are powers of 2 (including 1)
[ 10, 2, 279, 310, 308, 255, 216] Day numbers that fall in the first 2 weeks of its respective month
[360, 152, 265, 262, 184, 83, 363] {
n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
} second digit from the right is strictly the largest digit
[23, 293, 161, 147, 203, 11, 317] {
n ≡ 5 (mod 6)
} numbers equivalent to 5 mod 6
[69, 99, 269, 294, 96, 290, 129] numbers that contain a 9
[237, 205, 332, 257, 142, 26, 250, 254] numbers that start or end with 2
[46, 59, 164, 89, 61, 104, 106] {
n ≡ ±1 (mod 15)
} numbers equivalent to ±1 mod 15

Topology: Micc (0, skip), Not_Mafia (1, skip): 111 points

[171, 323, 77] palindromes
[249, 224, 292, 326] Remove each digit that is a 2 and you are left with a perfect square.
[328, 28, 276, 275, 273, 289] numbers that contain a 27 or 28
[49, 94, 148, 256] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
} digits sum to 13

Measure: StrangerCoug (1, skip), vincentw (1, skip): 106 points

[286, 207, 349, 103, 31] {
n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
} Numbers whose digit sum is a perfect square

Dynamics: lilith2013 (1, skip), skitter30 (5): 113 points

[81, 189, 324, 27, 297] {
27 | n
} multiples of 27

It is

skitter30

's turn.

If skitter passes then the game is over because she's the only one who can start a new sequence and everyone else is skipping

Plotinus · Mon Jul 13, 2020 12:59 am

Dynamics wins! Congrats skitter30 and lilith!

Plotinus · Post Post #855 (isolation #364) » Mon Jul 13, 2020 1:02 am

You can /in for next now

Do we want to discuss any rule changes for the next game? I think we should use a little bit smaller deck.

Plotinus · Post Post #858 (isolation #365) » Mon Jul 13, 2020 2:01 am

It was this deck, but we added the perfect cubes to it too

In post 247, StrangerCoug wrote:So I think we've all got the hang of this and can play Game 2 with a slightly bigger deck.

Spoiler: My proposed Game 2 deck
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 23, 23, 24, 24, 25, 25, 25, 26, 27, 27, 27, 28, 28, 28, 29, 29, 30, 30, 30, 31, 32, 32, 33, 34, 34, 35, 35, 35, 35, 36, 36, 36, 37, 38, 39, 40, 40, 41, 42, 42, 43, 44, 45, 45, 45, 46, 47, 48, 49, 49, 49, 50, 50, 51, 52, 53, 54, 55, 55, 55, 56, 56, 56, 57, 58, 59, 60, 61, 62, 63, 63, 64, 64, 64, 64, 65, 66, 67, 68, 69, 70, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 81, 82, 83, 84, 84, 85, 86, 87, 88, 89, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 100, 100, 120, 121, 125, 128, 144, 165, 169, 196, 200, 216, 220, 225, 250, 256, 256, 289, 300, 324, 343, 361, 400, 400, 441, 484, 500, 500, 512, 512, 529, 576, 600, 625, 676, 700, 729, 729, 750, 784, 800, 841, 900, 900, 961, 1000, 1000, 1000

This consists of the following "decks" shuffled together:
The Game 1 deck

Every multiple of 100 less than or equal to 1,000

Every multiple of 250 less than or equal to 1,000

Every square between 100 and 1,000 exclusive (since every square from 1 to 100 inclusive already appears at least twice in the Game 1 deck and √1000 is not an integer)
If a number occurs in multiple decks, it is shuffled in as many times as it occurs total in each deck.

I've been trying (without much effort, admittedly) to "reverse engineer" Plotinus's deck to see how he put it together, but the lowest number to appear once only in the Game 1 deck is 26 and every number above 100 in the Game 1 deck is at least one of a square, a power of two, or a tetrahedral number. For at least some sequences, though, he just puts in the first 10 numbers.

Plotinus · Post Post #865 (isolation #366) » Mon Jul 13, 2020 7:47 am

That's a good point about bingos. How many points should they be worth?

Spoiler: my own thoughts

but i'm open to other arguments

Plotinus · Post Post #870 (isolation #367) » Tue Jul 21, 2020 8:46 am

Noted, good luck with the move.

So with 3 /ins should we do a round without teams?

Is there anyone who forgot to in? So far we have:

D3f3nder
StrangerCoug
vincentw

Plotinus · Post Post #873 (isolation #368) » Sun Aug 02, 2020 7:07 am

Welcome Nancy and Errant! I think we'll start once we have 6 people (1 more!)

Plotinus · Post Post #875 (isolation #369) » Sun Aug 02, 2020 6:10 pm

Code: Select all

random.shuffle(players)                                                                                                                              
print(players)                                                                                                                                       
['vincentw', 'Sirius9121', 'StrangerCoug', 'ErrantParabola', 'Nancy Drew 39', 'D3f3nd3r']

Team Haversine: vincentw, ErrantParabola

Team Exsecant: Sirius9121, Nancy Drew 39

Team Chord: StrangerCoug, D3f3nder

Are these colours visibly distinct enough? Is anyone using a light background such that they're invisible? We can change up the colours if anyone doesn't like them. You can also change your team names if both team members find something they like better.

We're using deck 2 and bingos are now worth 14 points. I've updated the OP to reflect this.

It is

vincentw's

turn, or it will be as soon as I shuffle the deck and send him some cards.

Plotinus · Post Post #877 (isolation #370) » Sun Aug 02, 2020 8:19 pm

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 0 points

[9, 73, 90] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name

Exsecant: Sirius9121, Nancy Drew 39: 0 points

Chord: StrangerCoug, D3f3nd3r: 0 points

It is

Sirius9121

's turn.

Plotinus · Sun Aug 02, 2020 11:58 pm

Fixed, thanks.

You may not help your teammates in private, but you can discuss your cards in the public thread if you want.

Plotinus · Mon Aug 03, 2020 12:58 am

Are any of these better?

gold

,

goldenrod

,

darkgoldenrod?

Plotinus · Post Post #886 (isolation #373) » Mon Aug 03, 2020 1:31 am

I changed exsecant from orange to chocolate and chord from yellow to goldenrod:

haversine

,

exsecant

,

chord

I can move things around more if anybody needs me to

Plotinus · Post Post #890 (isolation #374) » Mon Aug 03, 2020 3:02 am

Done.

Sirius do you suggest

#ff7711

because it looks better or because you're having trouble telling it apart from the others? I'm trying to stick to words but

darkorange

, the nearest equivalent, might not be dark enough on mafSepia

Plotinus · Post Post #896 (isolation #375) » Mon Aug 03, 2020 6:28 pm

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 0 points

[9, 73, 90] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name

Exsecant: Sirius9121, Nancy Drew 39: 14 points

Chord: StrangerCoug, D3f3nd3r: 0 points

It is

Strangercoug

's turn.

If your poo is that colour you should see a doctor or eat less beets but exsecant can be darkorange until someone objects

Plotinus · Post Post #899 (isolation #376) » Tue Aug 04, 2020 3:06 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 0 points

[9, 73, 90] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name

Exsecant: Sirius9121, Nancy Drew 39: 14 points

Chord: StrangerCoug, D3f3nd3r: 0 points

[6, 10, 120, 750] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers

It is

ErrantParabola

's turn.

D3f3nd3r wrote:Darkorange is way too similar to whatever chord is. Not sure what the issue with exsecant in post 886 was?

Sirius thought it was ugly but I care more about legibility and differentiability and I disagree that it's ugly -- chocolate matches the other two better in saturation. I've changed it back to chocolate and I'm tired of changing the colours back and forth so these are the final colours.

Plotinus · Post Post #902 (isolation #377) » Tue Aug 04, 2020 4:37 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 7 points

[9, 73, 90] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name

Exsecant: Sirius9121, Nancy Drew 39: 14 points

Chord: StrangerCoug, D3f3nd3r: 0 points

It is

Nancy Drew 39

's turn.

Yes, you completed the sequence and earned 7 points

Plotinus · Post Post #906 (isolation #378) » Tue Aug 04, 2020 6:01 pm

@Nancy Drew 39: Yeah, you may post your cards in the public thread if you want to.

@D3f3nd3r: V/LA noted. These are the V/LA rules:

In post 0, Plotinus wrote:While V/LA, I'll nudge you if it's been 48 hours since you've gone and then at the 72 hour mark, I'll go for you, playing your leftmost hand to the topmost sequence it can fit into or passing otherwise.

You can also submit tentative actions by PM if you want to

Plotinus · Post Post #910 (isolation #379) » Tue Aug 04, 2020 9:18 pm

historically, we allowed this sequence viewtopic.php?f=10&t=81015&p=11324759&h ... #p11324759 but then later we disallowed this bingo viewtopic.php?p=11627763#p11627763 and there was some discussion following that about how we felt about ranges.

I think, without doing the math, that it meets the "rarer than every card is even" criteria.

I cannot tell without doing the math whether it meets the meta rule or not? How often can we get a bingo by following an algorithm like "the numbers (mod n) fit into a range of < n/2 "?

Plotinus · Post Post #919 (isolation #380) » Wed Aug 05, 2020 8:15 am

In post 917, Sirius9121 wrote:(changed)
x is a composite number where
x^3's first digit is in the sequenct T(n)=2^n
x^4's last digit squared's last digit is the same
x^5's first digit is in the sequence T(n) = T(n-1) + 2^(n-2)
x^6's first digit is not a composite number

This feels really over-engineered, but more importantly 100% of hands can make a bingo with this meta rule -- if you go digit by digit then the law of small number means you'll find something that fits them really quickly.

You can spend your remaining time ((expired on 2020-08-06 16:54:13)) trying to think up a bingo if you want to, but I suggest you come with a backup move in case you can't think of one that meets all the requirements.

Plotinus · Wed Aug 05, 2020 10:17 pm

In post 922, Sirius9121 wrote:ok
third bingo approval:

In base 8, at least 50% of the numbers are a same repeating digit and the repeating digit is a square of any non-negative integer (0,1,4)

I think this meets all the criteria. Does anyone have any objections to this bingo in particular?

--

More broadly, assuming sirius tries to get a bingo every turn for the rest of the game, is this going to impact everybody's enjoyment of the game and what can we do to ensure that everybody has a good time? I think in future games, bingos should be worth fewer points, to start with.

It's also important to me that we be welcoming to any players who are prone to being intimidated by math. Math at any level, whether you're trying to learn how to multiply or trying to prove the twin prime conjecture, can feel a lot like this:

I want to encourage everyone to play with numbers and draw connections between them, however silly and spurious.

I want it to be safe to draw owls that look like

Plotinus · Post Post #935 (isolation #382) » Thu Aug 06, 2020 7:22 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 7 points

[9, 73, 90] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name

Exsecant: Sirius9121, Nancy Drew 39: 24 points

Chord: StrangerCoug, D3f3nd3r: 0 points

It is

D3f3nd3r

's turn. D3f3nd3r is V/LA so I'll prod at 48 hours and auto-move or pass for them (details in OP) at 72 hours, counting from the timestamp on 922, except I'll be asleep then so +2 hours.

Sirius' bingos are now worth 10 points (unless his team falls behind in points). I was also thinking 10 points would be better than 14 for bingos across the board but letting him play with a handicap seems like okay. I do think that if he makes a bingo with Nancy's cards then that counts as him making a bingo for handicap purposes. If Nancy makes a bingo on her own it'll be 14 points.

Other options (for this or future games):

Diminishing returns: A player's first bingo is worth 10, the second 9, the third 8, and all the other bingos are worth 7
Clarifying the over-engineering part of the rules: A sequence is a set of numbers that have a single unifying coherent concept in common. [more words here]
- Can't words this right now but:
- in Python: [x
  for
  x
  in
  function
  if
  [predicate]], where neither equation nor predicate contain any logical operators, each is a single coherent thing:
- yes: [x
  for
  x
  in
  fibonacci
  if
  x %
  5
  >=
  3
  ]
  # fibonacci numbers equivalent to 3 or 4 mod 5
- no: [x
  for
  x
  in
  fibonacci
  if
  x %
  5
  =
  2
  
  or
  
  sum
  ([
  int
  (y)
  for
  y
  in
  
  str
  (x)])
  in
  primes]
  # fibonacci numbers that are either equivalent to 3 or 4 mod 5
  
  OR
  
  who digit sums are prime
  :
- yes: f(g(x))
  # evaluate some function on this number and then plug that result into some other function
- no: f(g(h(f(x))))
  # evaluate some function, plug the result into another function, then plug the result into another function and then plug it back into the first function

Suggestions and feedback are welcome

Plotinus · Post Post #936 (isolation #383) » Thu Aug 06, 2020 7:28 am

In post 934, Nancy Drew 39 wrote:
In post 932, lilith2013 wrote:I agree that bingos now seem to be overemphasized and should be worth fewer points so the game isn’t entirely trying to find bingos at the cost of the spirit of the game. (not currently a player, just my two cents)
If you have any advice for me on how to play this, I’m absolutely desperate and will 100% listen.

Please ask questions! It sounds like you're struggling figuring out how to get started but there are no stupid questions.

Plotinus · Post Post #937 (isolation #384) » Thu Aug 06, 2020 7:42 am

I wanted to keep things moving so that's why it's D3f3nd3r's turn now but Sirius did submit a valid non bingo move in case it wasn't accepted. So we can easily roll things back if there's a valid objection before 24 hours has passed since it was proposed.

Plotinus · Post Post #942 (isolation #385) » Fri Aug 07, 2020 9:11 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 7 points

[9, 73, 90] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name

Exsecant: Sirius9121, Nancy Drew 39: 24 points

Chord: StrangerCoug, D3f3nd3r: 0 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters

It is

vincentw

's turn.

Working out percentiles every turn would take a lot more time than I have, but you're welcome to explore that as a scoring option in solitaire play or games you moderate.

Plotinus · Post Post #943 (isolation #386) » Fri Aug 07, 2020 7:33 pm

Prodded vincentw. Remember, your turn starts as soon as the last person goes, not when I update the game.

Also I'm rethinking the "leftmost card to the topmost sequence" rule for automoving: this generates a slight bias towards adding to whichever sequences Haversine has contributed to. I'm not sure if this really matters but what if we imagine "topmost" as being the topmost sequence starting with your team and continuing around in a loop (so no change, if it comes up for vincent, but if it happens to Sirius then the first sequence I'd look at is the first one in their currently empty pile and then I'd look at the sequence(s) in Chord's pile, etc.)

Plotinus · Post Post #945 (isolation #387) » Fri Aug 07, 2020 8:47 pm

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 7 points

[9, 73, 90, 7] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name

Exsecant: Sirius9121, Nancy Drew 39: 24 points

Chord: StrangerCoug, D3f3nd3r: 0 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters

It is

Sirius9121

's turn.

Plotinus · Post Post #947 (isolation #388) » Sat Aug 08, 2020 6:46 pm

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 7 points

[9, 73, 90, 7] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name

Exsecant: Sirius9121, Nancy Drew 39: 24 points

[1, 8, 9] {
n < 10
} single digit numbers

Chord: StrangerCoug, D3f3nd3r: 0 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters

It is

StrangerCoug

's turn.

Plotinus · Sun Aug 09, 2020 11:56 pm

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 7 points

[9, 73, 90, 7] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name

Exsecant: Sirius9121, Nancy Drew 39: 24 points

[1, 8, 9] {
n < 10
} single digit numbers

Chord: StrangerCoug, D3f3nd3r: 0 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[10, 20, 200] Numbers with only one nonzero digit

It is

ErrantParabola

's turn.

Plotinus · Post Post #953 (isolation #390) » Mon Aug 10, 2020 6:40 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 7 points

[9, 73, 90, 7] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[62, 97, 68] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024

Exsecant: Sirius9121, Nancy Drew 39: 24 points

[1, 8, 9] {
n < 10
} single digit numbers

Chord: StrangerCoug, D3f3nd3r: 0 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[10, 20, 200] Numbers with only one nonzero digit

It is

Nancy Drew 39

's turn.

It's all right, D3f3nd3r, you don't need to restore it

Plotinus · Post Post #955 (isolation #391) » Tue Aug 11, 2020 2:44 am

Sirius (or anyone else who wants to chime in), I'd appreciate it if you talked Nancy through finding a sequence with these numbers in the public thread. You don't have to give away all your secret strategies for bingo finding, but on a more meta-level, if you were trying to draw a connection between three of these cards, what kinds of things should she look for. How do you get started? What do you test for?

You can (try to) find a bingo, too, if you like, but I'm hoping Nancy will feel brave enough to play soon

Plotinus · Post Post #961 (isolation #392) » Tue Aug 11, 2020 8:23 am

Plotinus · Post Post #965 (isolation #393) » Tue Aug 11, 2020 5:47 pm

ok, feel better soon.

Last week, Nancy wanted to go V/LA for her turn and I said no because she'd already posted her cards by then and since Sirius wasn't V/LA, I thought that it would be unfair to give someone more than 48 hours when they're not V/LA, but I felt bad about it.

I think a fairer way would be for Sirius to have the non-V/LA deadline (Timestamp on 950 + 2 days, a bit over 10 hours from now) to tell me what his backup move is and Nancy to have the V/LA deadline (Timestamp on 950 + 3 days, a bit over 34 hours from now) to think of something?

Plotinus · Post Post #967 (isolation #394) » Wed Aug 12, 2020 3:36 am

Sirius has submitted something a few hours ago via Discord, so it's there if we don't hear from Nancy

Plotinus · Post Post #969 (isolation #395) » Wed Aug 12, 2020 6:01 pm

Feel better soon!

Plotinus · Post Post #970 (isolation #396) » Thu Aug 13, 2020 8:35 am

The move that Sirius submitted was

the first number of x is a term of 'a(n) is the largest term in the continued fraction for a(n-1) + n^2/a(n-1), where a(1)=1.'

This amounts to "starts with 1, 5, 6, or 8" which is definitely less than half of the numbers below 100. Any complaints about it?

Plotinus · Thu Aug 13, 2020 10:52 pm

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 7 points

[9, 73, 90, 7] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[62, 97, 68] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024

Exsecant: Sirius9121, Nancy Drew 39: 34 points

[1, 8, 9] {
n < 10
} single digit numbers

Chord: StrangerCoug, D3f3nd3r: 0 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[10, 20, 200] Numbers with only one nonzero digit

It is

D3f3nd3r

's turn.

Plotinus · Post Post #977 (isolation #398) » Fri Aug 14, 2020 3:03 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 7 points

[9, 73, 90, 7] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[62, 97, 68] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024

Exsecant: Sirius9121, Nancy Drew 39: 34 points

[1, 8, 9] {
n < 10
} single digit numbers

Chord: StrangerCoug, D3f3nd3r: 0 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[10, 20, 200] Numbers with only one nonzero digit
[69, 529, 14] “integer multiples of the jersey numbers from the starters on the Los Angeles Lakers in their game on August 13” (those jersey numbers are 23, 88, 5, 7, and 14)

It is

vincentw

's turn.

Sweet, I like it!

Plotinus · Post Post #979 (isolation #399) » Fri Aug 14, 2020 6:36 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 15 points

[9, 73, 90, 7] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[62, 97, 68] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024

Exsecant: Sirius9121, Nancy Drew 39: 34 points

[1, 8, 9] {
n < 10
} single digit numbers

Chord: StrangerCoug, D3f3nd3r: 0 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[10, 20, 200] Numbers with only one nonzero digit

It is

Sirius9121

's turn.