Sequencer | StrangerCoug's turn

Plotinus · Fri Aug 14, 2020 11:23 pm

Too many subparts, any sequence of numbers can be made into a bingo by adding arbitrary restrictions until it applies to less than half the deck.

Plotinus · Post Post #986 (isolation #401) » Mon Aug 17, 2020 8:10 pm

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: 44 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

StrangerCoug

's turn.

Code: Select all

In [149]: rule = [1, 3, 6, 8, 13, 20, 26]
In [150]: len([n for n in range(1,101) if sum([int(m) for m in str(n)]) in rule])                                                                 
Out[150]: 29

This applies to 29/100 cards so it looks like a valid bingo to me. And a pretty cool one at that. The numbers below 101 that it applies to are [1, 3, 6, 8, 10, 12, 15, 17, 21, 24, 26, 30, 33, 35, 42, 44, 49, 51, 53, 58, 60, 62, 67, 71, 76, 80, 85, 94, 100]

It turns out that I don't have the time or energy to do this kind of evaluation multiple times per turn, so from now on, when you submit a bingo you should prove that it meets the "applies to less than half the numbers under 100" requirement on your own.

Plotinus · Post Post #997 (isolation #402) » Wed Aug 19, 2020 4:07 am

If we phrase 993 as "numbers that are odd mod 5" then it looks fine to me. I think we've settled on a soft limit of 2 filters*: odd(mod5(n)) is okay. "one or three" is two things but "odd" is only one thing, and they are equivalent in mod 5.

We allowed "within 2 of a perfect square" in a previous game, and I'd allow it again. Within 8 feels a little less on the nose -- 56 doesn't feel like almost 4³ to me -- but it does apply to less than half the deck so I guess that'd be okay too.

I don't necessarily object to helping people who aren't your teammates if everyone else is okay with it.

* if someone shows me something that needs 3 filters yet still feels like a single coherent thing that doesn't feel overengineered then I might change my mind, but I think the chances of this are low

Plotinus · Wed Aug 19, 2020 5:55 pm

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: 44 points

[1, 8, 9] {
n < 10
} single digit numbers

Chord: StrangerCoug, D3f3nd3r: 14 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 · Fri Aug 21, 2020 2:38 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
[9, 27, 35, 36] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)

Exsecant: Sirius9121, Nancy Drew 39: 44 points

[1, 8, 9] {
n < 10
} single digit numbers

Chord: StrangerCoug, D3f3nd3r: 14 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.

That's clever, Errant, I like this sequence. Is Sirius's summary right? Are only numbers <= 88 allowed?

Plotinus · Sat Aug 22, 2020 4:06 am

prodded nancy

Plotinus · Sat Aug 22, 2020 6:06 pm

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
[9, 27, 35, 36] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)

Exsecant: Sirius9121, Nancy Drew 39: 44 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20 and 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4

Chord: StrangerCoug, D3f3nd3r: 14 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

D3f3nder

's turn.

Your sequence is fine, Nancy.

Plotinus · Sun Aug 23, 2020 6:51 am

prodded d3f3nd3r

Plotinus · Sun Aug 23, 2020 5:15 pm

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
[9, 27, 35, 36] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)

Exsecant: Sirius9121, Nancy Drew 39: 44 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20 and 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4

Chord: StrangerCoug, D3f3nd3r: 14 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[10, 20, 200] Numbers with only one nonzero digit
[18, 29, 37, 82] Numbers whose digit sum is between 9 and 11 inclusive

It is

vincentw

's turn.

Plotinus · Mon Aug 24, 2020 8:34 am

prodded vincent

Plotinus · Mon Aug 24, 2020 6:46 pm

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
[9, 27, 35, 36] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[841, 576, 36] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 44 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20 and 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4

Chord: StrangerCoug, D3f3nd3r: 14 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[10, 20, 200] Numbers with only one nonzero digit
[18, 29, 37, 82] Numbers whose digit sum is between 9 and 11 inclusive

It is

Sirius9121

's turn.

Plotinus · Tue Aug 25, 2020 6:01 pm

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
[9, 27, 35, 36] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[841, 576, 36] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 44 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1

Chord: StrangerCoug, D3f3nd3r: 14 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[10, 20, 200] Numbers with only one nonzero digit
[18, 29, 37, 82] Numbers whose digit sum is between 9 and 11 inclusive

It is

StrangerCoug

's turn.

edit: i accidentally edited this post instead of quoting it to post the next one, but now i've edited it back to what it was.

Plotinus · Wed Aug 26, 2020 3:20 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
[9, 27, 35, 36] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[841, 576, 36] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 44 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1

Chord: StrangerCoug, D3f3nd3r: 14 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[10, 20, 200] Numbers with only one nonzero digit
[18, 29, 37, 82] Numbers whose digit sum is between 9 and 11 inclusive
[11, 32, 34] Numbers whose digit sum is prime

It is

ErrantParabola

's turn.

Plotinus · Wed Aug 26, 2020 4:34 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 22 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
[9, 27, 35, 36] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[841, 576, 36] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 44 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1

Chord: StrangerCoug, D3f3nd3r: 14 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[10, 20, 200] Numbers with only one nonzero digit
[11, 32, 34] Numbers whose digit sum is prime

It is

Nancy Drew 39

's turn.

Errantparabola wrote:
can I complete numbers whose digit sum is between 9 and 11 inclusive with 243, 81, and 55
?

yep, and now you have 7 more points

Plotinus · Thu Aug 27, 2020 6:58 am

Haversine has half as many points as Exsecant so Exsecant shouldn't be as worried as they seem to be.

Nancy Drew has requested an extra day for personal reasons -- she can have an extra day if she submits her own sequence, but the deadline is 2 days after 1021 (a bit less than a day from now) if someone else does.

We can require that incompleteable sequences be resubmitted if we catch them in time, if we don't catch them in time then the cards are just wasted. When crafting the rules, I assumed this would only happen by accident because it doesn't seem like a very good strategy.

Plotinus · Fri Aug 28, 2020 6:11 pm

Since only 6 numbers match that sequence in the deck, it's not valid.

Plotinus · Sat Aug 29, 2020 2:45 am

The > 50% rule only applies to bingos because bingos are supposed to be rare. To start a sequence, they just have to have something in common with each other without repeats or excluding numbers from a sequence they naturally belong to.

Multiple of two or seven: 2, 14, 64, 35, 144, 56 (6 numbers, but you don't have to play all of them right now, to reduce the chances it'll be completed before it gets back to you)

You could also do one of:
multiple of 2: 2, 14, 64, 144, 56, (5 numbers, or fewer if you don't want to spend them all)
multiple of 7: 14, 35, 56, (3 numbers)

Or something else.

These are all legal moves

Plotinus · Sat Aug 29, 2020 6:46 pm

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 22 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
[9, 27, 35, 36] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[841, 576, 36] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 44 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7

Chord: StrangerCoug, D3f3nd3r: 22 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[11, 32, 34] Numbers whose digit sum is prime

Nancy Drew 39 wrote:
Is it to late to change it to the latter?:

multiple of 7: 14, 35, 56 (3 numbers)
FINAL ANSWER

I'm accepting this because it's a component of the sequence you thought of for yourself and submitted before the deadline. Good job, Nancy, you're getting the hang of this!

Chord gets 8 points for completing that sequence.

It is

vincentw

's turn.

Plotinus · Sun Aug 30, 2020 2:27 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 29 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
[841, 576, 36] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 44 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7

Chord: StrangerCoug, D3f3nd3r: 22 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[11, 32, 34] Numbers whose digit sum is prime

Haversine gains 7 points.

It is

Sirius9121

's turn.

Siriuis has submitted his turn by PM

[34, 400, 9, 15, 27, 87, 53] as x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'

There are exactly 50 such numbers in between 1 and 100 inclusive. Complaints? Quibbles?

Plotinus · Sun Aug 30, 2020 3:07 am

I think I am too. He included this screenshot, and clarified that it means that x² starts with 1, 2, 7, or 8

As for the rest though, I think it means:

There is only one seven digit number that is palindromic in base 1 and it's palindromic in base 2 as well 1111111₁ = 101₂ = 7₁₀
Numbers that are palindromic in base 2: 1000001₂ = 2102₃, 1001001₂ = 2201₃ , 1010101₂ = 10011₃, 1011101₂ = 10110₃, 1100011₂ = 10200₃, 1110111₂ = 11102₃, 1111111₂ = 11201₃, so there are no such numbers that are also palindromic in base 3.

If I look up this sequence in the OEIS, I find https://oeis.org/A308918, which is worded exactly as Sirius worded it. It looks like the sequence is increasing, but do we know that it will always increase, that we'll never find a large base that has only a small number that fits this pattern?

Also, if your meta algorithm is to look up four single-digit numbers in the OEIS then this algorithm generates a bingo 100% of the time, which is 63/64 too many.

Plotinus · Sun Aug 30, 2020 10:50 pm

That makes sense

Plotinus · Mon Aug 31, 2020 8:22 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 29 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
[841, 576, 36] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 54 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7

Chord: StrangerCoug, D3f3nd3r: 22 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[11, 32, 34] Numbers whose digit sum is prime

Exsecant gets 10 points. It is StrangerCoug's turn.

Plotinus · Mon Aug 31, 2020 6:31 pm

63 isn't squarefree, it has a 9 in it. do you want to just do [5, 17, 70] or something else?

Plotinus · Thu Sep 03, 2020 8:16 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 29 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
[841, 576, 36] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 54 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7

Chord: StrangerCoug, D3f3nd3r: 22 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[11, 32, 34] Numbers whose digit sum is prime
[5, 17, 70] squarefree

It is

ErrantParabola

's turn.

oh sorry, thanks for the reminder.

Plotinus · Sat Sep 05, 2020 7:45 am

prodding errant

Plotinus · Sat Sep 05, 2020 8:38 pm

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 29 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[841, 576, 36] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 54 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7

Chord: StrangerCoug, D3f3nd3r: 22 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[11, 32, 34] Numbers whose digit sum is prime
[5, 17, 70] squarefree

It is

Nancy Drew 39

's turn.

Plotinus · Sun Sep 06, 2020 7:04 am

Yeah, you can do it, Nancy!

Plotinus · Sun Sep 06, 2020 7:34 pm

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 29 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[841, 576, 36] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 54 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12

Chord: StrangerCoug, D3f3nd3r: 22 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[11, 32, 34] Numbers whose digit sum is prime
[5, 17, 70] squarefree

It is

D3f3nd3r

's turn.

It's great, good job Nancy!

Plotinus · Mon Sep 07, 2020 6:17 pm

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 43 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[841, 576, 36] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 54 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12

Chord: StrangerCoug, D3f3nd3r: 22 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[11, 32, 34] Numbers whose digit sum is prime
[5, 17, 70] squarefree
[13, 16, 343] numbers containing a double letter when written out

It is

Sirius9121

's turn.

Haversine gains 14 points.

Sirius9121 wrote:Isn't this 5-smooth numbers w/ 7?

No, it's the 7-smooth numbers.

pedit: it's Sirius' turn, you can play that when it's your turn, nancy if you want to.

Plotinus · Mon Sep 07, 2020 6:19 pm

I hadn't updated the topic title after her turn so it's understandable that she got confused.

Plotinus · Mon Sep 07, 2020 6:22 pm

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 43 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[841, 576, 36] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 62 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12

Chord: StrangerCoug, D3f3nd3r: 22 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[5, 17, 70] squarefree
[13, 16, 343] numbers containing a double letter when written out

It is

StrangerCoug

's turn. Exsecant gains 8 points

Plotinus · Mon Sep 07, 2020 7:01 pm

They need to finish 3 sequences (or 1 bingo and 1 sequence) to overtake you

Plotinus · Mon Sep 07, 2020 7:42 pm

Your handicap goes away if your team falls into second place.

Next game, bingos will be worth 8 points each and we won't do handicaps. I think this will make the game be less stressful for everyone.

Ideally, the scores should be neck and neck for most of the game -- players get discouraged if they fall so far behind that they have no chance of winning, and players also lose interest if they get so far ahead that they can win even if they just phone it in.

Plotinus · Mon Sep 07, 2020 7:53 pm

I went back through the game, and if we were playing with "bingos are worth 8 points each for everybody", the scores would be

haversine: 37
exsecant: 48
chord: 16

we could switch to that scoring mechanism retroactively if all 6 players agree but if anyone disagrees then we can keep on as we are. (also feel free to check my math that i didnt do any miscounting)

Plotinus · Wed Sep 09, 2020 2:03 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 43 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[841, 576, 36] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 62 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12

Chord: StrangerCoug, D3f3nd3r: 22 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[5, 17, 70] squarefree
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

It is

ErrantParabola

's turn.

Plotinus · Thu Sep 10, 2020 7:38 am

prodding errant

Plotinus · Fri Sep 11, 2020 2:33 am

Playing Errant's leftmost card to the topmost sequence it fits: 49 to square numbers

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 43 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[841, 576, 36, 49] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 62 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12

Chord: StrangerCoug, D3f3nd3r: 22 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[5, 17, 70] squarefree
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

It is

Nancy Drew 39

's turn.

Plotinus · Fri Sep 11, 2020 7:28 am

It's all right. Feel better soon <3

Plotinus · Fri Sep 11, 2020 6:22 pm

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 43 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[841, 576, 36, 49] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 62 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[2, 64, 50, 6, 84] {
2n
} multiples of 2

Chord: StrangerCoug, D3f3nd3r: 22 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[5, 17, 70] squarefree
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

It is

D3f3nd3r's

's turn.

Plotinus · Sat Sep 12, 2020 5:30 pm

prodding d3f3nd3r

Plotinus · Sun Sep 13, 2020 2:29 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 50 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[841, 576, 36, 49] {
n²
}square numbers

Exsecant: Sirius9121, Nancy Drew 39: 72 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12

Chord: StrangerCoug, D3f3nd3r: 29 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

Chord gains 7 points. Haversine gains 7 points. Exsecant gains 10 points. It is

StrangerCoug's

's turn.

Plotinus · Sun Sep 13, 2020 2:41 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 50 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, 23, 84] 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: 72 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12

Chord: StrangerCoug, D3f3nd3r: 37 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

Chord gains 8 points.

ErrantParabola's

's turn.

Plotinus · Mon Sep 14, 2020 2:38 am

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 50 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83

Exsecant: Sirius9121, Nancy Drew 39: 72 points

[1, 8, 9] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12

Chord: StrangerCoug, D3f3nd3r: 37 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

Nancy Drew 39's

's turn.

Plotinus · Mon Sep 14, 2020 3:02 am

Fixed

Plotinus · Tue Sep 15, 2020 8:22 pm

Suppose my hand is 101, 102, 103, 104, 105, 106, 107 and I look at the sequence you have put, and I want to know if any of my cards fit your sequence. What should I ask myself about my cards?

Like if I want to know if my cards fit Errant's 2024 sequence, I can look at a calendar and check what day of the week the 100th day of the year falls on. The question is "Is the 101st day of the year a Saturday or Sunday?" Or if I want to know if they fit the divisible by 7 sequence, then the question I ask is "Is 105 divisible by 7?" For each sequence, there is one thing I can ask myself about each of my cards to see if they fit it or not.

For 2, 29, 32, 1, it's true that 2 + 29 = 32 - 1 but what is the rule that I could look at each of my cards and say "oh this is true of x so it fits" or "this is not true of y so it does not fit?"

It looks like you're thinking about the sums of digits, that's a good step. You can sum the digits of each of the numbers in your hand and see if there's anything special about the resulting digit sums. If I did that with my fictious hand I would get 2, 3, 4, 5, 6, 7, 8 and then I see I could make a "digit sums are even" sequence or "a digit sums are odd sequence" or a "digit sums are prime sequence" or a "digit sums are composite sequence"

Plotinus · Tue Sep 15, 2020 8:24 pm

Actually, I couldn't do "digit sum is prime" because that one was already done by someone this game. But I could do "digit sum is a power of two" with my fictious hand.

Plotinus · Wed Sep 16, 2020 8:08 am

Nancy Drew 39 has run out of time, so she plays her leftmost card to the topmost sequence it fits into, starting with her team's sequences. This card is a 2 and it fits into the single digit numbers sequence.

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 50 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83

Exsecant: Sirius9121, Nancy Drew 39: 72 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12

Chord: StrangerCoug, D3f3nd3r: 37 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

D3f3nd3r's

's turn.

Plotinus · Wed Sep 16, 2020 6:12 pm

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 50 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83

Exsecant: Sirius9121, Nancy Drew 39: 72 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12

Chord: StrangerCoug, D3f3nd3r: 51 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

Chord gains 14 points. It's

vincentw's

's turn.

Sirius, it's rude to insult people. Please stop.

Plotinus · Thu Sep 17, 2020 2:50 am

thank you

Plotinus · Thu Sep 17, 2020 7:18 am

Sirius has submitted his turn by PM

the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
equalivent to 'starts with 0,1,3,4'

I think this is okay -- the "starts with 0" part can be ignored, since no integers start with 0 and all of his numbers start with one of {1, 3, 4}. Wikipedia takes me to a disambiguation page with other possible meanings of binomial but I'm pretty sure binomial refers to the the n choose k thing, so the first number in the sequence is 1 choose 0 = 1, the second is 2 choose 0 = 1, the third is 3 choose 1 = 3, the fourth is 4 choose 1 = 4, the fifth is 5 choose 2 = 10 and then they get larger from there. I'll let people weigh in until I wake up tomorrow.

Spoiler: completed sequences

Haversine: vincentw, ErrantParabola: 50 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121, Nancy Drew 39: 72 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12

Chord: StrangerCoug, D3f3nd3r: 51 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

It's

Sirus's

's turn.

Plotinus · Thu Sep 17, 2020 7:47 pm

I do think you can tie any four numbers to each other. What percent of hands will have at most four different digits in any of the places?

Plotinus · Fri Sep 18, 2020 6:08 pm

Which is more than the 1/64th of hands.

My attempt at calculating it: 210 is 10 choose 4, the number of ways of choosing which 4 digits, and the rest is choosing 7 cards out of 100 that have one of those 4 numbers in that place. And then doubling it because it's the same calculation whether we get only 4 digits in the tens place or only 4 digits in the ones place -- the bingo seeker will choose tens place or ones place based on the hand they've drawn

In [223]: 210*40*39*38*37*36*35*34/100/99/98/97/96/95/94*2
Out[223]: 0.48916229635685654

or 48.9% of hands will have either at most of 4 of the same digit in at least one of the tens place or the ones place.

The true number is going to be a little higher because there's also "starts with" which means there'll be 11 numbers that start with each of the four digits, not ten.

It's true that there's an extra step here of finding something that fits those [up to four] digits that doesn't fit the other numbers below ten, but the required 1/64 is 0.015625, about 1.5%. If 95% of possible combinations of 4 numbers are hard to find a sequence for, then that's still okay, but I think a lot of them are quite trivial. For example about a quarter of them should fit a "x mod 3" pattern (3 choose 1) × 3⁴/1000 -- chosen with replacement because it's possible to draw cards such that all of them start with the same number)

On the other hand, Sirius hasn't been doing "x mod 3" for the second half, he's doing something with binomials this time, it's clear that he's put work and thought into it.

Next game with the different scoring rules it won't matter so much because getting a bingo won't always be the move that give the most points, so we won't have to think so hard about whether each individual bingo is rare enough to be worth it. This game, I'm thinking that since we have accepted digit stuff before, Sirius could have reasonably expected this sequence to be fine, so if we want to disallow digit stuff for bingos it might be best to do it starting after this turn, especially since his turn is almost up.

Plotinus · Sat Sep 19, 2020 5:48 pm

I guess we should vote on it.

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'

Haversine: vincentw, ErrantParabola: 50 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121, Nancy Drew 39: 82 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12

Chord: StrangerCoug, D3f3nd3r: 51 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

Exsecant gains 10 points. It's

StrangerCoug

's turn.

Plotinus · Sun Sep 20, 2020 8:11 pm

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'

Haversine: vincentw, ErrantParabola: 50 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89] numbers equivalent to ±1 mod 10
[8, 18, 44, 1, 324] digit sum is a perfect power (k^n with n > 1, k and n are integers)

Exsecant: Sirius9121, Nancy Drew 39: 82 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12

Chord: StrangerCoug, D3f3nd3r: 51 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

1² = 1 so that's fine, Errant. It's

Nancy Drew 39

's turn. There are 48 cards left in the deck.

I also feel like the bingo thing has broken the game in a bad way. I've been trying to find ways to unbreak it but it's been pretty unfun. I want to keep it as fun for all of you guys as we can. I think 8 point bingos for next game will fix a lot of the problem.

I thought "the consequence of posting your hand is that the other teams can see your cards" would be enough of a deterrent most of the time -- and when we nerf bingos it will be?

Maybe the rule can be "first time players may (but don't have to) post their very first hand if they need help for their turn but after that no more posting hands"?

votes to not allow "nth digit is / starts with / ends with" in bingos: strangercoug, presumably d3f3nd3r and vincent?

I apparently didn't send vincentw a new hand earlier so i'm doing that now

edit: actually added Errant's moved to the board this time.

Plotinus · Mon Sep 21, 2020 5:58 pm

prodding Nancy Drew 39

Plotinus · Mon Sep 21, 2020 6:24 pm

In post 1161, Errantparabola wrote:and for expediency's sake, if you accept that I will add to that as my turn (the numbers being 1 and 324)

This was the last move made, and it was made 38 hours ago, on Sun, 2020.09.20 17:02:05 (Europe time), so I should have prodded you yesterday afternoon (24 hours after Errant made her move), but because I was late to prod you, you can have until (expired on 2020-09-23 07:00:00).

Plotinus · Mon Sep 21, 2020 6:28 pm

Do players dislike the "your timer starts as soon as the last person goes" rule? Would players prefer it to instead start when I update the game?

Plotinus · Tue Sep 22, 2020 5:11 am

The way I see it is that you usually have about a few days to think of something from the time to get your cards to the time it's your turn and then you get two days after that, so it's basically a week the way things are right now.

Plotinus · Tue Sep 22, 2020 5:45 pm

I agree, that's a reasonable accommodation for players with disabilities. Thanks for speaking up, Nancy. Your turn can start when I update the thread and I'll prod you even if it looks like you're actively posting.

About allowing a combination of numbers to add up to or subtract to 13 or 31 -- until now the rules for sequences have had to apply to each number individually, but this one is well defined enough that I think it could work if we limit it to addition and subtraction and no more than two separate cards per combination? It does pass the test of "can i figure out which of the cards in my hand is allowed?" What do you guys think.

Plotinus · Wed Sep 23, 2020 6:52 pm

I PMed Nancy to ask her to clarify, since it's her rule.

In favour of yes: sequences are many-to-many relationship -- if the rule is "divisible by 7" then all the numbers have divisibility-by-sevenness in common with each other, so if we allow combinations between two numbers then it shouldn't matter whether the numbers are played at the same time or at diferent times.

In favour of no: without looking at anybody's hands, whoever goes next is probably going to be able to complete this sequence, and it's in the best interests of the team that played the sequence for the rule to be interpreted as narrowly as possible, requiring players to play the two cards that are being combined at the same time.

Plotinus · Wed Sep 23, 2020 7:02 pm

If we don't hear from Nancy by (expired on 2020-09-24 14:53:55), then the rule will be interpreted as "The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played together can be added to or subtracted from each other to achieve 13 or 31." I think this is closest to the spirit of what Nancy was trying to say without making the sequence be "whoever goes next gets 11 points".

I think allowing combinations like this doesn't break the game too much because it's never going to come up in a bingo (applies to too much of the deck), so it doesn't put the team that creates the sequence at an unfair point advantage.

Plotinus · Thu Sep 24, 2020 4:08 am

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'

Haversine: vincentw, ErrantParabola: 50 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, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89] numbers equivalent to ±1 mod 10
[8, 18, 44, 1, 324] digit sum is a perfect power (k^n with n > 1, k and n are integers)

Exsecant: Sirius9121, Nancy Drew 39: 82 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.

Chord: StrangerCoug, D3f3nd3r: 51 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

It's

D3f3nd3r

's turn. There are 44 cards left in the deck.

D3f3nd3r wrote:
In post 1187, D3f3nd3r wrote:Would I be allowed to do things with other numbers in the sequence too (ie. with 58 already played, could I hypothetically play 45 because 58 - 45 = 13)?

No, I think that'll make it too easy to complete, since it's already almost four fours. So it'll have to be two numbers you're playing at the same time. If you have a 45 and a 32 you could play 45-32 = 13, or if you have a 45 and a 22 then you could do 4 + 5 + 2 + 2 = 13, or 45 and 77 (45 - 7 - 7 = 31) but you have to play them both at once.

Plotinus · Thu Sep 24, 2020 6:54 am

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name

Haversine: vincentw, ErrantParabola: 50 points

[62, 97, 68, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89] numbers equivalent to ±1 mod 10
[8, 18, 44, 1, 324] digit sum is a perfect power (k^n with n > 1, k and n are integers)

Exsecant: Sirius9121, Nancy Drew 39: 82 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.

Chord: StrangerCoug, D3f3nd3r: 58 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

Chord gains 7 points. It's

vincentw

's turn. There are 41 cards left in the deck.

Plotinus · Thu Sep 24, 2020 9:08 am

Because I forgot to update it update it when Nancy went. I'll edit the previous one

Plotinus · Fri Sep 25, 2020 6:47 am

prodding vincent

Plotinus · Fri Sep 25, 2020 7:34 am

Sirius has submitted his turn by PM

the digit sum of the digit sum of y = k, k and k+1 are both squarefree
equalivent = digit sum of digit sum of y =1,2,5,6

Pretty sure that in the confines of our deck this is equivalent to n = (1, 2, 5, or 6) (mod 9), so it seems to meet all the rules. I was confused about whether 1, being a perfect square, is squarefree, but wikipedia says it is, because all numbers are divisible by 1, so it can't count.

Any complaints? I'll update the game tomorrow morning if not.

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)

Haversine: vincentw, ErrantParabola: 58 points

[62, 97, 68, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121, Nancy Drew 39: 82 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.

Chord: StrangerCoug, D3f3nd3r: 58 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

Haversine gains 8 points. It's

Sirius9121

's turn. There are 38 cards left in the deck.

Plotinus · Fri Sep 25, 2020 7:30 pm

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree

Haversine: vincentw, ErrantParabola: 58 points

[62, 97, 68, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121, Nancy Drew 39: 92 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.

Chord: StrangerCoug, D3f3nd3r: 58 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

Exsecant gains 10 points. It's

StrangerCoug

's turn. There are 31 cards left in the deck.

Plotinus · Sat Sep 26, 2020 7:50 am

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree

Haversine: vincentw, ErrantParabola: 58 points

[62, 97, 68, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121, Nancy Drew 39: 92 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.

Chord: StrangerCoug, D3f3nd3r: 58 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)
[10, 30, 35, 220] multiples of 5

It's

ErrantParabola

's turn. There are 27 cards left in the deck.

Plotinus · Sun Sep 27, 2020 5:28 am

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5

Haversine: vincentw, ErrantParabola: 65 points

[62, 97, 68, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121, Nancy Drew 39: 92 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.

Chord: StrangerCoug, D3f3nd3r: 58 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

Haversine gains 7 points. It's

Nancy Drew 39

's turn. There are 24 cards left in the deck.

Plotinus · Sun Sep 27, 2020 6:12 pm

D3f3nd3r has submitted his turn by PM

D3f3nd3r wrote:“The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16 (ie. the number is equivalent to 0, 1, 2, 4, or 6 in mod 11)”?

The only two characters that that applies to are X and O, by the way.

It looks okay to me because it clearly applies to less than half the deck and for the meta rule part, most of the tiny variations you could make to this wouldn't generate bingos. For example, if you changed it to exactly 15 then there are too many words with an E, N, W (anything but 4 or 6) so that wouldn't be an eligible bingo, so this algorithm produces rarer bingos than the explicitly allowed "x mod y" bingo seeking algorithm.

Any objections? I'll update the game this evening, if not.

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5

Haversine: vincentw, ErrantParabola: 65 points

[62, 97, 68, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121, Nancy Drew 39: 92 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.
[1, 26, 29 729] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9

Chord: StrangerCoug, D3f3nd3r: 58 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

It's

D3f3nd3r

's turn. There are 20 cards left in the deck.

Plotinus · Mon Sep 28, 2020 7:34 am

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5
[56, 79, 46, 13, 45, 88, 72] The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16

Haversine: vincentw, ErrantParabola: 65 points

[62, 97, 68, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121, Nancy Drew 39: 92 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.
[1, 26, 29 729] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9

Chord: StrangerCoug, D3f3nd3r: 72 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

Chord gains 14 points. It's

vincentw

's turn. There are 13 cards left in the deck.

Plotinus · Tue Sep 29, 2020 8:19 am

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5
[56, 79, 46, 13, 45, 88, 72] The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16
[1, 26, 29 729, 900, 78, 30] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9

Haversine: vincentw, ErrantParabola: 72 points

[62, 97, 68, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121, Nancy Drew 39: 92 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.

Chord: StrangerCoug, D3f3nd3r: 72 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

Haversine gains 7 points. It's

Sirius9121

's turn. There are 10 cards left in the deck.

Combining three cards together would be too permissive I think.

Plotinus · Tue Sep 29, 2020 11:18 pm

My understanding of the doubleletter sequence is that the letter is repeated immediately: thirt

ee

n, sixt

een

, thr

ee

hundred forty thr

ee

, but D3f3nd3r can clarify what they meant

Plotinus · Wed Sep 30, 2020 7:03 am

Sirius, I think that when you vowed to make the game unfun by bingoing every turn, you upset the other players, who were hoping that whether or not they won, they would have a good time. It is possible to have fun even when you are losing, but it requires the players to collaborate together to maintain the spirit of fun. It is especially important to be considerate of the spirit of fun when you're in the lead.

Part of that is being gracious when winning. if you have more points than everyone else, it's antifun to act like it's the end of the world whenever someone else gains points.

Part of that is being encouraging of people who are exploring new ideas, but not rushing in to do it for them. When you were learning math, if someone had said "oh don't bother learning to add, I'll just add them for you, I can do it quicker and I won't make any mistakes." and then a bit later "Don't bother trying to figuring out the proof for yourself I'll just tell you how Gauss did it," then you would never have learnt to do math or to love math. You learn math by doing math, by pausing and pondering and wrestling with the problem. It's not a spectator sport. Telling someone to post their cards is like saying a combination of "I don't think you'll ever be able to contribute anything of value on your own," and "I care more about points than I care about someone learning that they can do math after all."

Upsetting the other players has some natural consequences, like players wanting to team up against you because they feel that they are playing a broken game in which the only way to win is to adopt a high stress playstyle that isn't fun or what they signed up for. It's like if you signed up for a game of chess but discovered you had to spend 30 hours grinding carrots to level up the knight's horse, or that you had to check on your rook building every four hours or the bricks would fail. I am disinclined to intervene in attempts to get back to playing with numbers and discovering cool stuff together. I care about all of the players. I want all of the players to be able to win without tedious grinding because this isn't a grinding game.

Smart people often feel like intelligence is their entire personality, the only aspect of them that matters, because you've been praised for your intellect -- and nothing else -- for your entire life. So whenever you don't know something you worry that people are gonna find out that you're not a genius after all -- so you resolve to be better and brighter and cleverer and you think that if only you are the bestest brightest cleverest then you will be liked. But it doesn't work, it just makes people want to take you down a peg, because they feel like you're being clever at their expense. There is a better way to smart, an intelligence that lifts up all those around you, making everyone feel like they've become a better, smarter person because you're around.

Spoiler: like this

If you are gracious and encouraging, and if people feel like you would congratulate them if they won, then other people will generally be happy for you when you win.

Plotinus · Wed Sep 30, 2020 7:07 am

In post 1227, D3f3nd3r wrote:
In post 1225, Plotinus wrote:My understanding of the doubleletter sequence is that the letter is repeated immediately: thirt
ee
n, sixt
een
, thr
ee
hundred forty thr
ee
, but D3f3nd3r can clarify what they meant
Yeah that’s what I meant. I thought I clarified it, but I ISO’d myself and I guess I didn’t...sorry.

Also, you need to think of a different move because the one you submitted doesn't fit this sequence. I think this sequence would've been finished a long time ago if your interpretation were the right one because almost all numbers in english have repeated letters.

Plotinus · Thu Oct 01, 2020 9:02 am

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5
[56, 79, 46, 13, 45, 88, 72] The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16
[1, 26, 29 729, 900, 78, 30] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9

Haversine: vincentw, ErrantParabola: 72 points

[62, 97, 68, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121, Nancy Drew 39: 92 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.
[4,12,52,24] even numbers that have a 2 or a 4 in the ones place

Chord: StrangerCoug, D3f3nd3r: 72 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

Sirius9121 wrote:4,12,52,24 as numbers that start in a even number that is smaller than 5.

im sorry if i runied some people's fun.

Thank you for your apology. Do you mean even numbers that start in a number smaller than 5? If not, let me know and I'll change it.

It's

StrangerCoug

's turn. There are 6 cards left in the deck. When there is no cards left in the deck, we try to complete the sequences that are in play -- you don't have to start a new sequence if you don't want to but you do have to play at least one card to an existing sequence if you can. The game will end when nobody can make any moves (when all 6 people pass in a row)

Plotinus · Thu Oct 01, 2020 10:13 pm

I'm currently assuming that by starts with 2 or 4, you mean "equivalent to 2 or 4 mod 10", because you included the numbers 52 and 12. The confusion is because we aren't sure whether "starting" and "first" counts from the left or from the right - In English, it's customary to start on the left, but I assume other languages have other customs.

Plotinus · Thu Oct 01, 2020 10:16 pm

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5
[56, 79, 46, 13, 45, 88, 72] The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16
[1, 26, 29 729, 900, 78, 30] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9

Haversine: vincentw, ErrantParabola: 72 points

[62, 97, 68, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89, 289] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121, Nancy Drew 39: 92 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.
[4,12,52,24] even numbers that have a 2 or a 4 in the ones place

Chord: StrangerCoug, D3f3nd3r: 72 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)
[65, 89, 729] digit sum is greater than 10

It's

Nancy Drew 39

's turn. There are 2 cards left in the deck. When there is no cards left in the deck, we try to complete the sequences that are in play -- you don't have to start a new sequence if you don't want to but you do have to play at least one card to an existing sequence if you can. The game will end when nobody can make any moves (when all 6 people pass in a row)

Plotinus · Thu Oct 01, 2020 11:09 pm

Thanks for clarifying. It's interesting how different languages think about this

Plotinus · Fri Oct 02, 2020 1:38 am

In post 1252, Sirius9121 wrote:
In post 1251, D3f3nd3r wrote:So no ending in zero? That’s still an even digit less than five!
Let’s change the rule to ‘ends in 2 or 4’

Done.

I mix up left and right a lot too.

Plotinus · Fri Oct 02, 2020 2:05 am

My lifehack for using maps without knowing left from right is to hold a pen up parallel to the street i'm on, on the map, and turn it in the direction i'm supposed to go, and look if it's going clockwise or counterclockwise. That way, even if i'm facing some weird direction like SW and need to turn to go NNW i can figure out that it's a right turn (because clockwise is always right) even though i'm facing upside down compared to the map.

On sunny days I rely on the sun a lot for navigation because i can use it as a reference point but then I got a bit lost in my home town because it was cloudy one day so I got a compass. It's a lot easier for me to just hang onto one fact like "i want to be northwest of where i am right now so i need for my shadow to stay looking like this" than "I need to make a bunch of turns in a variety of directions"

Plotinus · Fri Oct 02, 2020 4:36 am

Nancy Drew 39 wrote:
There are 6 cards left in the deck. When there is no cards left in the deck, we try to complete the sequences that are in play -- you don't have to start a new sequence if you don't want to but you do have to play at least one card to an existing sequence if you can. The game will end when nobody can make any moves (when all 6 people pass in a row)
I’m not exactly sure what to do now. Can you give me some advice? Thanks.

Without looking at your hand (beyond remembering that you have a duplicate): We're nearing the end of the game, so it's a good idea to see if you can finish any of the sequences someone else started, especially if you can get points. The ones in the spoiler are already completed, so you can ignore them. The ones listed under the team names in colours are still active. When there are at least 7 numbers in the sequence, it's marked as completed and you get points for it. You can contribue to any active sequence, it doesn't matter whose name it is listed under.

So if my hand were 5, 7, 11, 13, 17, 19, 29

(then I could make a "twin primes" bingo)

then I could look at a 2024 calendar and see that 1/7 was on the weekend so I could play it to Errant's sequence, but that wouldn't get me any points. So, I would keep looking in case I saw something better. Further down, there's "numbers equivalent to ±1 mod 10" which needs 3 more numbers to complete, so I could play 11, 19, and 29 to it and get 7 points. Maybe I would do that or maybe I'd look for something better. There's your "13 or 31" sequence, I could play the 13 to do that and also 1 + 7 = 8 and 8 + 5 = 13 so I could play 17 and 5 to your 13 or 31 sequence too. That's enough to complete it for 7 points but I'd spend some trying to see if I can combine my 7, 11, 19, 29 to fit that too, to get more points, because if I could squeeze another two numbers in then I would get 9 points.

You can also submit a new sequence if you want to, but it's always a good move to check if you can complete an active sequence first.

I've quoted the game board so it'll be on this page

In post 1247, Plotinus wrote:
Spoiler: completed sequences
[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad

[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)

[14, 15, 5, 57, 81, 19, 60] 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.'

[69, 529, 14, 15, 28, 45, 92, 1000] “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)

[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'

[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5

[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive

[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit

[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)

[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'

[5, 25, 27, 36, 64, 96, 98 7 smooth numbers

[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime

[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2

[5, 17, 70, 7, 31, 39, 71.] squarefree

[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2

[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers

[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5

[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'

[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name

[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)

[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree

[10, 30, 35, 220, 250, 70, 20] multiples of 5

[56, 79, 46, 13, 45, 88, 72] The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16

[1, 26, 29 729, 900, 78, 30] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9

Haversine: vincentw, ErrantParabola: 72 points

[62, 97, 68, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024

[2, 86, 165] within 3 of a multiple of 83

[41, 51, 89, 289] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121, Nancy Drew 39: 92 points

[1, 8, 9, 2] {
n < 10
} single digit numbers

[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4

[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1

[14, 35, 56] {
7n
} divisible by 7

[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12

[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.

[4,12,52,24] even numbers that have a 2 or a 4 in the ones place

Chord: StrangerCoug, D3f3nd3r: 72 points

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

[13, 16, 343] numbers containing a double letter when written out

[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)

[65, 89, 729] digit sum is greater than 10
It's
Nancy Drew 39
's turn. There are 2 cards left in the deck. When there is no cards left in the deck, we try to complete the sequences that are in play -- you don't have to start a new sequence if you don't want to but you do have to play at least one card to an existing sequence if you can. The game will end when nobody can make any moves (when all 6 people pass in a row)

Plotinus · Fri Oct 02, 2020 8:33 pm

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5
[56, 79, 46, 13, 45, 88, 72] The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16
[1, 26, 29 729, 900, 78, 30] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9

Haversine: vincentw, ErrantParabola: 72 points

[62, 97, 68, 23, 84] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89, 289] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121, Nancy Drew 39: 92 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.
[4,12,52,24] even numbers that have a 2 or a 4 in the ones place
[29, 21, 27] two digit numbers starting with a two

Chord: StrangerCoug, D3f3nd3r: 72 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)
[65, 89, 729] digit sum is greater than 10

It's

D3f3nd3r

's turn. There are no cards left in the deck. We will continue playing until six people pass in a row. You may only pass if you have no cards that can be played to any active sequence.

Plotinus · Sat Oct 03, 2020 2:07 am

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5
[56, 79, 46, 13, 45, 88, 72] The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16
[1, 26, 29 729, 900, 78, 30] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9
[62, 97, 68, 23, 84, 91, 55] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024

Haversine: vincentw (7), ErrantParabola (7): 72 points

[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89, 289] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121 (7), Nancy Drew 39 (6): 92 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.
[4,12,52,24] even numbers that have a 2 or a 4 in the ones place
[29, 21, 27] two digit numbers starting with a two

Chord: StrangerCoug (7), D3f3nd3r (5): 79 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)
[65, 89, 729] digit sum is greater than 10

Chord gains 7 points. It's

vincentw

's turn. There are no cards left in the deck. We will continue playing until six people pass in a row. You may only pass if you have no cards that can be played to any active sequence. The number in parentheses after each name represents the number of cards in their hand.

Plotinus · Sat Oct 03, 2020 9:07 am

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5
[56, 79, 46, 13, 45, 88, 72] The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16
[1, 26, 29 729, 900, 78, 30] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9
[62, 97, 68, 23, 84, 91, 55] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[19, 23, 21, 99, 361, 7, 9] odd numbers

Haversine: vincentw (0), ErrantParabola (7): 86 points

[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89, 289] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121 (7), Nancy Drew 39 (6): 92 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.
[4,12,52,24] even numbers that have a 2 or a 4 in the ones place
[29, 21, 27] two digit numbers starting with a two

Chord: StrangerCoug (7), D3f3nd3r (5): 79 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)
[65, 89, 729] digit sum is greater than 10

Haversine gains 14 points. It's

Sirius9121

's turn. There are no cards left in the deck. We will continue playing until six people pass in a row. You may only pass if you have no cards that can be played to any active sequence. The number in parentheses after each name represents the number of cards in their hand.

Plotinus · Sun Oct 04, 2020 7:46 pm

I was waiting for someone else to comment but since your turn is half over now:

Whatever you feel is best. if you have a bingo that isn't overengineered, go ahead i guess. if you'd rather scoop up some of the active sequences, you can do that too.

Plotinus · Sun Oct 04, 2020 8:51 pm

That one's pretty cool actually, and it doesn't look overengineered to me.

So the single digit ones are like 7 -7 = 0, 0² = 0.

Plotinus · Sun Oct 04, 2020 8:52 pm

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5
[56, 79, 46, 13, 45, 88, 72] The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16
[1, 26, 29 729, 900, 78, 30] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9
[62, 97, 68, 23, 84, 91, 55] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[19, 23, 21, 99, 361, 7, 9] odd numbers
[4, 7, 512, 2, 55, 3, 100] the biggest digit minus the smallest digit is a perfect square

Haversine: vincentw (0), ErrantParabola (7): 86 points

[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89, 289] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121 (0), Nancy Drew 39 (6): 102 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.
[4,12,52,24] even numbers that have a 2 or a 4 in the ones place
[29, 21, 27] two digit numbers starting with a two

Chord: StrangerCoug (7), D3f3nd3r (5): 79 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)
[65, 89, 729] digit sum is greater than 10

Exsecant gains 10 points. It's

StrangerCoug

's turn. There are no cards left in the deck. We will continue playing until six people pass in a row. You may only pass if you have no cards that can be played to any active sequence. The number in parentheses after each name represents the number of cards in their hand.

Plotinus · Mon Oct 05, 2020 6:09 am

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5
[56, 79, 46, 13, 45, 88, 72] The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16
[1, 26, 29 729, 900, 78, 30] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9
[62, 97, 68, 23, 84, 91, 55] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[19, 23, 21, 99, 361, 7, 9] odd numbers
[4, 7, 512, 2, 55, 3, 100] the biggest digit minus the smallest digit is a perfect square
[4, 5, 40, 54, 125, 500, 961] Numbers whose first digit is the sum of at most two distinct perfect squares

Haversine: vincentw (0), ErrantParabola (7): 86 points

[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89, 289] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121 (0), Nancy Drew 39 (6): 102 points

[1, 8, 9, 2] {
n < 10
} single digit numbers
[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.
[4,12,52,24] even numbers that have a 2 or a 4 in the ones place
[29, 21, 27] two digit numbers starting with a two

Chord: StrangerCoug (0), D3f3nd3r (5): 93 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)
[65, 89, 729] digit sum is greater than 10

Chord gains 14 points. It's

ErrantParabola

's turn. There are no cards left in the deck. We will continue playing until six people pass in a row. You may only pass if you have no cards that can be played to any active sequence. The number in parentheses after each name represents the number of cards in their hand.

There were a few variations posted and I think they were each okay, so I went with the last one.

Plotinus · Tue Oct 06, 2020 5:49 pm

Prodding Errant

Plotinus · Thu Oct 08, 2020 6:02 am

Nancy Drew 39 has submitted her turn by PM

Nancy Drew 39 wrote:When it’s my turn again, I will play all but the [redacted] card for multiples of 10, either with the addition of two sets of numbers: 6+4=10 and 49+21=70 and the digits of 64 combined, also resulting in a sum of 10.

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5
[56, 79, 46, 13, 45, 88, 72] The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16
[1, 26, 29 729, 900, 78, 30] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9
[62, 97, 68, 23, 84, 91, 55] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[19, 23, 21, 99, 361, 7, 9] odd numbers
[4, 7, 512, 2, 55, 3, 100] the biggest digit minus the smallest digit is a perfect square
[4, 5, 40, 54, 125, 500, 961] Numbers whose first digit is the sum of at most two distinct perfect squares
[1, 8, 9, 2, 3, 4, 7] {
n < 10
} single digit numbers

Haversine: vincentw (0), ErrantParabola (4): 93 points

[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89, 289] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121 (0), Nancy Drew 39 (1): 102 points

[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.
[4,12,52,24] even numbers that have a 2 or a 4 in the ones place
[29, 21, 27] two digit numbers starting with a two
[6, 4, 49, 21, 64] multiples of ten, either with addition or two numbers together

Chord: StrangerCoug (0), D3f3nd3r (5): 93 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)
[65, 89, 729] digit sum is greater than 10

Haversine gains 7 points. It's

D3f3nd3r

's turn. There are no cards left in the deck. We will continue playing until six people pass in a row. You may only pass if you have no cards that can be played to any active sequence. The number in parentheses after each name represents the number of cards in their hand.

Plotinus · Thu Oct 08, 2020 6:35 am

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5
[56, 79, 46, 13, 45, 88, 72] The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16
[1, 26, 29 729, 900, 78, 30] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9
[62, 97, 68, 23, 84, 91, 55] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[19, 23, 21, 99, 361, 7, 9] odd numbers
[4, 7, 512, 2, 55, 3, 100] the biggest digit minus the smallest digit is a perfect square
[4, 5, 40, 54, 125, 500, 961] Numbers whose first digit is the sum of at most two distinct perfect squares
[1, 8, 9, 2, 3, 4, 7] {
n < 10
} single digit numbers
[6, 4, 49, 21, 64, 80, 10] multiples of ten, either with addition or two numbers together

Haversine: vincentw (0), ErrantParabola (4): 93 points

[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89, 289] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121 (0), Nancy Drew 39 (1): 102 points

[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.
[4,12,52,24] even numbers that have a 2 or a 4 in the ones place
[29, 21, 27] two digit numbers starting with a two

Chord: StrangerCoug (0), D3f3nd3r (3): 100 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)
[65, 89, 729] digit sum is greater than 10

Chord gains 7 points. It's

ErrantParabola

's turn. There are no cards left in the deck. We will continue playing until six people pass in a row. You may only pass if you have no cards that can be played to any active sequence. The number in parentheses after each name represents the number of cards in their hand.

Plotinus · Thu Oct 08, 2020 6:53 pm

Nancy has submitted her turn by PM

[13, 16, 343] numbers containing a double letter when written out
When it’s again my turn, I will add the 3 to this sequence.

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5
[56, 79, 46, 13, 45, 88, 72] The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16
[1, 26, 29 729, 900, 78, 30] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9
[62, 97, 68, 23, 84, 91, 55] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[19, 23, 21, 99, 361, 7, 9] odd numbers
[4, 7, 512, 2, 55, 3, 100] the biggest digit minus the smallest digit is a perfect square
[4, 5, 40, 54, 125, 500, 961] Numbers whose first digit is the sum of at most two distinct perfect squares
[1, 8, 9, 2, 3, 4, 7] {
n < 10
} single digit numbers
[6, 4, 49, 21, 64, 80, 10] multiples of ten, either with addition or two numbers together

Haversine: vincentw (0), ErrantParabola (3): 93 points

[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89, 289] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121 (0), Nancy Drew 39 (0): 102 points

[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.
[4,12,52,24] even numbers that have a 2 or a 4 in the ones place
[29, 21, 27] two digit numbers starting with a two

Chord: StrangerCoug (0), D3f3nd3r (3): 100 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343, 18, 3] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)
[65, 89, 729] digit sum is greater than 10

It's

D3f3nd3r

's turn. There are no cards left in the deck. We will continue playing until six people pass in a row. You may only pass if you have no cards that can be played to any active sequence. The number in parentheses after each name represents the number of cards in their hand.[/quote]

Plotinus · Fri Oct 09, 2020 2:25 am

Spoiler: completed sequences

[24, 2, 43, 15, 256, 4, 20] at least half of the digits of n² - 1 are the same number and this repeating number is a number that is shown on the middle or right hand side of a keypad
[6, 10, 120, 750, 9, 30, 1000] {
n = 2ⁱ × 3^j × 5^k for some non-negative integers
i
,
j
,
k
} 5-smooth numbers
[46, 59, 164, 89, 61, 104, 106] 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)
[14, 15, 5, 57, 81, 19, 60] 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.'
[69, 529, 14, 15, 28, 45, 92, 1000] “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)
[21, 8, 1, 42, 94, 35, 100] digit sum is a term of 'Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.'
[ 61, 56, 216, 66, 13, 1, 8]numbers that are odd mod 5
[18, 29, 37, 82, 243, 81, 55] Numbers whose digit sum is between 9 and 11 inclusive
[10, 20, 200, 1, 5, 400, 500, 700] Numbers with only one nonzero digit
[9, 27, 35, 36, 11, 63, 83] numbers that, when mapped onto the 88 keys of the keyboard with 1 being the lowest and 88 being the highest, represent notes that are members of a G7b9 chord (namely, the notes G, B, D, F, and Ab)
[34, 400, 9, 15, 27, 87, 53] x²'s first digit is a term of 'a(n) is the number of palindromic numbers with 7 digits in base n which are also palindromic in base n+1.'
[5, 25, 27, 36, 64, 96, 98 7 smooth numbers
[11, 32, 34, 128, 676, 3, 85, 21] Numbers whose digit sum is prime
[2, 64, 50, 6, 84, 74, 50] {
2n
} multiples of 2
[5, 17, 70, 7, 31, 39, 71.] squarefree
[95, 3, 17, 48, 11, 47, 45] the first digit of x, converted into base 3, has no 2
[841, 576, 36, 49, 25, 169, 484, 900] {
n²
}square numbers
[10, 13, 19, 81, 67, 16, 64] contains a digit equivalent to 1 mod 5
[196, 17, 441, 33, 42, 16, 3] the first digit of x fulfills 'a(n) = binomial(n, floor((n-1)/2)).'
[9, 73, 90, 7, 1, 6, 12] numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name
[8, 18, 44, 1, 324, 22, 800, 1000] digit sum is a perfect power (k^n with n > 1, k and n are integers)
[28, 5, 1, 100, 784, 6, 38] the digit sum of the digit sum of y = k, k and k+1 are both squarefree
[10, 30, 35, 220, 250, 70, 20] multiples of 5
[56, 79, 46, 13, 45, 88, 72] The number mod 11 contains a letter whose capital ASCII representation has a digit sum of exactly 16
[1, 26, 29 729, 900, 78, 30] The number contains the digit 9, or two numbers played at the same time add up to a multiple of 9
[62, 97, 68, 23, 84, 91, 55] numbers that, when represented in month/date format with leading zeroes removed, land on a weekend in the year 2024
[19, 23, 21, 99, 361, 7, 9] odd numbers
[4, 7, 512, 2, 55, 3, 100] the biggest digit minus the smallest digit is a perfect square
[4, 5, 40, 54, 125, 500, 961] Numbers whose first digit is the sum of at most two distinct perfect squares
[1, 8, 9, 2, 3, 4, 7] {
n < 10
} single digit numbers
[6, 4, 49, 21, 64, 80, 10] multiples of ten, either with addition or two numbers together

Haversine: vincentw (0), ErrantParabola (3): 93 points

[2, 86, 165] within 3 of a multiple of 83
[41, 51, 89, 289] numbers equivalent to ±1 mod 10

Exsecant: Sirius9121 (0), Nancy Drew 39 (0): 102 points

[12, 20, 28] {
n ≡ 4 (mod 8)
} divided by 8 leaves a remainder of 4
[1, 8, 15, 225] {
7n+1
} divided by 7 leaves a remainder of 1
[14, 35, 56] {
7n
} divisible by 7
[144, 75, 93] either the digits sum to 12, or the number is a multiple of 12
[32, 1, 58, 256] The card is itself 13, 31; or the digit sum of the card is 13 or 31; or two cards played together have a digit sum of 13, 31; or two cards played at the same time can be added to or subtracted from each other to achieve 13 or 31.
[4,12,52,24] even numbers that have a 2 or a 4 in the ones place
[29, 21, 27] two digit numbers starting with a two

Chord: StrangerCoug (0), D3f3nd3r (2): 100 points

[8, 10, 40] numbers that, when spelled normally in English, have no duplicated letters
[13, 16, 343, 18, 3] numbers containing a double letter when written out
[3, 63, 600] Numbers, all of whose digits are divisible by 3 (0 counts)
[65, 89, 729] digit sum is greater than 10

It's

ErrantParabola

's turn. There are no cards left in the deck. We will continue playing until six people pass in a row. You may only pass if you have no cards that can be played to any active sequence. The number in parentheses after each name represents the number of cards in their hand.[/quote]

Plotinus · Fri Oct 09, 2020 2:34 am

Fixed, thank you for pointing it out

Plotinus · Fri Oct 09, 2020 6:18 am

Neither of you can complete any sequences, even when combining your numbers, we can just call it a game if you'd rather.

Congrats to Sirius9121 and Nancy Drew 39!

Thank you to everyone for sticking it out.

Let's take a week to propose rule changes and collect new signups.

Bingos are worth 8 points. The rules for a sequence must apply to at least 10 unique cards in the deck. Players may only post their hand during the first round of the first game that they are playing, after that they will need to ask for advice without revealing their cards.

Plotinus · Fri Oct 09, 2020 6:55 am

I'm glad you're enjoying it! Are you /in for next round then?

Plotinus · Fri Oct 09, 2020 7:03 am

All right, we'll be glad to have you back when you're ready

Plotinus · Wed Oct 14, 2020 6:58 pm

Two players have signed up so far.

One option if we don't get enough players is that I could also play. If so, we could play with all hands visible, so you wouldnt have to trust me to forget what your hands are when it's my turn.

Plotinus · Thu Oct 15, 2020 5:59 pm

Great! I'll set this up later today. Sirius, I'll send you some cards too if you're still in, three players is enough but I think 4 is better. Thanks for being a good sport at the end of last game.

Plotinus · Thu Oct 15, 2020 6:00 pm

People may still /in up until I post the game board

Plotinus · Fri Oct 16, 2020 7:32 am

Spoiler: completed sequences

StrangerCoug

:

Nancy Drew 39

:

Sirius9121

:

Farren

:

I'm not attached to these colours so if you want to change yours let me know what you're changing it to. Each player can have 1 colour change.

Sending out cards within the next 5 minutes. It is

StrangerCoug's

turn ((expired on 2020-10-18 20:45:00))

Plotinus · Fri Oct 16, 2020 6:31 pm

Spoiler: completed sequences

StrangerCoug

:

[10, 25, 80, 220] multiples of 5

Nancy Drew 39

:

Sirius9121

:

Farren

:

JI don't mind spending a few more turns finding the colour you like best. MafiaScum's dark theme changes the colours a little bit to make them readable on a dark background so you don't always get what you expect, but you can find a list of colour names here https://en.wikipedia.org/wiki/Web_colors and try a few out to see which ones you like best. There are quite a few purples to choose from so as long as everyone is different enough from each other, that's okay. Specficially, I think the colour you get when you type "purple" looks nice but it doesn't actually look like purple to me, so let me know what to change it to if you don't like it.

If anyone is not using mafiaBlack then we should pick colours that work in all the schemes, but if we're all in mafiaBlack then we don't have to worry about it.

It is

Nancy Drew 39's

turn ((expired on 2020-10-19 07:45:00))

Plotinus · Fri Oct 16, 2020 8:45 pm

Alright, I've switched it to

darkslategray

until she expresses a preference

Plotinus · Fri Oct 16, 2020 9:44 pm

Spoiler: completed sequences

StrangerCoug

:

[10, 25, 80, 220] multiples of 5

Nancy Drew 39

:

Sirius9121

:

Farren

:

Just getting this onto the most recent page with the colour changes.

It is

Nancy Drew 39's

turn ((expired on 2020-10-19 07:45:00))

Plotinus · Sat Oct 17, 2020 1:59 am

We're using deck 2. I've changed Nancy's colour and bolded the names in 1326. Is that more readable or should I make some of them darker?

It's still Nancy's turn

Plotinus · Sat Oct 17, 2020 6:44 pm

Spoiler: completed sequences

StrangerCoug

:

[5, 10, 20, 25, 80, 220] multiples of 5

Nancy Drew 39

:

Sirius9121

:

Farren

:

It is

Sirius9121's

turn ((expired on 2020-10-19 13:24:50))

Plotinus · Sat Oct 17, 2020 7:25 pm

Spoiler: completed sequences

StrangerCoug

(0 points):

Nancy Drew 39

(0 points):

Sirius9121

(9 points):

Farren

(0 points):

It is

Farren's

turn ((expired on 2020-10-20 07:47:41))

Plotinus · Sat Oct 17, 2020 7:35 pm

Yeah, I'll let you change

Plotinus · Sat Oct 17, 2020 7:40 pm

Yeah, I was wondering why you hadn't done that. I'll edit the last post.

Plotinus · Sat Oct 17, 2020 7:44 pm

I looked it up and it applies to 34% of the numbers under 100. Nice one!

Spoiler: completed sequences

StrangerCoug

(0 points):

Nancy Drew 39

(0 points):

Sirius9121

(9 points):

Farren

(8 points):

Farren gets 8 points. It is

StrangerCoug's

turn ((expired on 2020-10-20 08:42:20))

Plotinus · Sat Oct 17, 2020 8:57 pm

Sure! Actually since we're just starting, everyone's only taken one turn so far, so if it you take your turn now then you won't have missed any turns. I'll send you some cards.

What color would you like to be?

Plotinus · Sat Oct 17, 2020 9:06 pm

yellow

will probably be too hard for the people using the light site theme to read. How do you (and the people using mafiaSilver) feel about

darkgoldenrod

,

peru

,

olive

(or something else, you're not limited to those three of course)

Plotinus · Sat Oct 17, 2020 9:23 pm

Spoiler: completed sequences

StrangerCoug

(0 points):

Nancy Drew 39

(0 points):

Sirius9121

(9 points):

Farren

(8 points):

Rockhopper

(0 points):

[3, 17, 31] primes

It is

StrangerCoug's

turn ((expired on 2020-10-20 10:19:20))

I'll go with

peru

for now because it's the shortest to type but we can switch to one of the others if anyone finds it hard to read.

You're doing fine so far

Plotinus · Sun Oct 18, 2020 2:16 am

Glad to see you again, Not_Mafia. If you'd rather join this round as a player we could also split into 3 teams

Plotinus · Sun Oct 18, 2020 6:33 am

All right, it's

Not_Mafia's

turn. ((expired on 2020-10-20 19:25:00))

Six players it the maximum and we'll split into 3 teams:

Swinnerton

-

Dyer

:

StrangerCoug

and

Farren

Navier

-

Stokes

:

Nancy Drew 39

and

Rockhopper

Yang

-

Mills

:

Sirius9121

and

Not_Mafia

What colour would you like to be, Not_Mafia? Everyone else picked theirs this time

Plotinus · Sun Oct 18, 2020 6:36 am

(ps: I know it's the Birch and Swinnerton-Dyer conjecture but that was too long)

Plotinus · Sun Oct 18, 2020 8:14 am

StrangerCoug has submitted his turn by PM:

StrangerCoug wrote:4, 144, 1000: Perfect powers (power must be greater than or equal to 2)

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(8 points):

[4, 144, 1000] perfect powers (power must be greater than or equal to 2)

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(0 points):

[3, 17, 31] primes

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(9 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8

It is

NancyDrews

turn ((expired on 2020-10-20 21:15:00))

Plotinus · Sun Oct 18, 2020 5:48 pm

4, 6, 20, 25, 50, 128, 625

2 × 2 = 4
2 × 3 = 6
2 × 2 × 5 = 20
5 × 5 = 25
2 × 5 × 5 = 50
2 × 2 × 2 × 2 × 2 × 2 × 2 = 128
5 × 5 × 5 × 5 = 625

So only 2s and 3s and 5s

Plotinus · Mon Oct 19, 2020 6:36 pm

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(8 points):

[4, 144, 1000] perfect powers (power must be greater than or equal to 2)

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(0 points):

[3, 17, 31] primes
[64, 37, 10, 21, 29] either the digit sum adds up to 10, or the number itself is ten, or two numbers submitted together add up to a multiple of ten

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(9 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8

It is

Sirius9121's

turn ((expired on 2020-10-21 09:41:00))

I've been thinking about that since you presubmitted it sirius and on the one hand, bingos are only worth 8 points now so I'm hoping it'll matter less if a sequence is overengineered, but on the otherhand, the cos of most numbers is an infinite string of randomish numbers, so the chance of finding something that matches your hand approaches 100%

like suppose my hand is

In [265]: random.choices(range(1,101), k=7)
Out[265]: [3, 18, 27, 49, 14, 56, 94]

Then

In [263]: [math.cos(x*math.pi/180) for x in [3, 18, 27, 49, 14, 56, 94]]

[0.9986295347545738,
0.9510565162951535,
0.8910065241883679,
0.6560590289905073,
0.9702957262759965,
0.5591929034707468,
-0.06975647374412533]

Then digit by digit, I have these options to choose from: 0, 5, 6, 8, 9
9, 5, 7, 6
8, 1, 6, 0, 9
6, 0, 2, 1, 7,
2, 5, 0, 9
9, 6, 5, 2
5, 0, 7, 9, 4
0, 1, 2, 3, 7
3, 4, 6, 8,
7, 2, 1, 9, 4
5, 9, 8, 9, 7, 4
4, 5, 8, 0,
1, 3, 5, 7, 9 --- probably you could have found a sequence before this point, but here is the first one that is jumping out to me, the 13th digit is odd.

So this one is still running into the meta rule that says only 1% of "is the nth digit of the cos(x) interesting" should be a bingo

Plotinus · Tue Oct 20, 2020 2:37 am

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(8 points):

[4, 144, 1000] perfect powers (power must be greater than or equal to 2)

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(0 points):

[64, 37, 10, 21, 29] either the digit sum adds up to 10, or the number itself is ten, or two numbers submitted together add up to a multiple of ten

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(16 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8

Edit: Yang-Mills gains 7 points. It is

Farren's

turn ((expired on 2020-10-22 10:26:35))

Plotinus · Tue Oct 20, 2020 2:42 am

whoops, thanks for correcting me. You get 7 points

Plotinus · Tue Oct 20, 2020 6:12 am

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(8 points):

[4, 144, 1000] perfect powers (power must be greater than or equal to 2)
[5, 57, 600] first digit is a 5 or a 6

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(10 points):

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(16 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8

Navier-Stokes gains 10 points. It is

Not_Mafia's

turn ((expired on 2020-10-22 19:03:45))

Plotinus · Wed Oct 21, 2020 12:31 am

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(8 points):

[5, 57, 600] first digit is a 5 or a 6

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(10 points):

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(16 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8
[4, 25, 144, 1000] perfect powers (power must be greater than or equal to 2)

It is

StrangerCoug's

turn ((expired on 2020-10-23 11:21:28))

Plotinus · Wed Oct 21, 2020 7:34 am

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(8 points):

[5, 57, 600] first digit is a 5 or a 6
[23, 56, 300] Numbers whose digit sum is prime

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(10 points):

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(16 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8
[4, 25, 144, 1000] perfect powers (power must be greater than or equal to 2)

It is

Nancy Drew 39

's turn ((expired on 2020-10-23 20:35:00))

Plotinus · Thu Oct 22, 2020 9:14 am

prodded Nancy Drew 39

Plotinus · Mon Oct 26, 2020 3:49 am

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(8 points):

[5, 57, 600] first digit is a 5 or a 6
[23, 56, 300] Numbers whose digit sum is prime

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(10 points):

[512, 529, 729] triple digit numbers

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(16 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8
[4, 25, 144, 1000] perfect powers (power must be greater than or equal to 2)

It is

Sirius9121

's turn ((expired on 2020-10-28 00:49:20))

sorry, i haven't been feeling well since Thursday and I haven't be able to tell whether your sequence meets the rules or not.

I suspect it doesn't because there are an infinite number of things i could multiply my cards by to get them to all start with something? You posted this 10 hours after Nancy did so you've only used up 10 hours of your turn.

Nancy is V/LA until Friday

Plotinus · Mon Oct 26, 2020 7:12 pm

Yeah, that's too many parts.

Plotinus · Tue Oct 27, 2020 9:21 am

prodded Sirius. i'm probably going out tomorrow morning, so he has until i get home -- if i haven't updated things yet then he can submit something

Plotinus · Wed Oct 28, 2020 8:10 am

primesixes = [6*n - 1 for n in range(1,101) if is_prime(6 * n - 1)]

len(primesixes)
57

sixes_start_with = [6*n -1 for n in range(1,101) if str(6*n-1)[0] in '1235']
len(sixes_start_with)
75

both of these are too common, and you've run out of time.

Plotinus · Wed Oct 28, 2020 8:13 am

Sirius' leftmostcard that fits into a sequence is 400 and the topmost sequence (starting from his team's sequences) that it fits into is triple digit numbers

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(8 points):

[5, 57, 600] first digit is a 5 or a 6
[23, 56, 300] Numbers whose digit sum is prime

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(10 points):

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(16 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8
[4, 25, 144, 1000] perfect powers (power must be greater than or equal to 2)
[400, 512, 529, 729] triple digit numbers

It is

Farren

's turn ((expired on 2020-10-30 20:10:00))
Nancy is V/LA until Friday

Plotinus · Wed Oct 28, 2020 8:15 am

Oops, fixed. Thanks for pointing it out. It is your turn

Plotinus · Wed Oct 28, 2020 8:25 am

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(15 points):

[5, 57, 600] first digit is a 5 or a 6
[23, 56, 300] Numbers whose digit sum is prime

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(10 points):

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(16 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8
[400, 512, 529, 729] triple digit numbers

Swinnerton-Dyer gains 7 points. It is

Rockhopper

's turn ((expired on 2020-10-30 20:17:00))
Nancy is V/LA until Friday

Plotinus · Thu Oct 29, 2020 7:24 pm

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(15 points):

[5, 57, 600] first digit is a 5 or a 6

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(17 points):

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(16 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8
[400, 512, 529, 729] triple digit numbers

Navier-Stokes gains 7 points. It is

Not_Mafia

's turn ((expired on 2020-11-01 06:13:27))
Nancy is V/LA until today.

Plotinus · Fri Oct 30, 2020 7:18 pm

prodded not_mafia

Plotinus · Sat Oct 31, 2020 2:31 am

Rockhopper completed that one last turn.

Plotinus · Sat Oct 31, 2020 7:45 am

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(15 points):

[5, 57, 600] first digit is a 5 or a 6

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(17 points):

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(24 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8
[400, 512, 529, 729] triple digit numbers

Yang-Mills gains 8 points. It is

StrangerCoug

's turn ((expired on 2020-11-02 19:34:44))

Plotinus · Sun Nov 01, 2020 2:00 am

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(15 points):

[5, 57, 600] first digit is a 5 or a 6
[3, 4, 8] single-digit numbers

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(17 points):

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(24 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8
[400, 512, 529, 729] triple digit numbers

It is

Nancy Drew

's turn ((expired on 2020-11-03 14:00:00))

Plotinus · Sun Nov 01, 2020 7:10 pm

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(15 points):

[5, 57, 600] first digit is a 5 or a 6
[3, 4, 8] single-digit numbers

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(17 points):

[76, 7, 165, 250] numbers either contain the digit 7 or they add up to a multiple of 7 (in the case of 3 digit numbers, two of the digits may be taken together as a two-digit number, e.g. 165 -> 16 + 5 = 21 = 7×3)

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(24 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8
[400, 512, 529, 729] triple digit numbers

It is

Sirius9121

's turn ((expired on 2020-11-03 15:10:00))

Plotinus · Mon Nov 02, 2020 4:11 am

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(15 points):

[5, 57, 600] first digit is a 5 or a 6
[10, 24, 35] when spelled out in English, starts with the letter "T" and has no spaces. (e.g. twenty-four)

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(17 points):

[76, 7, 165, 250] numbers either contain the digit 7 or they add up to a multiple of 7 (in the case of 3 digit numbers, two of the digits may be taken together as a two-digit number, e.g. 165 -> 16 + 5 = 21 = 7×3)

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(24 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8
[400, 512, 529, 729] triple digit numbers
[1, 3, 4, 8] single-digit numbers

It is

Rockhopper

's turn ((expired on 2020-11-04 08:39:09))

pedit: fixed that one vote count. As soon as Sirius contributed to it in 1402 the sequence got moved to his team's category, so it's in the right place now, but it was wrong in 1396.

I have been thinking that there is not much point to maintaining separate areas for the active sequences because it doesn't affect anything points-wise where the cards happen to be. We could arrange them all together next game under a single heading "Active sequences" without losing anything. I like the idea of stealing sequences but I think if we're going to have it then we need to tweak the mechanics to make it be something more than "the cards are temporarily in a different place now" -- though on a physical table that might be useful for physical space reasons.

Plotinus · Mon Nov 02, 2020 4:20 am

in that case, it might be useful to keep the sequence in front of the player who initially put it instead of moving it around

Plotinus · Mon Nov 02, 2020 7:01 am

I have only just now sent Farren and Sirius their new cards. I think that's all the people I owe cards to but let me know if I missed you

Plotinus · Mon Nov 02, 2020 6:19 pm

In post 1432, Rockhopper wrote:Are multiples of 7 included in Nancy's sequence?

I asked her about this by PM for you and she says yes

Nancy Drew 39 wrote:
Plotinus wrote:One of the players has a question about this sequence: is 28 allowed because you can write 028 = 0 + 28 = 28, a multiple of 7? Or is it not allowed?
28 is a multiple of 7, so it should still count.

Plotinus · Mon Nov 02, 2020 6:31 pm

In post 1430, Nancy Drew 39 wrote:I thought that might have changed later but I don’t understand how a sequence I made with the same exact 3 numbers that were directly quoted in my post not credited to me?

Initially, I just got lost when I was placing the sequence onto the board. I've fixed the post where that happened now. After that, it happened as Farren said.

Have you ever played rummy? In some versions of rummy, someone might put down a 2, 3, and 4 of hearts into a sequence (called a meld) and then if you have a 5 of hearts you can put your 5 of hearts into that sequence and make it yours.

Plotinus · Mon Nov 02, 2020 7:03 pm

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(15 points):

[5, 57, 600] first digit is a 5 or a 6
[10, 24, 35] when spelled out in English, starts with the letter "T" and has no spaces. (e.g. twenty-four)

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(24 points):

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(24 points):

[18, 81, 84] 2-digit numbers where exactly one digit is an 8
[400, 512, 529, 729] triple digit numbers
[1, 3, 4, 8] single-digit numbers

Navier

-

Stokes

gains 7 points. It is

Not_Mafia

's turn ((expired on 2020-11-05 06:47:06))

Plotinus · Wed Nov 04, 2020 5:30 am

prodding not mafia

Plotinus · Wed Nov 04, 2020 7:03 pm

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(15 points):

[5, 57, 600] first digit is a 5 or a 6
[10, 24, 35] when spelled out in English, starts with the letter "T" and has no spaces. (e.g. twenty-four)

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(24 points):

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(24 points):

[18, 81, 84, 86] 2-digit numbers where exactly one digit is an 8
[400, 512, 529, 729] triple digit numbers
[1, 3, 4, 8] single-digit numbers

It is

StrangerCoug

's turn ((expired on 2020-11-06 18:48:16))

Plotinus · Thu Nov 05, 2020 3:13 am

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(22 points):

[10, 24, 35] when spelled out in English, starts with the letter "T" and has no spaces. (e.g. twenty-four)

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(24 points):

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(24 points):

[18, 81, 84, 86] 2-digit numbers where exactly one digit is an 8
[400, 512, 529, 729] triple digit numbers
[1, 3, 4, 8] single-digit numbers

Swinnerton

-

Dyer

gains 7 points. It is

Nancy Drew 39

's turn ((expired on 2020-11-07 15:14:00))

Plotinus · Thu Nov 05, 2020 9:53 am

Spoiler: completed sequences

Swinnerton

-

Dyer

:

StrangerCoug

,

Farren

(22 points):

[10, 24, 35] when spelled out in English, starts with the letter "T" and has no spaces. (e.g. twenty-four)

Navier

-

Stokes

:

Nancy Drew 39

,

Rockhopper

(24 points):

[45, 81, 90] digits add up to nine

Yang

-

Mills

:

Sirius9121

,

Not_Mafia

(24 points):

[18, 81, 84, 86] 2-digit numbers where exactly one digit is an 8
[400, 512, 529, 729] triple digit numbers
[1, 3, 4, 8] single-digit numbers

Nice one, Nancy. It is

Sirius9121

's turn ((expired on 2020-11-07 21:48:00))

Sirius has submitted an invalid bingo by PM and needs to figure something else out.

Plotinus · Fri Nov 06, 2020 10:44 am

prodded sirius

Plotinus · Fri Nov 06, 2020 7:54 pm

There are 75 non prime numbers between 1 and 100 inclusive. [1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100]

Removing some of the digits does get it below 50 in this instance but:

Sirius can you prove this part mathematically:

If you are a following a meta rule to generate rules for sequences, then the meta rule shouldn't be able to generate sequences that are bingos for more than 1/64th of hands.

Plotinus · Fri Nov 06, 2020 7:55 pm

The metarule being "nonprime that doesn't contain the digits a, b, or c"

Plotinus · Sat Nov 07, 2020 7:11 am

In post 1450, Sirius9121 wrote:Hm. Thats false.

I'll change to 'nonprimes which the first digit from the left is a final digit of any triangular number'.

You'll notice that there are no triangular numbers that start with 2,4,7 or 9.
eq.t nonprimes which the first digit from left is 1.3.5.6 or 8

I think this might still be too overengineered: is "nonprimes which the first digit from the left is a, b, c, d, or e" going to generate a bingo with more than 1/64 of hands?

Plotinus · Sat Nov 07, 2020 7:15 am

In post 1452, Farren wrote:I'd object to that, because it would imply that I'd have to understand what's going on too, and my understanding of the meta-rule isn't as firm as I'd like.

Like, take your bingo. Numbers containing a 1. I can turn that into a meta-rule: "Numbers containing a specific single digit." But I'm not sure where exactly the dividing line is between "cases where there's a meta-rule" and "cases where there isn't."

I also have no idea how to prove that a given bingo falls foul (or doesn't) of the meta-rule clause; all I know how to do is experimental "proof" (generate hands of numbers and see how many are a match - which proves nothing; if you flip a coin three times and it comes up heads three times, that doesn't prove the coin's rigged). And I can't do that very fast with my current understanding of spreadsheets, so trying to do it 64 times is a major headache.

The simpler the bingo is, the more likely it fits the rules. For example "all the cards are even" or "is divisible by 3 with 1 left over" are acceptable bingos, and the meta rule in this case is "Are any of my cards divisible by 2? Divisible by 2 with 1 left over? Divisible by 3? Divisible by 3 with 1 left over? Divisible by 3 with 2 left over? Divisible by 5? ..."

If your method of generating bingos is "glance at my hand and notice something really obvious, like all of the numbers are prime" then that's always going to be allowed as long as less than half of the numbers below 100 have this property. (nonprime by itself is way more than 50 so that wouldn't work).

If you're playing without a spreadsheet, then you will never run afoul of the meta rule.

but if you're curious, the way you work out it without trying all the options is through a branch of mathematics called Combinatorics. It's pretty fun, especially early on when the problems are less hairy, but it's also pretty easy to make mistakes and real life combinatorics problems can get pretty ugly

Plotinus · Sat Nov 07, 2020 7:23 am

This site is aimed at teenagers and has questionable color scheme choices but it has some worked examples for learning the fun parts of Combinatorics https://www.coolmath.com/algebra/20-combinatorics

Plotinus · Sat May 01, 2021 7:07 pm

If it's just a matter of telling people what their cards are and reminding them that it's their turn, I can do it, but I don't have the energy for making a lot of decisions about edge cases or whether a sequence is too over engineered or not. If someone wants to volunteer to co-mod and make most of the hard decisions, then that could work.

I'm sorry for disappearing in the middle of this before and it'd be nice to see it through if we can

Plotinus · Mon May 03, 2021 5:27 am

I'll message rockhopper to see if they're still interested, it looks like everyone else has chimed in. Sirius can co-mod.

Plotinus · Tue May 04, 2021 5:41 am

With 5 players it's hard to do teams but if 1 person /ins we could have 3 teams of 2.

If we continue the old game, Sirius' cards would be reshuffled into the deck.

Looks like one person feels strongly about starting anew vs continuing and one person is okay with starting anew. How do the others feel? Does anyone else feel strongly about either option?

Plotinus · Wed May 05, 2021 6:23 pm

Spoiler: player order randomisation

Player order is: Not_Mafia', 'Farren', 'Rockhopper', 'Nancy Drew 39', 'StrangerCoug'

I'll get new hands out soon. If somebody new /ins midgame we can coalesce into teams if people want? Otherwise there are 5 teams of 1

Plotinus · Wed May 05, 2021 6:42 pm

Spoiler: completed sequences

Not_Mafia

(0 points):

[21, 24, 48] one digit is double the other digit

Farren

(0 points):

Rockhopper

(0 points):

Nancy Drew 39

(0 points):

StrangerCoug

(0 points):

It is

Farren

's turn ((expired on 2021-05-08 07:43:00))

Plotinus · Wed May 05, 2021 6:53 pm

Spoiler: completed sequences

Not_Mafia

(0 points):

[21, 24, 48] one digit is double the other digit

Farren

(0 points):

[81, 900, 441] multiples of 9

Rockhopper

(0 points):

Nancy Drew 39

(0 points):

StrangerCoug

(0 points):

It is

Rockhopper

's turn ((expired on 2021-05-08 01:53:33))

Plotinus · Mon May 10, 2021 7:32 pm

sorry, i had a migraine for a few days. I prodded Not_Mafia now, so they have another (expired on 2021-05-12 02:32:23) before we auto-move for them. I'm gonna figure out who to ask about getting Sirius editing privs on this thread so he can change the title

edit: PMed PrivateI

Plotinus · Wed May 12, 2021 5:59 pm

Yeah, just hands and prods.

I PMed the mishmash mod about giving Sirius9121 perms but I haven't heard back, I'll try PMing a different one. I'll edit the topic now and prod Nancy now and then she'll have (expired on 2021-05-14 00:59:39) to go

Plotinus · Wed May 12, 2021 7:34 pm

Nancy Drew 39 wrote: 8, 17, 52. Where the first two numbers are the inverse of the third? 8 + 17 = 25 which is the inverse of 52?

Can I do this?

We allowed this from Nancy last game so I think it's okay this game too. The sum of two numbers in the sequence backwards is a number in the sequence, so either you play 3 cards at once or you play two numbers together that sum to one of 8, 71 or 52.

Spoiler: completed sequences

Not_Mafia

(0 points):

[21, 24, 48] one digit is double the other digit

Farren

(0 points):

[81, 900, 441] multiples of 9
[20, 35, 53] two digit numbers where the difference between the digits is exactly 2

Rockhopper

(7 points):

[343, 88, 19] numbers whose product of digits is a perfect square not equal to zero

Nancy Drew 39

(0 points):

[2, 29, 25] numbers with a 2 in them
[8, 17, 52] sum 2 numbers and reverse the digits

StrangerCoug

(0 points):

It is

StrangerCoug

's turn ((expired on 2021-05-14 02:34:17) until prod)

Plotinus · Wed May 12, 2021 7:35 pm

i'm going to be really busy the next 7 days but I'll try to check in more often than I have been and update the game.

Plotinus · Thu May 13, 2021 4:01 am

Sirius should have editing privileges now, including title editing privileges. Thanks, xofelf!

Plotinus · Thu May 13, 2021 6:54 pm

Spoiler: completed sequences

Not_Mafia

(0 points):

[21, 24, 48] one digit is double the other digit

Farren

(0 points):

[81, 900, 441] multiples of 9
[20, 35, 53] two digit numbers where the difference between the digits is exactly 2

Rockhopper

(7 points):

[343, 88, 19] numbers whose product of digits is a perfect square not equal to zero

Nancy Drew 39

(0 points):

[2, 29, 25] numbers with a 2 in them
[8, 17, 52] sum 2 numbers and reverse the digits

StrangerCoug

(0 points):

[1, 3, 5] single-digit numbers

It is

Not_Mafia

's turn ((expired on 2021-05-15 01:54:10) until prod)

Plotinus · Fri May 14, 2021 7:00 pm

Prodded Not_Mafia (expired on 2021-05-16 02:00:43)

Plotinus · Fri May 14, 2021 8:08 pm

Spoiler: completed sequences

Not_Mafia

(7 points):

[21, 24, 48] one digit is double the other digit

Farren

(0 points):

[81, 900, 441] multiples of 9
[20, 35, 53] two digit numbers where the difference between the digits is exactly 2

Rockhopper

(7 points):

[343, 88, 19] numbers whose product of digits is a perfect square not equal to zero

Nancy Drew 39

(0 points):

[8, 17, 52] sum 2 numbers and reverse the digits

StrangerCoug

(0 points):

[1, 3, 5] single-digit numbers

Not_Mafia gains 7 points. It is

Farren

's turn ((expired on 2021-05-16 03:08:27) until prod)

pedit: idk, whatever sirius decides, but my inclination is to say "post it and ask the person who started the sequence if it meets their vision for the sequence"

Plotinus · Fri May 14, 2021 8:10 pm

if it takes 2 days to reach a decision then the auto-move for Farren's turn is to post the move he PMed us

Plotinus · Sat May 15, 2021 7:50 am

I've PMed nancy to ask her to weigh in