Sequencer | StrangerCoug's turn

[StrangerCoug]

Sure, I'll try this out.

/in

[StrangerCoug]

Play [17, 19, 43] as prime numbers

[StrangerCoug]

Mod: You misspelled my username (there should be only two R's).

[StrangerCoug]

Good bingo

[StrangerCoug]

Play [51, 55] to finish the 2-digit odds

[StrangerCoug]

[1, 10, 15] {n*(n-1)/2)}: the triangular numbers themselves

[StrangerCoug]

Mod: V/LA, no internet.

[StrangerCoug]

Mod: Out of V/LA.

[StrangerCoug]

Add 11 and 71 to the primes

[StrangerCoug]

• [9, 17, 69, 77] {
  n ≡ 1 (mod 4) ∧ n ≥ 7 (mod 10)
  } Numbers congruent to 1 mod 4 whose last digit, written in english, can have the letters "ty" appended to the end of it to multiply it by ten (e.g., "six" times ten is "sixty", but "fourty" is not a number, so the last digit cannot be four)

Mod: Are you sure the part after the ∧ shouldn't read n ≥ 6 (mod 10)?

Scratch that; n ≡ 1 (mod 4) implies it has to be odd. Missed that.

[StrangerCoug]

Add 28 to the triangulars

[StrangerCoug]

Dang, where is everyone?

[StrangerCoug]

[13, 27, 72]: Numbers whose digital sum is a square

1 + 3 = 4, √4 = 2
2 + 7 = 7 + 2 = 9, √9 = 3

[StrangerCoug]

Oh, and since 1, 4, and 9 are one-digit squares, their digital sums are trivially squares, so I don't mind them in the above.

[StrangerCoug]

Mod: By post #110, my intended clarification was that one-digit squares are allowed in the sequence I just played; are you sure your closed form doesn't imply the contrary?

[StrangerCoug]

Looks good

[StrangerCoug]

Add 42 and 56 to the numbers divisible by 7

[StrangerCoug]

Retroactive rule changes require all 5 players to agree to them. How do people feel about the rule "A sequence is a group of numbers that all have something in common with each other. Numbers may not be excluded from sequences they would naturally belong to."

Incentivising sequence theft

I think the "you can complete it in 6 if you stole it and it's currently in front of you" idea is interesting and worth a playtest. I definitely think we should brainstorm around the stealing mechanic to make it worthwhile to contribute to sequences you can't finish right away.

There would be more stealing if we let sequences grow indefinitely and only awarded points at the end, but in practice whoever had the evens or odds would win and that sucks.

These are both good

[StrangerCoug]

Score the numbers with 8s and 9s in them with 8 itself along with 18, 96, and 29

[StrangerCoug]

Add 5 to triangular numbers + 4

[StrangerCoug]

Add 24 to the multiples of 3

[StrangerCoug]

Since McMenno is probably not coming back, should i add his hand to the bottom of the deck?

Sure.

Edited to add:

If they're added back in, they should be shuffled into the remaining cards instead of being put at the bottom imo.

Though good point.

[StrangerCoug]

Add 52 to 16n+4

[StrangerCoug]

[28, 36, 50, 93]: Numbers with exactly two distinct prime factors

28 = 2² × 7
36 = 2² × 3²
50 = 2 × 5²
93 = 3 × 31

[StrangerCoug]

Play 1, 5, 35, 90 to finish off the coins one

From what I've tested, you

CAN

make change from a dollar with exactly 35 coins, but the way I found resorts to using all three of dimes, nickels, and pennies (1 quarter, 1 dime, 8 nickels, 25 pennies), and DRK's rule requires excluding at least one of those coins to be ruled out. I have been unable to find a way to do it without using all four denominations, but my check hasn't been completely thorough, so if someone can prove 35 doesn't belong I'll take it back and play something else.

[StrangerCoug]

Should we cannibalise Felissan's hand too if I don't find a replacement before we run out of cards or just leave it be?

I'm good with it.

[StrangerCoug]

1, 11, 1000 to finish off numbers whose digit sum is a power of 2

[StrangerCoug]

So I think we've all got the hang of this and can play Game 2 with a slightly bigger deck.

Spoiler: My proposed Game 2 deck

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

This consists of the following "decks" shuffled together:

• The Game 1 deck
  
• Every multiple of 100 less than or equal to 1,000
  
• Every multiple of 250 less than or equal to 1,000
  
• Every square between 100 and 1,000 exclusive (since every square from 1 to 100 inclusive already appears at least twice in the Game 1 deck and √1000 is not an integer)

If a number occurs in multiple decks, it is shuffled in as many times as it occurs total in each deck.

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

[StrangerCoug]

I propose adding 1, 3, 9, 27, 81, 243, 729 to StrangerCoug's deck, or at the very least adding 243 in, because it is sad that you can only put 6 numbers in 3^n.

Sure Let's add them all.

[StrangerCoug]

Pass

[StrangerCoug]

WAIT this game isn't Sequence?

i wonder if i could /in now...

we're starting a new round soon with a new deck and slightly different rules, and we'd be glad to have you. It is probably not Sequence because it is a game I made up.

Sequence is essentially a commercial version of One-Eyed Jack, though it's not clear to me which came first.

[StrangerCoug]

I don't think it's that critical unless you're trying to release it commercially, but something that invokes rummy? Seqrummy, perhaps?

[StrangerCoug]

And I think that makes game over with implosion the winner.

[StrangerCoug]

Good game.

/in

[StrangerCoug]

1, 3, 5: single-digit numbers

Oh, and

mod: None of Team Analysis's numbers are divisible by 7.

[StrangerCoug]

I won't be able to make anything but the simplest closed forms myself and having the closed form isn't particularly useful to me, but I do like having it just for the sake of learning about stuff.

Ditto.

[StrangerCoug]

20, 16, 200: Composite numbers whose digit sum is prime

[StrangerCoug]

Play 165, 576, 6, 42, 27, and 21 to claim the numbers whose digit sums are multiples of 3

[StrangerCoug]

Sounds good

[StrangerCoug]

97, 441, 225, 90: Numbers whose digit sum is a perfect square

[StrangerCoug]

is treble meant to be triple?

They're synonyms in this case.

[StrangerCoug]

Nice, Jackal

[StrangerCoug]

Mod: Why is 17 listed twice in the powers of primes sequence?

Give me time to think of what to play.

[StrangerCoug]

Play 10, 88, 100 to finish the "digit sum is a perfect square" sequence

[StrangerCoug]

Mod: Why is 17 listed twice in the powers of primes sequence?

One of those should be a 16, and the 6 should be a 5.

[StrangerCoug]

3, 11, 77: Palindromes

[StrangerCoug]

Fixed the powers of primes sequence

No you haven't

[StrangerCoug]

...Is that even within the spirit of the rules?

Edited to add:

I'm not arguing that it's within the letter of the rules as Plotinus gave them; I'm questioning whether that was quite what he had in mind.

[StrangerCoug]

Since his teammate is against it and I'm the one who first publicly questioned whether it should be counted as a bingo, count me as against it, too.

[StrangerCoug]

Add 56 to the numbers that end in 6

[StrangerCoug]

@plot i think you completed the wrong sequence for micc; he completed 'numbers with a factor that is a square', not 'square numbers'

Further, only 81 is itself a square

[StrangerCoug]

We recently discussed numbers less than 27 and ruled against it for being uninteresting / not having something meaningful in common. Does framing "n <= 31" in terms of days of the year make it interesting enough to rule this one differently?

I think some day of the year sequences could be interesting, like intercalary days, prime days of prime months, palindromic dates, [nationality] name days for names starting with [letter]. Months with 31 days would have a stronger case for being interesting than January but would also be easier to steal.

I'm cold about allowing the current rule for the same reason you describe, but I do like the idea of date-based sequences in principle. We could use a deck in Game 3 that is amenable to that.

[StrangerCoug]

Mod: Where are my new cards?

[StrangerCoug]

Finish the odd digital roots with 61, 41, 1, 45, 63, 484

[StrangerCoug]

*grumbles loudly*

29, 71, 89: Primes

[StrangerCoug]

Add 61 to the primes

[StrangerCoug]

42, 7, 8, 1000, numbers whose last digit is less than or equal to its first digit

5, 6, 121, 750 to finish it off

[StrangerCoug]

38, 55, 2 as numbers divisible by their digital root

27, 54, 70, 512 to finish it off

[StrangerCoug]

49 and 625 to complete the numbers equivalent to 1 mod 8

[StrangerCoug]

Add 9 to the numbers three times a prime

[StrangerCoug]

Add 14 to the numbers containing at least one 1

[StrangerCoug]

Pass

Good game.

/in

[StrangerCoug]

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

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

Fair, and I'd still like being allowed to submit by PM.

[StrangerCoug]

I think three months can be a bit long but not impossible for a forum game. Four months takes a Survivor-game level of dedication in my opinion.

[StrangerCoug]

3, 7, 229: Primes

[StrangerCoug]

78, 126, 336, 348: Composite numbers whose digit sum is also composite

[StrangerCoug]

Finish off the numbers divisible by their last digit with 52, 62, 88, 175

[StrangerCoug]

125, 270, 320: 5-smooth numbers

A number is 5-smooth if it can be written as 2

i

3

j

5

k

for some non-negative integers

i

,

j

, and

k

.

[StrangerCoug]

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

1 sounds like the fairest option to me.

[StrangerCoug]

140, 173, 200, 280, 299 to complete 3-digit numbers whose last digit is less than the sum of the first two

[StrangerCoug]

Can I propose that "other than 1" be added to the end of lilith's rule? Otherwise, it allows every number since every number is divisible by 1, which is a perfect square.

[StrangerCoug]

116, 217, 219: Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero

116: January 16 or November 6 in month/day format, 11 June in day/month format
217: February 17 in month/day format, 21 July in day/month format
219: February 19 in month/day format, 21 September in day/month format

As a clarification, 229, but not 292, is intended to be legal in my sequence—the former gives you either February 29 or 22 September, while there's no valid way to make a date in month/day format with the latter.

[StrangerCoug]

45, 100, 150 to finish off the 5-smooth numbers

[StrangerCoug]

Oh, and...

256 (37*7)

37 × 7 = 259, not 256. Did you make a typo?

[StrangerCoug]

72 hours is good

[StrangerCoug]

Acknowledging it's my turn; will play when I'm on desktop.

[StrangerCoug]

202, 351, 204 have a three digit factor other than itself

Complete this sequence with 260, 296, 300, and 354

[StrangerCoug]

95, 138, 246: Squarefree composite numbers

[StrangerCoug]

Add 27 to the multiples thereof

[StrangerCoug]

Finish off the single-digit digital sums with 42, 107, 201, 213, 230

[StrangerCoug]

36, 41, 66, 79, 82 to complete the two-digit numbers

[StrangerCoug]

105, 122, 239, 287: Numbers whose digit sum is squarefree

[StrangerCoug]

Oh, and 1 is squarefree for the purposes of my sequence despite being a square.

[StrangerCoug]

286, 207, 349: Numbers whose digit sum is a perfect square

[StrangerCoug]

73, 231, 318 to complete the "remove digits that are powers of two to get a prime" sequence

I am not sure of the spirit of the rule as regards numbers that don't contain digits that are powers of two, but that is my play if it is allowed.

[StrangerCoug]

Since the person who played the sequence gave her own interpretation of the intent, I will retract it as invalid. Give me time to think of something else...

[StrangerCoug]

73, 157, 231: Numbers none of whose digits are composite

[StrangerCoug]

318, 266, 208: Even numbers whose digit sum is also even

[StrangerCoug]

Could I be PM'd an updated hand, please? I can't find it.

[StrangerCoug]

69. 99, 269: Numbers that contain a 9

[StrangerCoug]

Redacted; see following post.

[StrangerCoug]

Oops Will replay it on my turn since you've seen what it was.

[StrangerCoug]

203 to 5 mod 6

*gets nervous*

[StrangerCoug]

Add 317 ≡ 5 (mod 6)

[StrangerCoug]

Add 31 to numbers whose digit sum is a perfect square

[StrangerCoug]

26, 250, 254 to finish off numbers that start or end with a 2

[StrangerCoug]

/in

I like the Game 2 deck, but the Game 3 deck posed an interesting challenge and resulted in some interesting sequences. I wouldn't mind, say, the numbers from 1 to 250 once or from 1 to 300 once.

[StrangerCoug]

I would just say you get double points for 14, 13 feels kinda arbitrary

I agree with this.

[StrangerCoug]

Mod: Please note sig.

[StrangerCoug]

Sirius's sequence gets my seal of approval *gives thumbs up*

[StrangerCoug]

6, 10, 120, 750 {n = 2

i

× 3

j

× 5

k

for some non-negative integers

i

,

j

,

k

}: 5-smooth numbers

[StrangerCoug]

I believe so

[StrangerCoug]

Another bingo rule approval thing:
All of these numbers mod 14 fit into the range of 6 - 9

I'd give it a weak no, but then again, I haven't bothered to check it against this rule:

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.

[StrangerCoug]

I approve of the base 8 one.

[StrangerCoug]

10, 20, 200: Numbers with only one nonzero digit

[StrangerCoug]

Seems OK at first glance.

[StrangerCoug]

A bit hard-pressed to come up with a complaint.

[StrangerCoug]

61, 56, 216, 66, 13, 1, 8

Do you see a bingo, D3f3nd3r?

[StrangerCoug]

Everyone else, would that be fair to you?

[StrangerCoug]

To add on to my previous post: n % 50 ≤ 20 is equivalent to the intent if there are complaints that one-digit numbers don't "have" a tens digit.

[StrangerCoug]

Let's do that.

1, 8, 13, 56, 61, 66, 216: Numbers equivalent to 1 or 3 mod 5

2/5 = 40%, so I doubt I really need to say more

[StrangerCoug]

If 993 is rejected, then

1, 8, 13, 56, 61, 66, 216: Numbers within 8 of a perfect cube

[StrangerCoug]

If we phrase 993 as "numbers that are odd mod 5" then it looks fine to me.

Do that, then

[StrangerCoug]

11, 32, 34: Numbers whose digit sum is prime

[StrangerCoug]

I'm OK with it.

[StrangerCoug]

484, 17, 70, 600, 5, 63, 25

Do you see anything, D3f3nd3r?

[StrangerCoug]

5, 25, 600: 5-smooth numbers

[StrangerCoug]

Scratch that, then

Let me think...

[StrangerCoug]

5, 17, 63, 70: Squarefree numbers

[StrangerCoug]

Remove 63 from the squarefree numbers, then

[StrangerCoug]

*taps foot impatiently*

[StrangerCoug]

I have to sign into work soon and don't have a lot of time to think, but:

484, 600, 63, 25, 89, 169, 3

Anything, D3f?

[StrangerCoug]

And I'm one number short of being able to finish the squares sequence. Damn.

[StrangerCoug]

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

[StrangerCoug]

25, 169, 484, 900 to complete the squares

[StrangerCoug]

Chord gains 8 points.

I wish we did, but you had credited us with the points already

[StrangerCoug]

"Contains a digit congruent to 1 mod 5"?

[StrangerCoug]

I think it's fair. I just helped D3f3nd3r find a bingo involving digits in the number

[StrangerCoug]

8, 18, 44: Numbers whose digit sum is a perfect power

[StrangerCoug]

Oh, and the power in question has to be at least 2; otherwise you can play literally anything to it

[StrangerCoug]

One is valid, the concern is with the exponent being 1 (because otherwise you’d be able to say any number is a perfect power because itself to the first is itself).

This. Feel free to play them.

[StrangerCoug]

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.

I'm good with disallowing any further such bingos. I do feel like we broke the game, part from this and part from being allowed to post our hands to allow our partners to help us find good sequences. (As for the latter, though, there

is

the game of bridge...)

[StrangerCoug]

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?

Yeah, it's really only been a problem this game where we've been trying to find 14-point bingos. Let's nerf them to 8 points and see if it's still a problem then.

[StrangerCoug]

That's why I propose we first check if nerfing the bingos to 8 points helps before we ban posting hands.

[StrangerCoug]

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?

I prefer the current rule.

[StrangerCoug]

In that case, I think it's reasonable to make an exception for accommodating Nancy.

[StrangerCoug]

10, 30, 35, 220: Multiples of 5

[StrangerCoug]

I have something to gain by allowing it, so I will recuse myself

[StrangerCoug]

65, 89, 729: Numbers whose digit sum is greater than 10

[StrangerCoug]

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

If you know anybody who natively speaks Arabic or Hebrew, I'd be interested in what they consider the first digit. They write right-to-left, but they put the most significant digit on the left, and I believe both read numbers left-to-right.

[StrangerCoug]

54, 5, 500, 125, 4, 40, 961

Do you see any bingos/sequences that can be completed, partner?

[StrangerCoug]

4, 5, 40, 54, 125, 500, 961: Numbers whose first digit is the sum of two distinct perfect squares

Or "at most two distinct perfect squares" if you don't want to allow for 0² + n²

[StrangerCoug]

Or "at most two distinct perfect squares" if you don't want to allow for 0² + n²

[StrangerCoug]

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.

I know I suggested the original variant of this, but wasn't the consensus to nix this? Other than that, looks good

/in

[StrangerCoug]

I'm not opposed to being red, but if someone wants to change theirs to red, then I will take purple so they can have it.

10, 25, 80, 220: Multiples of 5

[StrangerCoug]

Fine by me, too.

[StrangerCoug]

I will submit my move via PM so Not_Mafia can decide whether he'd like to join in. I don't want him to feel like I shut him out of the game out of negligence or to be mean.

[StrangerCoug]

Bingo.

4, 6, 20, 25, 50, 128, 625 - all 5-smooth numbers.

What does that mean - “smooth” numbers?

An

n

-smooth number is a number all of whose prime factors are at most

n

. I've played 5-smooth sequences before, and I believe 3- and 7-smooth numbers have shown up as sequences on occasion, too.

[StrangerCoug]

23, 56, 300: Numbers whose digit sum is prime

[StrangerCoug]

3, 4, 8: Single-digit numbers

[StrangerCoug]

51, 56, 69, 512 to complete "First digit is a 5 or a 6"

[StrangerCoug]

Good idea

[StrangerCoug]

I'm still interested in continuing

[StrangerCoug]

If we break up the teams, then I see Nancy's point in a reboot being more worthwhile.

[StrangerCoug]

If we keep the teams, then continue; if we break them up, then start anew.

[StrangerCoug]

1, 2, 16, 512: Powers of 2

[StrangerCoug]

1, 3, 5: Single-digit numbers