Sequencer | StrangerCoug's turn

[DeathRowKitty]

Eventually this game is going to turn into people giving ridiculous sequence definitions or creating Scrabble-related sequences in some misguided attempt to fit the theme of this game. In fact, why don't I get us started on that?

[8, 18, 34]

My sequence is numbers that are the sum of the Scrabble point values of the (not-necessarily distinct) letters in the American English* spelling of numbers in the deck for this game.

8 is the number of points for 3 (three)
18 is the number of points for 22 (twenty-two)
34 is the number of points for 512 (five hundred twelve)



*American English by convention doesn't include "and" in numbers (e.g. 101 would be written as "one hundred one" rather than "one hundred and one")

[DeathRowKitty]

[38, 82, 84]

Consider a standard 52 card deck that starts in Ace - King, Ace - King, Ace - King, Ace - King order. Number the cards 1-52 in order with the first ace as 1 and the final king as 52. Suppose you perform an infinite sequence of perfect out-shuffles on this deck, each time renumbering the cards in the deck according to their new order. My sequence is those numbers that do not differ by a multiple of 52 from any number that ever indexes a non-face card (face cards are jack, queen, and king) that is 1 greater than a multiple of 4. So basically no ace, 5, or 9 can ever be numbered with a number in the sequence or any number ≡ mod 52 to any number in the sequence.

Every card ever numbered 38 is a 3, 6, 8, 10, J, or Q
Every card ever numbered 32 (84) is also a 3, 6, 8, 10, J, or Q
Every card ever numbered 30 (82) is a 2, 3, 4, 6, 8, or J

[DeathRowKitty]

add [6, 7, 13, 20, 24, 40] to scrabble sequence

Example numbers for which those numbers are the Scrabble point values:

6: two
7: four
13: fifteen
20: twenty-three
24: fifty-five
40: one hundred sixty-five

[DeathRowKitty]

Oh come on, I was building up to stealing it

git gud

[DeathRowKitty]

[56, 57, 64] integers n for which there exists some integer m such that (n-1)/3^m and (n-2)/3^m are each endpoints of intervals removed during (possibly different) steps of the usual construction of the Cantor set (i.e. the construction in which each step removes the middle third of intervals existing after the previous step)


56: (1/3, 2/3) = (27/81,

54

/81) is removed in step 1, (

55

/81, 56/81) is removed in step 4
57: (

55

/81,

56

/81) is removed in step 4
64: (61/81,

62

/81) is removed in step 4, (7/9, 8/9) = (

63

/81, 72/81) is removed in step 2

[DeathRowKitty]

[12, 62, 85]

numbers that are the sum of the proper divisors of some number < 1000 not in the deck for this game.

12 is the sum of the proper divisors of 121 (1 and 11)
62 is the sum of the proper divisors of 118 (1, 2, and 59)
85 is the sum of the proper divisors of 923 (1, 13, and 71)

[DeathRowKitty]

Ha, nice

that's what I get for being lazy about my sequence choices

[DeathRowKitty]

We were trying to set up the sequence of post numbers of 7 consecutive posts in this thread all made by Plotinus

[DeathRowKitty]

Add [13, 15, 16, 27] to numbers in the opening post

[DeathRowKitty]

Can you clarify what you mean by that? The interpretation I'm taking out of it would exclude 55.

[DeathRowKitty]

Ohhh okay I misread it and thought "take the greatest factor" meant you were subtracting it from your original number before subtracting the other factor from that. I reread it like 3 times and never caught my mistake. Oops.

[DeathRowKitty]

Add [36, 78, 120] to triangular numbers

[DeathRowKitty]

I don't know why implosion excluded 19 and 27 in particular but it's perhaps worth noting that there are no 27s remaining in the deck, so I'm not sure he gains much from excluding that particular number.

[DeathRowKitty]

Assuming your rule counts as a meta rule, it's disallowed as a bingo by the meta rule rule and I think most such silliness is in fact covered by that rule. The meta rule

those numbers that end in any of the following 4 or fewer digits

captures > 30% of possible sets of 7 numbers, while the meta rule rule caps meta rules at 1%.

Edit: I oopsied, it's actually just under 20% rather than just over 30%, but still way too high for a meta rule.

[DeathRowKitty]

I agree with most of what implosion said.

As far as bingos are concerned, I agree that the current rules are pretty solid and agree that some degree of subjectivity helps to plug up any gaps. The statement in the rules that you should be thinking forwards rather than backwards for bingos I think covers well what kind of subjectivity you'd want - if a bingo sequence seems like it was specifically constructed awkwardly around one's hand, it had better be good or it's really no fun. Ultimately, Plotinus is a good mod who I trust not to make any sort of egregious calls, so it works out fine.

Not sure how noticeable it was, but the bingo rule actually changed mid-game in response to Plotinus judging a sequence as acceptable that the original reading of the rule probably disallowed. Both the original rule and current rule really aren't perfect (the original rule, while probably more "accurate", was also too cumbersome to expect people to deal with properly), but it's just quibbling over edge cases and trying to rules lawyer the exact line rather than allowing for mod judgment calls would make the game less fun.

For non-bingos, I'm perhaps a bit hesitant about introducing much in the way of rules. I agree that implosion's against-the-spirit-of-the-game-and-also-just-super-unfun examples shouldn't be acceptable, but I'd want to be really careful about where the line is drawn. For example, I thought Felissan was hinting in her comment for this sequence that matches exactly 7 numbers in the deck that she had the only 165 and that no one else should bother trying to complete it. At this point we know that's not actually the case, but I thought it was good strategy to put down a sequence whose completion requires a card that only you have and that it's fair to have that as a perk of having a unique card. It might be unfun with a different starting distribution that causes the situation to arise more often, but I think that, with the current deck, it's fairly unobjectionable. Perhaps I'll feel differently when I see how the end of this game plays out and more cards become effectively unique. Who knows.

Personally, I think the biggest flaw in gameplay is that it's rarely good to add to a sequence without completing it. Every time you do so, you're making a sequence easier for someone else to snipe without making it any easier for yourself. I think the variation Plotinus mentioned in which players pair (or maybe even triple) up would suffer far less from this problem, both because there are fewer people to snipe before it's "your" turn again and because you are in fact making it easier for your teammates to complete the sequences. For the current version of the game, one possible solution (that I don't think I like very much, but will mention anyway) is to say that you can finish a sequence with 6 cards if it's not your first time adding to it. I think 6 may be too few cards to complete a sequence that has to start out with at least 3 cards, which is why I don't think I like it as a solution, but I do think that giving more incentive to add to sequences would be really beneficial to gameplay. Also, having a ton of active sequences that have to be checked on every turn is a bit tedious.

[DeathRowKitty]

My 6 card suggestion is probably better if it only applies to the person who currently owns the sequence. Not sure why I didn't think of that when I was writing my post.

[DeathRowKitty]

Add [8, 47, 49] to the exactly one prime factor sequence, regardless of whether or not it gets retroactively changed :p

I wasn't under the impression that the 6-cards-for-stolen-sequences rule was being considered for being implemented now, but I'd mildly prefer it not be introduced mid-game with so many sequences active.

p.s. that pun by implosion was amazing

[DeathRowKitty]

That was a cool bingo. Very satisfying to look at for some reason

[DeathRowKitty]

[3, 54, 80] numbers n for which there exists some positive integer with exactly 2n primitive roots

27 has 2*3 = 6 primitive roots
379 has 2*54 = 108 primitive roots
401 has 2*80 = 160 primitive roots

[DeathRowKitty]

Add [1, 6, 26, 220] to primitive roots sequence

5 has 2*1 = 2 primitive roots
29 has 2*6 = 12 primitive roots
107 has 2*26 = 52 primitive roots
1331 has 2*220 = 440 primitive roots


I had far too much fun playing around with this sequence tbh and didn't even check if there's another sequence I could/should be completing instead.

[DeathRowKitty]

I want to be angry at DRK about hurting my brain about outshuffles even if someone adds 1 number to it. And I want to see the full portfolio of what a troll implosion is all in one place.

Aw, you don't need that sequence to be angry at me! I'll tell you what...if someone steals that one, I'll try to come up with something far more obnoxious so you don't forget to be mad, okay? <3


As for the points thing, I have a number of points not divisible by 7 because I completed a sequence with 9 cards and you get 1 point for each card in a sequence you complete.

[DeathRowKitty]

Add [21, 33, 84] to multiples of 3

[DeathRowKitty]

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

[DeathRowKitty]

will get to this in the morning, sorry

[DeathRowKitty]

[1, 31, 61] numbers relatively prime to 210

[DeathRowKitty]

[3, 74, 512]

numbers n for which there exists no way to make change for a dollar using exactly n coins, each of which may be a penny, nickel, dime, or quarter, without using at least one penny, one nickel, and one dime

[DeathRowKitty]

hi new popsofctown!

[DeathRowKitty]

Yeah, SC's numbers all work. Numbers that could not be put into that sequence are those n with 4 ≤ n ≤ 100 that satisfy at least one of the following 3 properties:
1) n ≡ 1 (mod 3)
2) n ≡ 0 (mod 4)
3) 6 ≤ n ≤ 19

[DeathRowKitty]

I never got new cards after my last turn btw

[DeathRowKitty]

Forgot it was my turn, sorry.

[10,45,86] to numbers with 2 prime factors

[DeathRowKitty]

pass

also the second number listed for digit-reversed primes should be 14, not 4

[DeathRowKitty]

Whoa, someone actually used the out-shuffles sequence. I thought everyone had just decided to ignore it forever.

For the record, allowable congruence classes were:
6, 11, 21, 41, 30, 8, 15, 29
12, 23, 45, 38, 24, 47, 42, 32
and 52

grouped and ordered above based on cycles of individual cards during the shuffles.

[DeathRowKitty]

pass