Sequencer | StrangerCoug's turn

[vincentw]

/in next game, looks neat.

[vincentw]

/in please!

[vincentw]

Play 134, 146, 248 as three-digit numbers whose digits are in strictly ascending order.

[vincentw]

Complete the digit sum = 10 sequence with 19, 352, 334.

[vincentw]

Finish the repdigit sequence with 155, 144, and 338.

[vincentw]

For me, 2 deprives the magenta team of half their turns, and 3 essentially means skitter has the ability look at both hands and find the best move that suits the situation, whereas other teams can only hope that their partner has the necessary cards to complete/extend a sequence.

I feel 1 is the most fair here. It's a slight disadvantage, but not too great of one.

[vincentw]

Play 39, 86, and 261 as numbers that, when spelled digit by digit, altogether take 10 or fewer letters. No leading zeroes when spelling, and 0 is spelled as "zero".

[vincentw]

Add 30 to the 5-smooth numbers.

[vincentw]

A throwback to the first bingo: play 120, 143, and 194 as numbers within 2 of a perfect square.

[vincentw]

Add 238 to the strictly ascending sequence.

[vincentw]

Add 339 to the all odds sequence.

[vincentw]

Playing a bingo! I play my whole hand (16, 113, 153, 281, 325, 353, 364) as "any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck".
Primitive meaning that the triangle is as small as possible (no 6, 8, 10 because there's already a 3, 4, 5).
Altogether, there are 143 valid numbers, which cover less than half the deck.

Spoiler: all such triples (duplicates ｢31｣ in red, my hand in blue)

3,   4,   5
5,
  12,  13
8,  15,  17
7,  24,  25
20,  21,  29
12,
  35,  37
9,  40,  41
28,  45,  53
11,  60,  61
16,
  63,  65
33,  56,  
65
48,  55,  73
36,  77,  85
13,
  84,  
85
39,  80,  89
65,
  72,  97
20,
  99, 101
60,
  91, 109
15,
 112, 
113
44, 117, 125
88, 105, 137
24,
 143, 145
17,
 144, 
145
51, 140, 149
85,
 132, 157
119, 120, 169
52, 165, 173
19, 180, 181
104, 
153,
 185
57, 176, 
185
95, 168, 193
28,
 195, 197
84,
 187, 205
133, 156, 
205
140,
 171, 221
21,
 220, 
221
60,
 
221,
 229
105,
 208, 233
120,
 209, 241
32, 255, 257
96, 247, 265
23, 264, 
265
69, 260, 269
115, 252, 277
160, 231, 
281
161, 240, 289
68, 285, 293
136, 273, 305
207, 224, 
305
25,
 312, 313
75, 308, 317
36,
 323, 
325
204, 253, 
325
175, 288, 337
180,
 299, 349
225, 272, 
353
76, 357, 365
27, 
364,
 
365

[vincentw]

Play 121, 209, and 252 as numbers one away from a triangular number (120+1, 210-1, 253-1). The triangular numbers themselves don't count.

[vincentw]

Add 251 to the odd middle sequence.

[vincentw]

Add 240 to multiples of 5.

[vincentw]

Hate to be the bearer of bad news, but it's over the 1% limit.
I've got the number of applicable cards for each two-digit combination:

0 and 1	169	1 and 2	224	2 and 4	177	3 and 7	163	5 and 7	122
0 and 2	169	1 and 3	200	2 and 5	177	3 and 8	163	5 and 8	122
0 and 3	145	1 and 4	177	2 and 6	174	3 and 9	163	5 and 9	122
0 and 4	122	1 and 5	177	2 and 7	169	4 and 5	130	6 and 7	121
0 and 5	122	1 and 6	174	2 and 8	169	4 and 6	127	6 and 8	121
0 and 6	119	1 and 7	169	2 and 9	169	4 and 7	122	6 and 9	121
0 and 7	114	1 and 8	169	3 and 4	153	4 and 8	122	7 and 8	114
0 and 8	114	1 and 9	169	3 and 5	153	4 and 9	122	7 and 9	114
0 and 9	114	2 and 3	200	3 and 6	156	5 and 6	127	8 and 9	114

I think to calculate each probability, it's (matching cards choose 7) / (366 choose 7).
For the overall, take one minus each probability, multiply them all, then finally take one minus that. I got 14.1%.

Bit of a lame brute force proof but it is one regardless. Lists and calculations: https://docs.google.com/spreadsheets/d/ ... d=72116676

Feel free to correct if it's wrong, though!

[vincentw]

Glad to be of help!

I noticed that summing row 371 didn't give the same answer as multiplying row 372 and I'm curious about why summing those isn't another way of arriving at the answer.

Some arrangements of cards can satisfy more than one sequence. For example: [5, 72, 105, 127, 159, 287, 351] satisfies both (2 or 5) and (5 or 7). An extreme example is something like [40, 123, 132, 213, 231, 312, 321] which satisfies 6 such sequences at once. That would make adding all of them incorrect, I think.

[vincentw]

Play 46, 59, and 164 as numbers equivalent to ±1 mod 15.

[vincentw]

Complete the threes sequence with 133, 307, 340, and 362.

[vincentw]

Complete the L with 156, 178, 185, and 344.

[vincentw]

Play 23, 293, and 161 as numbers equivalent to 5 mod 6.

[vincentw]

Add 294 to the 9s sequence.

[vincentw]

This late in the game, a bingo might not be the smartest move, but my hand can't complete any one sequence and I don't wanna risk playing one number and drawing a number that doesn't fit this sequence, so this will have to do.

Play my whole hand as "Day numbers that fall in the first 2 weeks of its respective month". A day number is such that 1 corresponds to 1st Jan, 2 to 2nd Jan and so on until 366 meaning 31st Dec. Because the deck reaches 366, it's only natural for the day number to include a leap day; however, my hand also works with day numbers for non-leap years, if it matters.
My hand translates to 2nd Jan, 10th Jan, 3rd Aug, 11th Sep, 5th Oct, 3rd Nov, and 5th Nov.

There are 168 qualifying numbers, which is less than half the deck. The only meta rule that I can think of is if I switch out "first" for "last", and it has 168 different numbers. Doing 2×(168 choose 7)/(366 choose 7) comes up to be around .8%.

(Shouldn't it be 6 because we have 6 players?)

[vincentw]

Add 11 to 5 mod 6.

[vincentw]

I have to pass, unfortunately.

[vincentw]

/in

Congrats Lilith and Skitter! Also thanks Stranger for putting us over 100 points haha. That 27/28 sequence was so close though, if anyone had that last card it would have won them the game (or tie in our case)!

If I have an input, it's probably to increase the value of a bingo, since it's usually set up over several turns and you could score a few sequences for the same amount of turns as trying to get that last card in your hand. If bingos are worth more, maybe there would be more of an incentive to do them aside of style points. (but that's just me)

About the deck, yeah a smaller one would be nice.

Having played it once, I really enjoyed it! It's really fun seeing the sequences all of us came up with. Thanks Plot for the game, and I don't mind joining again.

[vincentw]

Good to be back, and I like the new bingo rule!

Play 90, 9 and 73 as numbers that, when written in English, have its most common letter represent at least one third of all the letters in the name.
N is in one-third of ninety and one-half of nine, and E is in one-third of seventy three.

[vincentw]

at least 1/2 of the digits of n^2-1 are the same number and the repeating number is a number that is shown on the middle or right hand side of a keypad


anyone have objections?

I think it's in the clear. It matches 57 out of the 139 unique numbers in the deck.

Here's a table with all of them. From left to right: number (n), n²-1, the most common number, proportion of that number over all the digits.

Spoiler: 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 16, 17, 18, 20, 24, 30, 33, 34, 35, 40, 43, 45, 47, 48, 50, 53, 56, 58, 60, 62, 65, 66, 67, 70, 74, 76, 80, 81, 83, 84, 85, 90, 91, 93, 94, 100, 165, 200, 256, 300, 400, 500, 600, 700, 800, 900, 1000

Card	n²-1	Mode	Prop	Card	n²-1	Mode	Prop	Card	n²-1	Mode	Prop
2	3	3	100%	40	1599	9	50%	83	6888	8	75%
3	8	8	100%	43	1848	8	50%	84	7055	5	50%
4	15	5	50%	45	2024	2	50%	85	7224	2	50%
5	24	2	50%	47	2208	2	50%	90	8099	9	50%
6	35	5	50%	48	2303	3	50%	91	8280	8	50%
7	48	8	50%	50	2499	9	50%	93	8648	8	50%
8	63	6	50%	53	2808	8	50%	94	8835	8	50%
9	80	8	50%	56	3135	3	50%	100	9999	9	100%
10	99	9	100%	58	3363	3	75%	165	27224	2	60%
15	224	2	67%	60	3599	9	50%	200	39999	9	80%
16	255	5	67%	62	3843	3	50%	256	65535	5	60%
17	288	8	67%	65	4224	2	50%	300	89999	9	80%
18	323	3	67%	66	4355	5	50%	400	159999	9	67%
20	399	9	67%	67	4488	8	50%	500	249999	9	67%
24	575	5	67%	70	4899	9	50%	600	359999	9	67%
30	899	9	67%	74	5475	5	50%	700	489999	9	67%
33	1088	8	50%	76	5775	5	50%	800	639999	9	67%
34	1155	5	50%	80	6399	9	50%	900	809999	9	67%
35	1224	2	50%	81	6560	6	50%	1000	999999	9	100%

If 0 is included in the keypad limitation, it matches 5 more numbers: 1, 49, 51, 71, and 99; still below half.

[vincentw]

Apologies, between the whole discussion I didn't realise it's already my turn. I feel like I'm at least a little bit responsible for bringing up the bingo rule at the end of the last game. Seems like the balance has gone the other way. I'm not sure how to proceed, but the "what counts as a sequence" rule seems good probably.

The top-most sequence would work better like in Plot's post, yeah.

Don't have much of a good idea for my turn, I guess I'll just add 7 to my sequence.

[vincentw]

Finish the jersey sequence with 15, 28, 45, 92, and 1000.

(I like the sequence too)

[vincentw]

Play 841, 576, and 36 as square numbers.

[vincentw]

From what I checked (up to 1000), I got 1, 2, 14, 35, 77, 98, and 686, and that last one isn't in the deck, so that's 6 numbers. Do you know more numbers that fit?

I'm not sure if sequences with less than 7 qualifying numbers are allowed; the closest the main post has regarding this is the following:

They can be as complicated or as simple as you like, though for complicated ones it is worth checking the deck to make sure there are at least 7 such numbers.

which doesn't explicitly forbid it I suppose (?), but even so it's a dead sequence either way.

[vincentw]

Complete the G7b9 sequence with 11, 63, and 83.

[vincentw]

Playing a bingo! Play 5, 25, 27, 36, 64, 96, and 98 as numbers whose prime factorisations use single digit numbers only.
In order: 5, 5², 3³, 2² × 3², 2⁶, 2⁵ × 3, and 2 × 7².

There are 45 numbers up to 100 that satisfy this rule: 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 50, 54, 56, 60, 63, 64, 70, 72, 75, 80, 81, 84, 90, 96, 98, and 100. I think the proportion gets smaller as we include larger numbers.

[vincentw]

Complete the squarefree sequence with 7, 31, 39, and 71.

[vincentw]

Play 41, 51, and 89 as

numbers equivalent to ±1 mod

15

10

.

now ¹/₃ off! prices revert tomorrow morning

[vincentw]

If it's "all the numbers are comprised of only 4 distinct digits", e.g. [44, 42, 2, 51, 11, 25, 1]:

Spoiler:

we can separate the count to

ones without 0

and

ones with 0

. (For simplicity, I'm considering 1-99)

Without 0 (e.g. 1/4/7/9), any 4 digits will match 4 numbers from 1-9 and 16 from 10-99, a total of 20.

P_{no 0} = (20 choose 7) / (99 choose 7) = 5.21 × 10⁻⁶.

With 0 (e.g. 0/3/5/8), it and the other 3 digits will match 3 numbers from 1-9 and 12 from 10-99, a total of 15.

P_{with 0} = (15 choose 7) / (99 choose 7) = 4.32 × 10⁻⁷.

There are

(9 choose 4) = 126

possibilities without 0 and

(9 choose 3) = 84

with 0.
1−(

(1−P_{no 0})^9C4

×

(1−P_{with 0})^9C3

) should give the answer, if I calculated correctly.

(1 − 5.21 × 10⁻⁶)¹²⁶

×

(1 − 4.32 × 10⁻⁷)⁸⁴

= 99.931%, and 1 minus that is 0.069%.

If it's something like "number ends in any of these 4 digits", then it always matches 40 numbers from 1-100.
(40 choose 7) / (100 choose 7) = 0.00116.
There are (10 choose 4) = 210 possible combinations, so it's 1 − (1 − 0.00116)²¹⁰ = 21.7%.

Do tell me if anything's off!

[vincentw]

Ah Def, I was about to complete that one

I'll instead complete the digit sum = power sequence with 22, 800, and 1000.

[vincentw]

Thank you for the offer, but it kind of feels wrong to have everyone gang up against Sirius.
I'll just take one of their sequences.

Complete the 9s sequence with 900 as well as 78 and 30 which add up to 108.

(If adding 3 numbers together is allowed then I can actually use all 7 in my hand. I can see how it's probably too permissive if interpreted that way though)

[vincentw]

I was going to complete one of my sequences, but I noticed that my hand is a bingo! And it's so satisfying too. I feel like if I split my hand into chunks, I'll only score 2 sequences at most, so might as well cash out.

Play my whole hand as odd numbers.
I believe in you to finish the fight, EP!

[vincentw]

Thanks for the game Plot, congrats team Exsecant, and thanks to Errant for being a good teammate.
I'll take a break for the next game. Good luck to everyone in Game 5!
The rule changes are sound.