| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | AA | AB | AC | AD | AE | AF | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2 | Solution to FiveThirtyEight Riddle Classic 2021-05-14: who wins the game of "Veinte" when all payers play optimally - GENERALIZED SOLUTION | |||||||||||||||||||||||||||||||
3 | max. increment per turn | final ranking if all later moves are optimal | total number of players | |||||||||||||||||||||||||||||
4 | 4 | number played at a certain turn | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
25 | This easily extendable spreadsheet shows the general solution under optimal play which can be used for an arbitrary number of players, target number (here: 20) and max. increment per turn (here: 4). The final rankings of players are based on the number of rounds survived. To see more explanations, hover on the highlighted cells. - Stefano | 20 | 1 | 1 | 1 | 3 | 3 | 4 | 3 | 1 | 1 | 9 | 8 | 7 | 4 | 9 | 7 | 6 | 11 | 6 | 17 | 18 | 3 | 16 | 15 | 9 | 4 | 19 | 22 | 12 | 10 | 16 |
26 | 19 | 1 | 2 | 2 | 1 | 1 | 5 | 1 | 2 | 2 | 1 | 10 | 3 | 5 | 1 | 3 | 13 | 8 | 13 | 11 | 6 | 19 | 20 | 7 | 1 | 5 | 17 | 16 | 23 | 14 | 20 | |
27 | 18 | 1 | 2 | 2 | 2 | 2 | 5 | 2 | 2 | 2 | 2 | 10 | 11 | 5 | 2 | 11 | 13 | 10 | 13 | 8 | 13 | 19 | 20 | 21 | 2 | 5 | 11 | 20 | 23 | 14 | 20 | |
28 | 17 | 1 | 2 | 2 | 2 | 2 | 5 | 2 | 2 | 2 | 2 | 10 | 11 | 5 | 2 | 11 | 13 | 10 | 13 | 10 | 13 | 19 | 20 | 21 | 2 | 5 | 8 | 20 | 23 | 14 | 20 | |
29 | 16 | 1 | 2 | 2 | 2 | 2 | 5 | 2 | 2 | 2 | 2 | 10 | 11 | 5 | 2 | 11 | 13 | 10 | 13 | 10 | 13 | 19 | 20 | 21 | 2 | 5 | 10 | 20 | 23 | 14 | 20 | |
30 | 15 | 1 | 1 | 3 | 2 | 2 | 3 | 2 | 6 | 6 | 2 | 9 | 11 | 12 | 2 | 11 | 4 | 10 | 4 | 10 | 13 | 17 | 18 | 21 | 2 | 12 | 10 | 20 | 15 | 24 | 18 | |
31 | 14 | 1 | 2 | 3 | 4 | 4 | 1 | 6 | 6 | 6 | 6 | 1 | 8 | 12 | 6 | 8 | 5 | 14 | 5 | 10 | 4 | 11 | 6 | 3 | 22 | 12 | 10 | 18 | 7 | 24 | 6 | |
32 | 13 | 1 | 2 | 3 | 4 | 4 | 2 | 6 | 6 | 6 | 6 | 2 | 10 | 12 | 6 | 10 | 5 | 14 | 5 | 14 | 5 | 8 | 13 | 19 | 22 | 12 | 10 | 6 | 21 | 24 | 13 | |
33 | 12 | 1 | 2 | 3 | 4 | 4 | 2 | 6 | 6 | 6 | 6 | 2 | 10 | 12 | 6 | 10 | 5 | 14 | 5 | 14 | 5 | 10 | 13 | 19 | 22 | 12 | 14 | 13 | 21 | 24 | 13 | |
34 | 11 | 1 | 2 | 1 | 4 | 4 | 2 | 6 | 4 | 4 | 6 | 2 | 10 | 7 | 6 | 10 | 5 | 14 | 5 | 14 | 5 | 10 | 13 | 19 | 22 | 23 | 14 | 13 | 21 | 9 | 13 | |
35 | 10 | 1 | 1 | 2 | 3 | 5 | 2 | 4 | 5 | 5 | 4 | 2 | 10 | 3 | 13 | 10 | 12 | 9 | 12 | 14 | 5 | 10 | 13 | 19 | 16 | 23 | 14 | 13 | 21 | 1 | 13 | |
36 | 9 | 1 | 2 | 2 | 1 | 5 | 6 | 5 | 5 | 5 | 5 | 6 | 9 | 11 | 13 | 14 | 12 | 1 | 12 | 9 | 12 | 10 | 4 | 17 | 20 | 23 | 14 | 13 | 3 | 2 | 25 | |
37 | 8 | 1 | 2 | 2 | 2 | 5 | 6 | 5 | 5 | 5 | 5 | 6 | 1 | 11 | 13 | 14 | 12 | 2 | 12 | 1 | 12 | 14 | 5 | 11 | 20 | 23 | 24 | 25 | 26 | 2 | 25 | |
38 | 7 | 1 | 2 | 2 | 2 | 5 | 6 | 5 | 5 | 5 | 5 | 6 | 2 | 11 | 13 | 14 | 12 | 2 | 12 | 2 | 12 | 14 | 5 | 8 | 20 | 15 | 24 | 25 | 26 | 2 | 25 | |
39 | 6 | 1 | 2 | 3 | 2 | 3 | 6 | 5 | 7 | 7 | 5 | 6 | 2 | 11 | 4 | 14 | 15 | 2 | 15 | 2 | 12 | 14 | 5 | 10 | 20 | 7 | 24 | 25 | 26 | 2 | 25 | |
40 | 5 | 1 | 1 | 3 | 2 | 1 | 4 | 7 | 7 | 7 | 7 | 4 | 2 | 8 | 5 | 9 | 15 | 2 | 15 | 2 | 15 | 14 | 5 | 10 | 18 | 21 | 24 | 25 | 26 | 27 | 4 | |
41 | Twitter: @s_perfetti | 4 | 1 | 2 | 3 | 4 | 2 | 5 | 7 | 7 | 7 | 7 | 5 | 2 | 10 | 5 | 1 | 15 | 16 | 15 | 2 | 15 | 9 | 12 | 10 | 6 | 21 | 9 | 4 | 19 | 27 | 5 |
42 | 3 | 1 | 2 | 3 | 4 | 2 | 5 | 7 | 7 | 7 | 7 | 5 | 6 | 10 | 5 | 2 | 15 | 16 | 15 | 16 | 15 | 1 | 12 | 10 | 13 | 21 | 1 | 5 | 17 | 27 | 5 | |
43 | 2 | 1 | 2 | 1 | 4 | 2 | 5 | 7 | 3 | 3 | 7 | 5 | 6 | 10 | 5 | 2 | 7 | 16 | 7 | 16 | 15 | 2 | 12 | 14 | 13 | 21 | 2 | 5 | 11 | 27 | 5 | |
44 | 1 | 1 | 2 | 2 | 4 | 2 | 5 | 3 | 8 | 8 | 3 | 5 | 6 | 10 | 12 | 2 | 3 | 16 | 3 | 16 | 7 | 2 | 12 | 14 | 13 | 3 | 2 | 5 | 8 | 22 | 5 | |
45 | the riddle answers are here in green => | the final round is won by player letter | A | B | B | C | B | E | G | H | H | G | E | C | L | G | B | K | C | L | C | L | B | K | V | H | Q | B | L | X | D | M |
46 | i.e. player nr. | 1 | 2 | 2 | 3 | 2 | 5 | 7 | 8 | 8 | 7 | 5 | 3 | 12 | 7 | 2 | 11 | 3 | 12 | 3 | 12 | 2 | 11 | 22 | 8 | 17 | 2 | 12 | 24 | 4 | 13 | |
47 | next number | final rankings under optimal play | ||||||||||||||||||||||||||||||
48 | player letter | player nr. | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 |
49 | A | 1 | 1 | 2 | 2 | 4 | 2 | 5 | 3 | 8 | 8 | 3 | 5 | 6 | 10 | 12 | 2 | 3 | 16 | 3 | 16 | 7 | 2 | 12 | 14 | 13 | 3 | 2 | 5 | 8 | 22 | 5 |
50 | B | 2 | 1 | 1 | 2 | 1 | 4 | 7 | 3 | 3 | 7 | 4 | 2 | 8 | 5 | 1 | 7 | 2 | 7 | 2 | 15 | 1 | 5 | 10 | 6 | 21 | 1 | 4 | 11 | 27 | 4 | |
51 | C | 3 | 3 | 1 | 3 | 6 | 5 | 7 | 7 | 5 | 6 | 1 | 11 | 4 | 9 | 15 | 1 | 15 | 1 | 12 | 9 | 4 | 8 | 18 | 7 | 9 | 25 | 17 | 2 | 25 | ||
52 | D | 4 | 3 | 5 | 2 | 4 | 5 | 5 | 4 | 2 | 9 | 3 | 13 | 14 | 12 | 9 | 12 | 9 | 5 | 14 | 13 | 11 | 20 | 15 | 24 | 13 | 19 | 1 | 13 | |||
53 | E | 5 | 4 | 1 | 6 | 4 | 4 | 6 | 1 | 10 | 7 | 6 | 10 | 5 | 14 | 5 | 14 | 4 | 10 | 6 | 17 | 16 | 23 | 14 | 6 | 26 | 9 | 6 | ||||
54 | F | 6 | 3 | 2 | 6 | 6 | 2 | 9 | 8 | 12 | 2 | 8 | 4 | 10 | 4 | 10 | 13 | 8 | 18 | 19 | 22 | 12 | 10 | 18 | 3 | 24 | 18 | |||||
55 | G | 7 | 1 | 2 | 2 | 1 | 10 | 11 | 5 | 1 | 11 | 13 | 8 | 13 | 8 | 6 | 11 | 20 | 3 | 2 | 5 | 8 | 20 | 21 | 14 | 20 | ||||||
56 | H | 8 | 1 | 1 | 9 | 8 | 3 | 4 | 9 | 3 | 6 | 11 | 6 | 11 | 18 | 17 | 16 | 21 | 1 | 4 | 11 | 16 | 7 | 10 | 16 | |||||||
57 | I | 9 | 9 | 10 | 11 | 7 | 13 | 14 | 7 | 16 | 17 | 18 | 17 | 20 | 19 | 22 | 7 | 9 | 25 | 17 | 22 | 15 | 29 | 30 | ||||||||
58 | J | 10 | 8 | 3 | 12 | 6 | 10 | 15 | 2 | 3 | 16 | 19 | 16 | 3 | 2 | 15 | 24 | 13 | 19 | 27 | 23 | 8 | 22 | |||||||||
59 | K | 11 | 7 | 5 | 2 | 8 | 12 | 1 | 7 | 2 | 3 | 2 | 21 | 1 | 23 | 14 | 6 | 26 | 2 | 12 | 11 | 27 | ||||||||||
60 | L | 12 | 4 | 1 | 11 | 5 | 9 | 15 | 1 | 7 | 1 | 7 | 9 | 12 | 10 | 18 | 3 | 1 | 28 | 17 | 2 | |||||||||||
61 | M | 13 | 9 | 3 | 4 | 14 | 12 | 9 | 15 | 9 | 15 | 14 | 5 | 8 | 20 | 21 | 9 | 5 | 19 | 1 | ||||||||||||
62 | N | 14 | 7 | 13 | 10 | 5 | 14 | 12 | 14 | 12 | 10 | 4 | 11 | 16 | 7 | 24 | 4 | 26 | 9 | |||||||||||||
63 | O | 15 | 6 | 8 | 4 | 10 | 5 | 10 | 5 | 8 | 13 | 17 | 22 | 15 | 14 | 25 | 3 | 24 | ||||||||||||||
64 | P | 16 | 11 | 13 | 8 | 4 | 8 | 4 | 11 | 6 | 19 | 2 | 23 | 10 | 13 | 21 | 14 | |||||||||||||||
65 | Q | 17 | 6 | 11 | 13 | 11 | 13 | 17 | 18 | 3 | 1 | 12 | 8 | 6 | 7 | 10 | ||||||||||||||||
66 | R | 18 | 17 | 6 | 17 | 6 | 19 | 20 | 21 | 9 | 5 | 11 | 18 | 15 | 29 | |||||||||||||||||
67 | S | 19 | 18 | 19 | 18 | 3 | 16 | 7 | 24 | 4 | 17 | 20 | 23 | 8 | ||||||||||||||||||
68 | T | 20 | 3 | 20 | 21 | 22 | 15 | 14 | 25 | 19 | 16 | 12 | 11 | |||||||||||||||||||
69 | U | 21 | 16 | 7 | 2 | 23 | 10 | 13 | 26 | 22 | 28 | 17 | ||||||||||||||||||||
70 | V | 22 | 15 | 1 | 12 | 8 | 6 | 3 | 27 | 5 | 19 | |||||||||||||||||||||
71 | W | 23 | 9 | 5 | 11 | 18 | 21 | 2 | 4 | 26 | ||||||||||||||||||||||
72 | X | 24 | 4 | 17 | 20 | 7 | 1 | 25 | 3 | |||||||||||||||||||||||
73 | Y | 25 | 19 | 16 | 15 | 9 | 13 | 21 | ||||||||||||||||||||||||
74 | Z | 26 | 22 | 23 | 24 | 6 | 7 | |||||||||||||||||||||||||
75 | AA | 27 | 12 | 14 | 18 | 15 | ||||||||||||||||||||||||||
76 | AB | 28 | 10 | 20 | 23 | |||||||||||||||||||||||||||
77 | AC | 29 | 16 | 12 | ||||||||||||||||||||||||||||
78 | AD | 30 | 28 |