[seqfan] Re: nice new board game puzzle A337663
hv at crypt.org
hv at crypt.org
Wed Oct 21 17:44:01 CEST 2020
Peter Kagey <peterkagey at gmail.com> wrote:
:This is a really lovely sequence. I'd be interested to know more about
:this, such as [...] How many maximal games?
Here's some data on that for k = 2, 3, 4; I'll have it for 5 sometime
later. Currently working on making runs continuable, so I can start
a many-day run for n=6 without having to complete it in one go.
Hugo
---
n = 2: best = 16, count(best) = 2;
n = 3: best = 28, count(best) = 8;
n = 4: best = 38, count(best) = 4.
n = 2
=====
9 . 12 . .
5 4 8 . .
10 1 3 . 13
11 . 2 6 7
. . . 1 14
. . 16 15 .
9 . 12 . .
5 4 8 . .
10 1 3 . .
11 . 2 6 7
. 13 . 1 .
. . 14 15 16
n = 3
=====
26 17 . 24 . . . . .
. 9 8 16 . . . . .
. 23 1 7 27 . . . .
. 3 2 4 . . . . .
. 15 10 1 5 11 . . .
. 25 . 22 6 . 12 13 14
. . . 28 . 18 . 1 .
. . . . . . 19 20 21
26 17 . 24 . . . . .
. 9 8 16 . . . . .
. 23 1 7 . . . . .
. 3 2 4 28 . . . .
. 15 10 1 5 11 . . 27
. 25 . 22 6 . 12 13 14
. . . . . 18 . 1 .
. . . . . . 19 20 21
26 17 . 24 . . . . .
. 9 8 16 . . . . .
. 23 1 7 . . . . .
. 3 2 4 . . . . .
. 15 10 1 5 11 . . 27
. 25 . 22 6 . 12 13 14
. . . 28 . 18 . 1 .
. . . . . . 19 20 21
. . . . 12 26 .
. . 21 11 1 13 .
. . . 10 . 14 27
23 18 9 . 24 . .
. 5 4 . . . .
25 . 1 3 . 28 .
. 20 . 2 6 . 22
. . 19 . 1 7 15
. . . 17 16 8 .
. . . . 12 26 .
. . 21 11 1 13 .
. . . 10 . 14 27
23 18 9 . . . .
. 5 4 . . . .
25 . 1 3 . 28 .
. 20 . 2 6 . 22
. . 19 . 1 7 15
. . . 17 16 8 .
. . . . . 24 .
. . . . 12 26 .
. . 21 11 1 13 .
. . . 10 . 14 27
. 18 9 23 . . .
. 5 4 . . . .
25 . 1 3 . 28 .
. 20 . 2 6 . 22
. . 19 . 1 7 15
. . . 17 16 8 .
. . . . . 24 .
. . . 27 . . .
. . . 14 13 26 .
. . 24 . 1 12 .
. . . 10 11 . .
23 18 9 . 21 . .
. 5 4 . . . .
25 . 1 3 . 28 .
. 20 . 2 6 . 22
. . 19 . 1 7 15
. . . 17 16 8 .
. . . 27 . . .
. . . 14 13 26 .
. . . . 1 12 .
. . . 10 11 . .
23 18 9 . 21 . .
. 5 4 . . . .
25 . 1 3 . 28 .
. 20 . 2 6 . 22
. . 19 . 1 7 15
. . . 17 16 8 .
. . . . . 24 .
n = 4
=====
. . . . 31 32 . . .
. 36 21 30 1 . . . .
. 15 . 6 2 27 20 . .
24 8 7 . 3 1 . 19 33
. 1 16 26 34 4 5 14 .
18 17 . . . . 9 28 .
35 . 29 . 11 10 . 37 .
. . . 12 1 22 . . .
. . 25 13 . 23 . . .
. . 38 . . . . . .
. . . . 31 32 . . .
. 36 21 30 1 . . . .
. 15 . 6 2 27 20 . .
24 8 7 . 3 1 . 19 33
. 1 16 26 34 4 5 14 .
18 17 . . . . 9 28 .
35 . 29 . 11 10 . 37 .
. . . 12 1 22 . . .
. . 25 13 . 23 . . .
. . . 38 . . . . .
. . . . 31 32 . . .
. . 21 30 1 . . . .
. 15 . 6 2 27 20 . .
24 8 7 . 3 1 . 19 33
. 1 16 26 34 4 5 14 .
18 17 . . . . 9 28 .
35 . 29 . 11 10 . 37 .
. . . 12 1 22 . . .
. . 25 13 . 23 . . .
. . 38 . 36 . . . .
35 18 36 . 23 . 21 . 32 . . . .
. 17 1 . 14 9 . 12 20 . . . .
. 34 16 15 . 5 4 8 . . 26 27 .
. . . 31 . 10 1 3 19 25 . 1 28
. . . . . 11 . 2 6 . 33 . 29
. . . . . 24 13 22 1 7 . . .
. . . . . 37 . . 30 38 . . .
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