# [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  .  .  .

__END__
```