[Magictour] Rectangles

Jelliss asks on his site if the tours 4×10, 4×14, 8×6, 8×10, 8×14, 12×6,
12×10 and 12×14 can be magic.

I modified my program to handle rectangular boards (and discovered a bug in
the bounds thanks to the 4x10 tour).
I ran it on 4x10, 4x14 and 6x8 starting at a1.
On the 4x10 and 4x14, no solution found in a few milliseconds (I think no
solution exists on 4xn boards).
But on 6x8, I got no solution in a few seconds:
0 solutions in 17469 ticks (39680388264 cycles)
Nodes:
0 1 2 10 47 183 738 2433 9006 25257 81671 196791 539952 1085720 2461965
4039892 7346211 9443931 13354738 13779910 16565113 15249976 16050418
13229097 11921716 7863698 5664214 2944456 1621137 640840 284273 84648 32691
8330 1590 126 10 0 0 0 0 0 0 0 0 0 0 0

This means that 10 tours starting at a1 obey the constraints upto square 36.
There is little chance that a 6x8 tour exists.

8x10 tours and above seem reachable, but slow...

JC

PS: The footer is now in english.


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Received on Thu Dec 04 14:24:18 2001