[Magictour] Symmetric non-crossing tours

I've modified my program to handle symmetric non-crossing knight tours.

Symmetric tours occur on odd-sized boards, and I have explored the 9x9 =
board with the 7 possible symmetries.
If my program is correct, the longest non-crossing symmetric knight tour =
on 9x9 is the following:

d2-b1-c3-a2-b4-a6-c5-b3-d4-c2-e3-d1-f2-h1-i3-g2-h4-f5-g3-e2-f4-d3-e5-f7-d=
6-e8-c7-d5-b6-c8-a7-b9-d8-f9-e7-g8-f6-h7-g5-i4-h6-i8-g7-h9-f8
44 jumps
I have also shorter tours with different symmetries.

For the 11x11 board, there are 2 tours with 70 jumps.
Here are the first 35 moves of both:
f5 e3 g4 f2 h3 g1 i2 k1 j3 h2 i4 g3 h5 f4 g6 e5 d3 e1 c2 a1 b3 d2 c4 d6 =
b5 c3 a4 b6 a8 c9 b7 d8 c6 e7 d5 f6
f1 e3 g4 f2 h3 g1 i2 k1 j3 h2 i4 g3 h5 f4 g6 e5 d3 e1 c2 a1 b3 d2 c4 d6 =
b5 c3 a4 b6 a8 c9 b7 d8 c6 e7 d5 f6

I'm computing the symmetric 13x13, and got 47*2=94 jumps at this =
moment.

It seems that Robin Merson used the symmetric approach to reduce the =
computations on large boards.

JC



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Received on Thu Dec 04 14:24:18 2001