On a 4 x 4 board what is the longest and the shortest 'tour' that a knight may make subject to no valid next destination being available, and not being able to revisit a prior square. The knight starts in the top left cell (A).

A B C D E F G H I J K L M N O P

Dismissing mirrored tours (A-P being the mirror) how many such routes are there?

Note: the 4x4 grid is symmetrical along the diagonal axis AFKP.
Dismissing the "mirrored" paths along this axis there are four 6-move paths and twenty-four 14-move paths. 

Shortest (6 move) paths:
A,J,C, L, N,G,P
A,J,C, E, N,G,P
A,J,H, B, I,G,P
A,J,H, O, I,G,P
[Mirrored paths]
A,G,I, B, H,J,P
A,G,I, O, H,J,P
A,G,N, E, C,J,P
A,G,N, L, C,J,P

Longest (14 move) paths:
A,J,C, L,N,E, K,D,F, O,H,B, I,G,P
A,J,C, L,N,E, K,M,F, O,H,B, I,G,P
A,J,C, E,N,L, F,D,K, B,H,O, I,G,P
A,J,C, E,N,L, F,M,K, B,H,O, I,G,P
A,J,H, B,I,O, F,D,K, E,C,L, N,G,P
A,J,H, B,I,O, F,M,K, E,C,L, N,G,P
A,J,H, O,I,B, K,M,F, L,C,E, N,G,P
A,J,H, O,I,B, K,D,F, L,C,E, N,G,P
A,J,P, G,I,B, H,O,F, M,K,E, N,L,C
A,J,P, G,I,B, H,O,F, M,K,E, C,L,N
A,J,P, G,I,B, H,O,F, D,K,E, N,L,C
A,J,P, G,I,B, H,O,F, D,K,E, C,L,N
A,J,P, G,I,O, H,B,K, M,F,L, N,E,C
A,J,P, G,I,O, H,B,K, M,F,L, C,E,N
A,J,P, G,I,O, H,B,K, D,F,L, N,E,C
A,J,P, G,I,O, H,B,K, D,F,L, C,E,N
A,J,P, G,N,E, C,L,F, M,K,B, I,O,H
A,J,P, G,N,E, C,L,F, M,K,B, H,O,I
A,J,P, G,N,E, C,L,F, D,K,B, I,O,H
A,J,P, G,N,E, C,L,F, D,K,B, H,O,I
A,J,P, G,N,L, C,E,K, M,F,O, I,B,H
A,J,P, G,N,L, C,E,K, M,F,O, H,B,I
A,J,P, G,N,L, C,E,K, D,F,O, I,B,H
A,J,P, G,N,L, C,E,K, D,F,O, H,B,I
[Mirrored paths]
A,G,I, O,H,B, K,M,F, L,N,E, C,J,P
A,G,I, O,H,B, K,D,F, L,N,E, C,J,P
A,G,I, B,H,O, F,M,K, E,N,L, C,J,P
A,G,I, B,H,O, F,D,K, E,N,L, C,J,P
A,G,N, E,C,L, F,D,K, B,I,O, H,J,P
A,G,N, E,C,L, F,M,K, B,I,O, H,J,P
A,G,N, L,C,E, K,D,F, O,I,B, H,J,P
A,G,N, L,C,E, K,M,F, O,I,B, H,J,P
A,G,P, J,C,E, N,L,F, D,K,B, H,O,I
A,G,P, J,C,E, N,L,F, D,K,B, I,O,H
A,G,P, J,C,E, N,L,F, M,K,B, H,O,I
A,G,P, J,C,E, N,L,F, M,K,B, I,O,H
A,G,P, J,C,L, N,E,K, D,F,O, H,B,I
A,G,P, J,C,L, N,E,K, D,F,O, I,B,H
A,G,P, J,C,L, N,E,K, M,F,O, H,B,I
A,G,P, J,C,L, N,E,K, M,F,O, I,B,H
A,G,P, J,H,B, I,O,F, D,K,E, C,L,N
A,G,P, J,H,B, I,O,F, D,K,E, N,L,C
A,G,P, J,H,B, I,O,F, M,K,E, C,L,N
A,G,P, J,H,B, I,O,F, M,K,E, N,L,C
A,G,P, J,H,O, I,B,K, D,F,L, C,E,N
A,G,P, J,H,O, I,B,K, D,F,L, N,E,C
A,G,P, J,H,O, I,B,K, M,F,L, C,E,N
A,G,P, J,H,O, I,B,K, M,F,L, N,E,C

Edited on May 6, 2009, 4:14 am

Posted by Dej Mar on 2009-05-05 18:13:03