Knights' Tours - Long & Short (Posted on 2009-05-05)
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?
I have been able to find two solutions for the shortest path, the light yellow, 6 moves; the visitation layout of the second is the reverse of the first.
For the longest there were 14 moves and I found 3 occasions of that, light blue, and each having the same visitation layout even though routes were different.
Note: Within comments are quite a few other solutions listed by Charlie and Dej Mar.
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