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?

(In reply to solution by Dej Mar)

Pardon but I haven't yet looked at the significance of the variance between this solution and that proposed by Charlie.

I counted moves 6 and 14 as did you, Charlie counted occupied positions being 7 and 15 which momentarily confused me.

The comment which does need addressing is his claim to 24 routes for the longer pathways while you have just 8.

Irrespective, you both did better than I.

Posted by brianjn on 2009-05-06 02:59:41