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Knights' Tours - Long & Short (Posted on 2009-05-05) Difficulty: 3 of 5
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?

  Submitted by brianjn    
Rating: 4.0000 (1 votes)
Solution: (Hide)
1   5  
4   2  
  6    
  3   7
1   3  
    6  
  2   4
  5   7
1 14 5 10
8 11 2 13
15 4 9 6
  7 12 3
1 10 5 8
4 7 2 13
11 14 9 6
  3 12 15
1 13 5 10
6 9 2 14
12 4 11 8
  7 15 3
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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionNo Subjectalisha sturdivant2009-05-27 16:42:04
re(3): solution (and variance)Dej Mar2009-05-06 14:34:38
re(2): solution (and variance)Charlie2009-05-06 11:06:54
re: solution (and variance)brianjn2009-05-06 02:59:41
SolutionsolutionDej Mar2009-05-05 18:13:03
re: computer solutionCharlie2009-05-05 17:51:17
Solutioncomputer solutionCharlie2009-05-05 17:34:37
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