## Monday, 8 November 2010

### Five-Directional Knight's Tour Problem

It's over a month since I posted a message on this Diary, but since I seem to be the only person to whom it is of any interest that probably won't have been noticed.

The most interesting occurrence of the past month was that one of my correspondents. Harold Cataquet, sent me details of a new knight's tour discovery by Jonathan Welton from Crowthorne, Berks. This can be presented in the form of a puzzle:

To construct a closed knight's tour of the standard chessboard that uses moves in exactly five of the eight possible knight-move directions.

There is just one solution, apart from rotations and reflections. I was able to confirm this by trying to construct a tour. It required only one page of workings on a sheet of squared paper, and involved 21 diagrams though this is far more than is really necessary. I won't publish the answer here, since Mr Welton will probably want it to appear somewhere in print first.

However here is an open-tour solution that I found, starting and finishing on adjacent cells.

17 32 21 28 47 52 45 50
20 29 18 15 22 49 26 53
33 16 31 48 27 46 51 44
30 19 34 23 14 43 54 25
09 38 13 42 55 24 59 04
12 35 10 07 60 03 64 01
39 08 37 56 41 62 05 58
36 11 40 61 06 57 02 63

This was my first attempt at finding a solution on 25 October.