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Knight's Tour (2) (Posted on 2004-03-06) Difficulty: 2 of 5
On a normal 8x8 chessboard, find a complete Knight's Tour.

A Knight's move is as in chess, an L shaped move, 2 squares in one direction and 1 square in the other direction.)

A Knight's Tour is one where the knight passes through each square exactly once.

You may start on any square you wish.

* For extra credit, come up with a re-entrant tour: at the end, the knight is exactly one knight's move away from the starting square.

* For EXTRA extra credit, make sure that the path is, in some way, symmetrical.

Since "Knight's Tour" is a term used outside the scope of this problem, I'm sure you can find an answer on the internet. Please find an independent solution.

This does not require a computer program.

No Solution Yet Submitted by SilverKnight    
Rating: 2.6667 (3 votes)

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Some Thoughts more method | Comment 6 of 9 |

I went on google to look for a site that would allow you to try the tour and didn't give you a solution.  I swear that I didn't look at any solutions.  I got this.  That's, in case the link doesn't work.

After trying it many times, I developed a little technique.  I split the tour into four parts.  Each part goes around in a circle in almost the same path.  For example, in the grid below, the numbers represent the number of the path.  The paths go together to complete the whole square.


I hope that turns out.  As you can see, the four paths come in from the left and come out on the bottom.  I also thought up other transformations for all four paths to move at once.  Unfortunately, for this to work out, the paths have to go in a circle, and they all must connect.  I'm having trouble making it both symmetrical and connective.  I've tried radial symmetry, symmetry over a line, over a dot, but I can't get it to work out.

Here's some other transformations:




I can't get those arrows to work!  And the link too!  It would have been clearer if I could fix them.

Edited on March 7, 2004, 1:41 am

Edited on March 7, 2004, 1:41 am

Edited on March 7, 2004, 1:43 am

Edited on March 7, 2004, 1:44 am

Edited on March 7, 2004, 1:50 am
  Posted by Tristan on 2004-03-07 01:35:16

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