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 Knight's Tour (2) (Posted on 2004-03-06)
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.
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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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 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 http://www.geocities.com/allentownchess/knightstour.html, 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.

3221
1132
2212
4213
^^^^

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:

1234
3412

412
234
1
3

AAAAAAAAUUUUUUUGGGGGGGGGGGGGGGHHHHHHH!!!!!!!!!

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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