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.
Symmetrical Knight Tours can be done on various boards sizes such as 6x6 and 10x10. I've found it very difficult to make a symmetrical Knight's Tour on an 8x8 board. The first 59 moves of the following 8x8 re-entrant tour develop symmetry around the chessboard. However, the last five moves break the symmetry, but do allow for a closed tour.
If you connect move 59 (d5) to (b6), you have 60 squares with symmetry.
To see additional Knight Tours and how to make them, check out http://www.borderschess.org/KnightTour.htm.
Posted by Dan
on 2005-04-28 02:56:25