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.
This beautiful puzzle goes back to the days of Leonhard Euler and before.
One simple strategy in Knight's Tours is to start in a corner and keep rotating in the same direction, moving on the outer edges of the board.
a8; b6; a4; b2; d1; f2; h1; g3; h5; g7; e8; c7; a6; b4; a2; c1; e2; g1; h3; g5; h7; f8; d7; b8; c6; a5; b3; a1; c2; e1; g2; h4; g6; h8; f7; d8; b7; c5; d3; f4; e6; d4; f3; e5; c4; a3; b1; d2; f1; h2; g4; h6; g8; e7; c8; a7; b5; c3; e4; f6; d5; e3; f5; d6
This is neither re-entrant nor symmetrical.
Not even Garry Kasparov can visualize all possible Knight's Tours in his head. To achieve a Knight's Tour which is both symmetrical and re-entrant, without being allowed to write a program, you must do a lot of trial and error and backtracking.
Edited on March 7, 2004, 6:38 am
Posted by Penny
on 2004-03-07 01:19:06