knight's tour

i just found out that there's a way for a knight to go from square to square on a chess board, and visit every square without visiting any square more than once.

The great card mechanic and prestidigitator Ricky Jay performed this trick blindfolded, or without looking.

http://everything2.com/title/Knight%2527s+Tour?lastnode_id=1305319

In my opinion, practically anyone can learn how to do this:

http://www.frezcogames.com/Knights_Tour.php

This kind of thing may be helpful with visualiztion.

You can break the task down as follows: A knight can't tour on a 4x4 board (try it out if you must) but there are two basic four-square patterns in a 4x4: corner-centre-corner-centre and edge-edge-edge-edge. If you subdivide the board into four 4x4 quarters, start a knight in any quarter and make one of those patterns, you can then make another of them in an adjacent quarter, and then another in the next quarter, and so on. With a little practice you can string sixteen of these together.

I've also written a simple computer program that uses this algorithm:

Define each square in terms of accessibility (the number of squares from which a Knight can reach it: e.g. a1 has accessibility 2, d4 has 8) and remoteness (the number of orthogonal moves it is from d4/d5/e4/e5, whichever is nearest). Start a Knight anywhere and move it to whichever square is the least accessible, and in case of ties, the most remote. As each square is visited, decrease the accessibility of all squares within range by 1. Continue until all squares have been visited.