Knight's Dilemma

The object of the game is to place a knight on a chess board and, moving it only as knights may in the game of chess, move it from square to square such that it visits every square on the board once and only once.

In chess, the knight moves in an L-shaped path -- two squares in any of the four cardinal directions, then over one. That is, it can move up or down two squares, then left or right one square; alternately, it can move left or right two squares, then up or down one.

Source: The Game Website.