Consider an 8×8 chessboard and a piece, R, that starts at the lowest left square and takes a tour of the board, visiting each square, never visiting a square twice, and ending up at the starting square. Each move goes from a square to an adjacent square in either the horizontal or vertical direction. Thus the tour requires 64 moves.

Is it possible that in such a tour, R takes the same number of horizontal moves as vertical ones?

Source: A review of "International Mathematical Tournament of Towns 1997-2002," by Clint Lee in *Crux Mathematicorum*, May 2007.

© Copyright 2007 Stan Wagon. Reproduced with permission.