Across the board: the Mathematics of Chessboard Problems.

Watkins melds the classic game of chess with the equally entertaining realm of recreational mathematics. He surveys well-known challenges based on the movements of chess pieces. For instance, the Knight's Tour Problem considers how a knight can cover every square on the board once and end on its starting square. Queen's Domination examines how many queens would have to be on a board for every square to be either targeted or occupied by one of the queens. Watkins also turns back 5 centuries to explore Guarini's Problem, which deals with moves required to exchange different-colored knights from four corners of the board. The puzzles also extend to three-dimensional chessboards. A full history and the solution to each problem are detailed in these pages. By offering challenges and then giving the answers, Watkins introduces readers to graph theory and other ideas at the forefront of mathematics--all laid out in black and white on a chessboard. Princeton U Pr, 2004, 257 p., b&w illus., hardcover, $24.95.