One of the oldest and best known of chessboard problems is to place the largest possible number of similar pieces on the board such that no two of these pieces are attacking each other. In his book Amusements in mathematics [1], Dudeney considered this problem on a generalised square chessboard containing n 2 cells, and proved that for rooks, queens and bishops this maximum number is equal to n, n and 2 n – 2 respectively.