In how many ways can we place two rooks of different colors on a chessboard so that they do not attack each other?
A rook is placed on any square of a chessboard, and the other rook can be placed on any of the remaining 63 squares, except for the 7-7 squares that are in the same row or column as the square occupied by the first rook. Therefore, the first rook can be placed in 64 different ways, while the second rook can choose from $63-2 \cdot 7=49$ squares. Thus, the two rooks can be placed in a total of $64 \cdot 49=3136$ ways that meet our condition.

Tolnai Tibor (Szombathely, Nagy Lajos g. II. o. t.)