$7 \cdot 11$ Place the chess pieces on the squares of a chessboard, requiring that in each row, each column, and each diagonal there are exactly an even number of pieces. How many pieces can be placed at most?
［Solution］The maximum number of chess pieces that can be placed is 48.
Since there are 16 diagonals on the chessboard that contain an odd number of squares and they do not share any squares. Therefore, the number of chess pieces cannot exceed
$$
64-16=48
$$

pieces.
In fact, by placing one chess piece on each square except for the 16 squares on the two main diagonals (as shown in the figure), we obtain a configuration with 48 chess pieces that meets the condition.