9.7. Place an even number of pawns on each row, each column, and each diagonal of a chessboard. Question: For this arrangement, what is the maximum number of pawns that can be placed?
Solution
9. 7. 48.
Firstly, note that on a chessboard, there are 16 diagonals containing an odd number of squares, and these diagonals do not share any squares. Therefore, the number of pieces will not exceed . If a piece is placed in each square except those on the two main diagonals, the condition will be satisfied, as shown in the figure above.
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