7,8

What is the maximum number of rooks that can be placed on an 8x8 chessboard so that they do not attack each other

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Obviously, 8 rooks can be placed, for example, along the diagonal from a1 to h8. Let's prove that it is impossible to place 9 rooks that do not attack each other.

On one horizontal row, there cannot be more than one rook - otherwise, they would attack each other; therefore, the number of rooks that can be placed cannot exceed the number of rows on the board, which is eight. Consequently, it is impossible to place more than 8 rooks on the board.