The answer is 5 rooks. Here's an example placement 123456789 ||||||||| 1-. . . . . 2-R. . . .R 3-. . . . . 4- .R. . . 5-. . . . . 6- . .R. . 7-. . . . . 8- . . .R. 9-. . . . . (the white squares are exactly the squares with coordinates with the same parity; every odd column and even row contains a rook.) If only 4 rooks are placed, consider the odd-numbered columns and rows, of which there are each 5. At least one column doesn't contain a rook, and at least one row doesn't contain a rook. The intersection of such a column and row is white but not attacked. (EDIT: also you should fix the typo in the title)