Zhendarov R.G.

Cells of a $9 \times 9$ board are painted in a checkerboard pattern with black and white colors (corner cells are white). What is the minimum number of rooks needed to be placed on this board so that all white cells are under attack by these rooks? (A rook attacks all cells in the row and column where it is placed.)
Evaluation. A rook attacks no more than two cells of a white diagonal, so four rooks are insufficient.

Example. Let's place the rooks on the squares indicated in the figure.

![](https://cdn.mathpix.com/cropped/2024_05_06_3b3613da627e706c6878g-15.jpg?height=489&width=472&top_left_y=1&top_left_x=799)

## Answer

5 rooks.