Task 1. The squares of a $9 \times 9$ board are chess-colored, with the corner squares being white. What is the minimum number of rooks that need to be placed on the board so that they threaten all the white squares? (A rook threatens all the squares in the row and column it is in.)
Solution: An example with 5 towers threatening all white fields is shown in the drawing.

![](https://cdn.mathpix.com/cropped/2024_06_03_50a7166c9c4d457d4b4dg-1.jpg?height=411&width=419&top_left_y=925&top_left_x=790)

On the other hand, a tower on a white field threatens 7 or 9 white fields, and a tower on a black field threatens 9 white fields. Since there are 41 white fields, four towers are clearly not sufficient.