5. Vasya came up with a new ship for a naval battle - the "combat donut." This ship consists of all the cells of a 3 x 3 square, except for its central cell. On an 8 x 8 field, one combat donut was placed. What is the minimum number of shots needed to guarantee hitting it?
5. Answer: 8 shots.

Solution. Note that if the donut is placed on a 4x4 field, one shot is not enough to guarantee hitting it. Indeed, if the shot is fired into a cell adjacent to the side of the square, the donut can be placed next to the opposite side. If the shot is fired into one of the four central cells of the square, the donut can be placed such that its center coincides with the cell that was shot. Therefore, at least two shots are needed to guarantee hitting it. By dividing the $8 \times 8$ field into four $4 \times 4$ squares, we get that at least 8 shots are required to guarantee hitting the donut.

![](https://cdn.mathpix.com/cropped/2024_05_06_c9b4ec60b8dbc8f81bb3g-2.jpg?height=314&width=320&top_left_y=711&top_left_x=157)

If 8 shots are made as shown in the figure, we will definitely hit the donut.