2. Anya has a chocolate bar of size 5 x 6 squares. It contains 6 squares, forming a $2 \times 3$ rectangle, in which there are nuts (the rectangle can be positioned either vertically or horizontally). Anya does not know exactly where the nuts are. She wants to eat the smallest number of squares, but in such a way that at least one of them contains nuts. How many squares does she need to eat? Show which squares she should eat and prove that a smaller number is not sufficient.
2. Answer: 5.

Solution. An example of which slices to eat.

![](https://cdn.mathpix.com/cropped/2024_05_06_b2c3f772c20d8092b8ccg-1.jpg?height=369&width=422&top_left_y=318&top_left_x=106)

Evaluation. Let's number the slices as shown in the figure.

| 1 | 1 | 2 | 2 | 3 | 3 |
| :--- | :--- | :--- | :--- | :--- | :--- |
| 1 | 1 | 2 | 2 | 3 | 3 |
| 1 | 1 | 2 | 2 | 3 | 3 |
| 4 | 4 | 4 | 5 | 5 | 5 |
| 4 | 4 | 4 | 5 | 5 | 5 |

Note that we need to eat at least one slice with each number, otherwise the nuts could be in all the slices marked with the number we did not touch.