10.5. On an $8 \times 8$ battleship game field, a "piglet" figure is placed. What is the minimum number of shots needed to definitely hit one "piglet"? (7 points)

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# Solution:

![](https://cdn.mathpix.com/cropped/2024_05_06_89eb40249b21b160d5e6g-4.jpg?height=283&width=283&top_left_y=721&top_left_x=1640)

## Evaluation:

Divide the board into rectangles $4 \times 2$. To ensure that a piglet cannot be placed inside one such figure, at least two shots are required. There are 8 such figures, so at least $8 \cdot 2 = 16$ shots are needed. Example:
![](https://cdn.mathpix.com/cropped/2024_05_06_89eb40249b21b160d5e6g-4.jpg?height=648&width=1534&top_left_y=1326&top_left_x=228)

Answer: 16 shots.

| Criteria | Points |
| :--- | :---: |
| Complete solution to the problem. | 7 |
| Estimation through division into 2x2 squares, without explaining what to do with the fifth cell + correct answer with an example. | 6 |
| Only estimation, without an example. | 4 |
| -Correct answer with an example. -Only estimation through division into 2x2 squares, without explaining what to do with the fifth cell. | 3 |
| Only the correct answer, without estimation and example. | 0 |