9.5. What is the maximum number of figures consisting of 4 1x1 squares, as shown in the diagram, that can be cut out from a $6 \times 6$ table, if cutting can only be done along the grid lines?

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# Solution:

Example:

![](https://cdn.mathpix.com/cropped/2024_05_06_84d1d0b2835d227e7074g-3.jpg?height=343&width=488&top_left_y=388&top_left_x=264)

The diagram shows that 8 figures can be cut out.

Evaluation:

![](https://cdn.mathpix.com/cropped/2024_05_06_84d1d0b2835d227e7074g-3.jpg?height=357&width=488&top_left_y=458&top_left_x=1452)

We will color the even-numbered columns in gray and the odd-numbered columns in white. For each figure cut out, there will be 2 more cells of one color than the other. Therefore, to cut out the entire table, we need the number of figures with three gray cells to be equal to the number of figures with three white cells, which means the number must be even. 36:4=9, which is an odd number, so it is impossible to cut out the entire figure.

Answer: 8 figures.

| Criteria | Points |
| :--- | :---: |
| Complete solution of the problem. | 7 |
| Only the evaluation, without an example. | 5 |
| Correct answer with an example. | 2 |
| Only the correct answer, without evaluation and example. | 0 |
| Incorrect solution. | 0 |