3. Is it possible to cut a grid rectangle $5 \times 10$ along the grid lines into rectangles of areas $1, 2, 4, 8$ such that no rectangles of the same area touch each other, neither by vertices nor by sides? (Cells are squares of unit area.)
3. Answer: it is possible.

The cutting is shown in the figure.

![](https://cdn.mathpix.com/cropped/2024_05_06_ecbb22e5990386df1db8g-1.jpg?height=286&width=539&top_left_y=901&top_left_x=740)

Grading criteria:

A correct example of cutting is provided: 7 points.