8. (4 points) In an $11 \times 11$ table, integers from 0 to 10 are arranged (naturally, numbers can repeat, not all specified numbers necessarily appear). It is known that in each $3 \times 2$ or $2 \times 3$ rectangle, the sum of the numbers is 10. Find the smallest possible value of the sum of the numbers in the entire table.

Answer: 200

#
# Solution:

The right part of the figure below shows the table divided into 20 rectangles and one cell. This means that the sum of the numbers in the entire table is no less than the sum of the numbers in these 20 rectangles, which is 200.

An example is provided in the left part of the figure, cells filled with zeros are left blank for convenience.

|  |  | 5 |  |  | 5 |  |  | 5 |  |  |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
|  | 5 |  |  | 5 |  |  | 5 |  |  | 5 |
| 5 |  |  | 5 |  |  | 5 |  |  | 5 |  |
|  |  | 5 |  |  | 5 |  |  | 5 |  |  |
|  | 5 |  |  | 5 |  |  | 5 |  |  | 5 |
| 5 |  |  | 5 |  |  | 5 |  |  | 5 |  |
|  |  | 5 |  |  | 5 |  |  | 5 |  |  |
|  | 5 |  |  | 5 |  |  | 5 |  |  | 5 |
| 5 |  |  | 5 |  |  | 5 |  |  | 5 |  |
|  |  | 5 |  |  | 5 |  |  | 5 |  |  |
|  | 5 |  |  | 5 |  |  | 5 |  |  | 5 |

![](https://cdn.mathpix.com/cropped/2024_05_06_f3802874779b2cbb336bg-6.jpg?height=474&width=639&top_left_y=1533&top_left_x=797)