Problem 8.1. (15 points) In a $5 \times 5$ grid, each cell is painted one of three colors: red, blue, or green. To the right of each row, the total number of blue and red cells in that row is written, and below each column, the total number of blue and green cells in that column is written.

To the right of the table, the numbers $1,2,3,4,5$ appear in some order. Could the numbers $1,2,3,4,5$ also appear below the table in some order?
Answer: Yes.

Solution. For example, the following coloring will work:

| c | K | k | k | K |
| :---: | :---: | :---: | :---: | :---: |
| 3 | C | K | K | K |
| 3 | 3 | c | K | K |
| 3 | 3 | 3 | c | k |
| 3 | 3 | 3 | 3 | c |
|  | 4 | 3 | 2 | 1 |

## Criteria

The most suitable criterion is used:

15 p. A correct example is provided.

0 p. Only the answer is provided.