5. In each cell of a $10 \times 10$ table, a natural number was written. Then, each cell was shaded if the number written in it was less than one of its neighbors but greater than another neighbor. (Two numbers are called neighbors if they are in cells sharing a common side.) As a result, only two cells remained unshaded, and neither of them is in a corner. What is the minimum possible sum of the numbers in these two cells?
Solution. Answer: 20. The estimate matches the estimate in problem 7.5. One of the possible examples is shown below.

| 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: |
| 8 | 10 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| 7 | 8 | 10 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| 6 | 7 | 8 | 10 | 12 | 13 | 14 | 15 | 16 | 17 |
| 5 | 6 | 7 | 8 | 10 | 12 | 13 | 14 | 15 | 16 |
| 4 | 5 | 6 | 7 | 8 | 10 | 12 | 13 | 14 | 15 |
| 3 | 4 | 5 | 6 | 7 | 8 | 10 | 12 | 13 | 14 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 10 | 12 | 13 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 10 | 12 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |