Place different positive integers, not greater than 25, in the cells of a $3 \times 3$ square, such that in any pair of adjacent cells (sharing a side), one number is divisible by the other.
The central cell has the most neighbors - let's put 1 there. In the cells adjacent to the central one, we will place smaller numbers - 2, 3, 4, 5. Every number is divisible by the central number (any number is divisible by 1). To ensure the condition is met for the corner cells as well, we will place in each corner the product of its neighbors. This way, one possible example is:

| 10 | 2 | 8 |
| :--- | :--- | :--- |
| 5 | 1 | 4 |
| 15 | 3 | 12 |

Other examples can also be devised.