The code lock will open if the numbers from 1 to 16 are arranged in the cells of a $4 \times 4$ square such that the sum of the numbers in each $2 \times 2$ square is divisible by 17. Is it possible to open such a lock?
See fig. The sum of the numbers in each $2 \times 2$ square is 34.

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

Answer

It is possible.

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