In some 16 cells of an $8 \times 8$ board, rooks were placed. What is the minimum number of pairs of rooks that could end up attacking each other?
Evaluation. Note that if there are $a$ rooks on a row, then there are $a-1$ pairs of rooks attacking each other in that row. Therefore, the number of pairs of rooks attacking each other horizontally is no less than the number of rooks minus the number of rows, which is no less than 8. Similarly, the number of pairs of rooks attacking each other vertically is no less than 8.

An example for 16 rooks can be achieved, for instance, by placing 8 rooks on the main diagonals.

## Answer

16. 

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