10.5. Place 16 rooks on an $8 \times 8$ chessboard. How many pairs of rooks can attack each other (a pair of rooks can attack each other if they are in the same row or column and there are no other rooks between them)?
10.5.16 Correct.

It should be noted that if there are $a$ rooks in a row, then there are $a-1$ pairs of rooks that can attack each other in that row. Therefore, the number of rooks that can attack each other horizontally will not be less than 8 pairs.

Similarly, the number of rooks that can attack each other vertically will not be less than 8 pairs.

There exists an arrangement where exactly 16 pairs of rooks can attack each other, for example, by placing all the rooks on the two main diagonals (top-left to bottom-right, top-right to bottom-left).