64. A nearsighted rook attacks all the cells in its row and column that can be reached in no more than 60 steps, moving from cell to adjacent cell by side. What is the maximum number of non-attacking nearsighted rooks that can be placed on a $100 \times 100$ square?
64. Answer: 178 myopic rooks.

Evaluation. Divide the $100 \times 100$ square into a central $22 \times 22$ square and $4 \cdot 39=156$ rectangles of $1 \times 61$. In each rectangle of the partition and in each row of the $22 \times 22$ square, no more than one rook can be placed, so there are no more than 178 rooks.

Example: Place the rooks on the cells of the main diagonal and two diagonals parallel to it, consisting of 39 cells each. In this arrangement, there are exactly 60 empty cells between any two rooks located in the same column or row, so no two rooks attack each other.