Question 39
The upper right quarter of a chess board (with dimensions $8 \times 8$) is covered with paper. How many rooks (at most) can we place on the remaining part of the board so that no two of them attack each other? In how many ways can they be placed?
(Two rooks are mutually attacking each other if they are in the same row or the same column.)
(Two rooks are mutually attacking each other if they are in the same row or the same column.)