Question 45
A *crazy bishop* is an unorthodox chess piece which turns towards one of the four diagonally contiguous cells and attacks all cells directly in front, to the left, and to the right of it (just like a regular chess bishop which cannot see behind his back). We say that two cells of a board are *diagonally contiguous* if they have exactly one vertex in common.
Determine the largest positive integer $N$ with the following property: It is possible to put $N$ crazy bishops on an $8 \times 8$ gaming table so that none of them is attacked by another crazy bishop. (Russia 2013)
Determine the largest positive integer $N$ with the following property: It is possible to put $N$ crazy bishops on an $8 \times 8$ gaming table so that none of them is attacked by another crazy bishop. (Russia 2013)