Question 55
Let $n$ be the maximum number of bishops that can be placed on the squares of a $6 \times 6$ chessboard such that no two bishops are attacking each other. Let $k$ be the number of ways to put bishops on an $6 \times 6$ chessboard such that no two bishops are attacking each other. Find $n+k$. (Two bishops are considered to be attacking each other if they lie on the same diagonal. Equivalently, if we label the squares with coordinates $(x, y)$, with $1 \leq x, y \leq 6$, then the bishops on $(a, b)$ and $(c, d)$ are attacking each other if and only if $|a-c|=|b-d|$.)