The n-queens solution count Q(n) is divisible by 4

Abstract

We consider the classical $n$-queens problem, which asks how many ways one can place $n$ mutually non-attacking queens on an $n$ x $n$ chessboard. We prove that the total number of solutions to the $n$-queens problem $Q(n)$ is divisible by 4 whenever $n\ge 6$.

6 pages, 3 figures