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arXiv · 2601.05856

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

Hugo Nielsen
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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 $n \ge 6$.

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Hugo Nielsen. 2026-01-09. The n-queens solution count Q(n) is divisible by 4. https://arxiv.org/abs/2601.05856

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