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

Hugo Nielsen

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

Combinatorics 2026-01-12 v1

Authors: Hugo Nielsen

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 $n \ge 6$ .

Cite

@article{arxiv.2601.05856,
  title  = {The n-queens solution count Q(n) is divisible by 4},
  author = {Hugo Nielsen},
  journal= {arXiv preprint arXiv:2601.05856},
  year   = {2026}
}

Comments

6 pages, 3 figures

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