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

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Hugo Nielsen
Cited by: 0

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 $n \ge 6$.

Fields of Study & Subjects

Advanced Combinatorial Mathematics Advanced Graph Theory Research Analytic Number Theory Research

Publication details

Journal / source
arXiv (Cornell University)
Publication date
9 January 2026
Document type
Preprint