The n-queens solution count Q(n) is divisible by 4
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915719257522176 |
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| author | Nielsen, Hugo |
| author_facet | Nielsen, Hugo |
| contents | 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 $n \ge 6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05856 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The n-queens solution count Q(n) is divisible by 4 Nielsen, Hugo Combinatorics 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 $n \ge 6$. |
| title | The n-queens solution count Q(n) is divisible by 4 |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.05856 |