John D. Cook • 6/22/2026

Queens on a prime order board

This article discusses the n queens problem, specifically when n is a prime number greater than or equal to 5. It explains that placing queens on lines of slope 2, 3, ..., n-2 (mod n) on a toroidal board (where opposite edges are joined) yields solutions. While all solutions for n=5 have this form, larger primes like 7 have solutions where queens do not all lie on a constant slope line. The post includes references and links to related topics like SAT formulations and chess puzzles.

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#mathematics #prime numbers #N Queens Problem