A group-based search for solutions of the n-queens problem Original Research Article

The n-queens problem is a well-known problem in mathematics, yet a full search for n-queens solutions has been tackled until now using only simple algorithms (with the exception of the Rivin–Zabih algorithm). In this article, we discuss optimizations that mainly rely on group actions on the set of n-queens solutions. Most of our arguments deal with the case of toroidal queens; at the end, the application to the regular n-queens problem is discussed, and also the Rivin–Zabih algorithm.