The number of n-queens configurations

Complexity of n-Queens Completion

The n-Queens problem is to place n chess queens on an n by n chessboard so that no two queens are on the same row, column or diagonal. The n-Queens Completion problem is a variant, dating to 1850, in which some queens are already placed and the solver is asked to place the rest, if possible. We show that n-Queens Completion is both NP-Complete and #P-Complete. A corollary is that any non-attack...

The n-queens problem in higher dimensions

The 8-queens problem is a well-known chessboard problem, whose constraints are to place eight queens on a normal chessboard in such a way that no two attack each other, under the rule that a chess queen can attack other pieces in the same column, row, or diagonal. This problem can be generalized to place n queens on an n by n chessboard, otherwise known as the n-queens problem. The mathematicia...

Properties of Queens graphs and the irredundance number of Q7

We prove results concerning common neighbours of vertex subsets and irredundance'in the queens graph Qn. We also establish that the lower irredundance number of Q7 is equal to four.

On the Existence of Infinite Size Costas Arrays Configurations of Nonattacking Queens on the Chessboard

Graphical Simulation of N Queens Problem

Graphical simulation is an attempt of predicting the aspects of behavior of some system by developing an approximate model of it. Simulations have great impact on education and in training. Simulation based learning is a practical way of learning of practices that involves building connections: connections among what is being learned and what is important to the actor and the situations in whic...