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 mathematicians Gauss and Polya studied this problem [3], and Ahrens [1] showed that for all n ≥ 4, solutions exist. This problem can be further generalized to d dimensions, where two queens attack one another if they lie on a common hyperplane. It can then be described as the n-queens problem in d dimensions. (The traditional 8-queens problem, as described above, is 2-dimensional.) The n-queens problem is classically considered a theoretical one, but has also been studied [5] for its many applications: in distributed memory storage schemes [4], VLSI test-