A survey of known results and research areas for nn-queens

In this paper we survey known results for the nn-queens problem of placing nn nonattacking queens on an n×nn×n chessboard and consider extensions of the problem, e.g. other board topologies and dimensions. For all solution constructions, we either give the construction, an outline of it, or a reference. In our analysis of the modular board, we give a simple result for finding the intersections of diagonals. We then investigate a number of open research areas for the problem, stating several existing and new conjectures. Along with the known results for nn-queens that we discuss, we also give a history of the problem. In particular, we note that the first proof that nn nonattacking queens can always be placed on an n×nn×n board for n>3n>3 is by E. Pauls, rather than by W. Ahrens who is typically cited. We have attempted in this paper to discuss all the mathematical literature in all languages on the nn-queens problem. However, we look only briefly at computational approaches.