A survey of known results and research areas for -queens

In this paper we survey known results for the n -queens problem of placing n nonattacking queens on an n × 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 n -queens that we discuss, we also give a history of the problem. In particular, we note that the first proof that n nonattacking queens can always be placed on an n × n board for n > 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 n -queens problem. However, we look only briefly at computational approaches.