Successful strategies for a queens placing game on an n x n chess board

Abstract

In his list of open problems, Martin Erickson described a certain game: "Two players alternately put queens on an n x n chess board so that each new queen is not in range of any queen already on the board (the color of the queens is unimportant). The last player who can move wins." Then he asked: "Who should win?" Obviously, for n up to 3, the first player wins, if he does not miss to start at the central position in the case n=3. In this article, we give very simple always winning strategies for the first player if n is 4 or odd. The additionally (in the source package) provided computer program QPGAME3 has been used to check that there are successful strategies for the first player if n is 6 or 8, and for the second player if n is 10, 12, 14, or 16. As discovered during the submission process of the first version of this article, Hassan A Noon presented consistent results concerning values of n which are odd or at most 10, in his B.A. thesis and, together with Glen Van Brummelen, in a journal article.