Numerical and Symbolic Studies of the Peaceable Queens Problem

By Yukun Yao and Doron Zeilberger


First Written: Feb. 14, 2019.

One of the fascinating problems mentioned in a recent beautiful article (Oct. 2018 issue of the Notices of the American Mathematical Society), by guru Neil Sloane, is that of the maximal number of placing the same number of white queens and black queens on an n by n chess board so that no queen attacks any queen of the opposite color. Benoit Jubin found the lower-bound of [7/48 n2], that is conjectured to be the right value. Here we don't quite prove it completely, but we do show that if one restricts attention to configurations similar to his construction, consisting of the interiors of two pentagons, then it is optimal.

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