Numerical and Symbolic Studies of the Peaceable Queens Problem

By Yukun Yao and Doron Zeilberger


[Appeared in Experimental Mathematics v. 31 (2022), issue 1, 269-279]

First Written: Feb. 14, 2019.

Last Update of this web-page: May 21, 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.

Added April 28, 2019: Don Knuth informed us that Jubin's construction goes back to Stephen Ainley in 1977, see Don Knuth's note

Added May 21, 2019: It can be found in Fig. 28(A) (p. 33) in Stephen Ainley's delightful puzzle book.

Added May 15, 2019, watch this

great video on this problem, by guru Neil Sloane.

Maple package

Sample Input and Output


Yukun Yao's Home Page

Articles of Doron Zeilberger

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