Numerical and Symbolic Studies of the Peaceable Queens Problem

Abstract

We discuss, and make partial progress on, the peaceable queens problem, the protagonist of OEIS sequence A250000. Symbolically, we prove that Jubin’s construction of two pentagons is at least a local optimum. Numerically, we find the exact numerical optimums for some specific configurations. Our method can be easily applied to more complicated configurations with more parameters.

Keywords:

• experimental mathematics
• combinatorics
• OEIS
• peaceable queens

AMS Subject Classification:

• 05A15

Acknowledgments

We are thankful to Neil J.A. Sloane for introducing us to this interesting problem and we are also grateful to Lun Zhang for pleasant conversations and helpful remarks. We sincerely thank the anonymous referee for careful review and useful suggestions. We appreciate Shalosh B. Ekhad’s impeccable computing support.