# Numerical and Symbolic Studies of the Peaceable Queens Problem

## TL;DR

This paper explores the peaceable queens problem by combining symbolic proofs of local optima with numerical methods to identify exact solutions for specific configurations, advancing understanding of this combinatorial challenge.

## Contribution

It provides a symbolic proof of Jubin's pentagon construction as a local optimum and introduces a numerical approach for finding exact solutions in complex configurations.

## Key findings

- Jubin's pentagon construction is at least a local optimum.
- Numerical methods successfully find exact optima for specific configurations.
- The approach can be extended to more complex configurations with additional parameters.

## 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.