A stronger model for peg solitaire, II

TL;DR

This paper introduces a new, more effective test for determining the possibility of transitioning between positions in peg solitaire, improving upon existing methods by unifying and strengthening the testing framework.

Contribution

It presents a unified formalism for existing tests and introduces a novel, strictly stronger test for peg solitaire position transitions.

Findings

The new test outperforms previous tests in detecting impossibility.

A formal framework unifies existing impossibility tests.

The approach enhances decision-making accuracy in peg solitaire.

Abstract

The main problem addressed here is to decide whether it is possible or not to go from a given position on a peg-solitaire board to another one. No non-trivial sufficient conditions are known, but tests have been devised to show impossibility. We expose the way these tests work in a unified formalism and provide a new test which is strictly stronger than all previous ones.