Designing peg solitaire puzzles

TL;DR

This paper explores computational methods to generate and analyze challenging peg solitaire puzzles, focusing on symmetric starting positions and unique solution paths to enhance puzzle difficulty and solvability.

Contribution

It introduces a novel search technique for identifying board positions with unique starting jumps, uncovering challenging puzzles and aiding solver strategies.

Findings

Computed solvable symmetric positions for four board shapes

Identified puzzles with unique starting jumps

Demonstrated puzzles' increased challenge and solver advantage

Abstract

Peg solitaire is an old puzzle with a 300 year history. We consider two ways a computer can be utilized to find interesting peg solitaire puzzles. It is common for a peg solitaire puzzle to begin from a symmetric board position, we have computed solvable symmetric board positions for four board shapes. A new idea is to search for board positions which have a unique starting jump leading to a solution. We show many challenging puzzles uncovered by this search technique. Clever solvers can take advantage of the uniqueness property to help solve these puzzles.