English

Diamond Solitaire

Combinatorics 2007-11-29 v1 Discrete Mathematics

Abstract

We investigate the game of peg solitaire on different board shapes, and find those of diamond or rhombus shape have interesting properties. When one peg captures many pegs consecutively, this is called a sweep. Rhombus boards of side 6 have the property that no matter which peg is missing at the start, the game can be solved to one peg using a maximal sweep of length 16. We show how to construct a solution on a rhombus board of side 6i, where the final move is a maximal sweep of length r, where r=(9i-1)(3i-1) is a "rhombic matchstick number".

Cite

@article{arxiv.0711.2749,
  title  = {Diamond Solitaire},
  author = {George I. Bell},
  journal= {arXiv preprint arXiv:0711.2749},
  year   = {2007}
}

Comments

11 pages, 12 figures

R2 v1 2026-06-21T09:44:28.920Z