TL;DR
This paper explores peg solitaire on diamond and rhombus-shaped boards, revealing unique properties and constructing solutions with maximal sweeps related to rhombic matchstick numbers.
Contribution
It introduces the concept of rhombic matchstick numbers and provides methods to construct solutions with maximal sweeps on larger rhombus boards.
Findings
Rhombus boards of side 6 have solutions with a maximal sweep of length 16.
Solutions can be constructed for larger boards of side 6i with maximal sweep length r=(9i-1)(3i-1).
The properties of these boards depend on their geometric shape and size.
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".
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsArtificial Intelligence in Games · Limits and Structures in Graph Theory · Advanced Combinatorial Mathematics