Diagonal Peg Solitaire

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2006Embargo end date: 01 Jun 2006Publisher:ZenodoJournal:CoRR, volume abs/math/0606122Funded by:FCT | D4

Authors: George I. Bell;

doi: 10.5281/zenodo.8337208 , 10.5281/zenodo.8337209 , 10.48550/arxiv.math/0606122

arXiv: math/0606122

Diagonal Peg Solitaire

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Abstract

We study the classical game of peg solitaire when diagonal jumps are allowed. We prove that on many boards, one can begin from a full board with one peg missing, and finish with one peg anywhere on the board. We then consider the problem of finding solutions that minimize the number of moves (where a move is one or more jumps by the same peg), and find the shortest solution to the "central game", which begins and ends at the center. In some cases we can prove analytically that our solutions are the shortest possible, in other cases we apply A* or bidirectional search heuristics.

20 pages, 11 figures

Keywords

FOS: Computer and information sciences, Discrete Mathematics (cs.DM), 00A08, 97A20, Computer Science - Data Structures and Algorithms, FOS: Mathematics, Mathematics - Combinatorics, Combinatorial games, Data Structures and Algorithms (cs.DS), Combinatorics (math.CO), 00A08; 97A20, Enumerative combinatorics, Computer Science - Discrete Mathematics

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