Diamond Solitaire

Details Diamond Solitaire Diamond Solitaire

2007-11-19

arxiv.org/abs/0711.2749v1

The Games and Puzzles Journal, Issue 41, September-October 2005 http://gpj.connectfree.co.uk/gpjw.htm

Mathematics

Combinatorics

11 pages, 12 figures

Scientific paper

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".

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