Interesting Esoterica

Solving Triangular Peg Solitaire

Article by Bell, George I.
  • Published in 2007
  • Added on
In the collection
We consider the one-person game of peg solitaire on a triangular board of arbitrary size. The basic game begins from a full board with one peg missing and finishes with one peg at a specified board location. We develop necessary and sufficient conditions for this game to be solvable. For all solvable problems, we give an explicit solution algorithm. On the 15-hole board, we compare three simple solution strategies. We then consider the problem of finding solutions that minimize the number of moves (where a move is one or more consecutive jumps by the same peg), and find the shortest solution to the basic game on all triangular boards with up to 55 holes (10 holes on a side).

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BibTeX entry

@article{Bell2007,
	author = {Bell, George I.},
	month = {mar},
	title = {Solving Triangular Peg Solitaire},
	url = {http://arxiv.org/abs/math/0703865v6 http://arxiv.org/pdf/math/0703865v6},
	year = 2007,
	archivePrefix = {arXiv},
	eprint = {math/0703865},
	primaryClass = {math.CO},
	abstract = {We consider the one-person game of peg solitaire on a triangular board of
arbitrary size. The basic game begins from a full board with one peg missing
and finishes with one peg at a specified board location. We develop necessary
and sufficient conditions for this game to be solvable. For all solvable
problems, we give an explicit solution algorithm. On the 15-hole board, we
compare three simple solution strategies. We then consider the problem of
finding solutions that minimize the number of moves (where a move is one or
more consecutive jumps by the same peg), and find the shortest solution to the
basic game on all triangular boards with up to 55 holes (10 holes on a side).},
	urldate = {2014-11-10},
	collections = {Puzzles}
}