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# One-Dimensional Peg Solitaire, and Duotaire

## Author Info

Listed author(s):
• Cristopher Moore
• David Eppstein
Registered author(s):

## Abstract

We solve the problem of one-dimensional Peg Solitaire. In particular, we show that the set of configurations that can be reduced to a single peg forms a regular language, and that a linear-time algorithm exists for reducing any configuration to the minimum number of pegs. We then look at the impartial two-player game, proposed by Ravikumar, where two players take turns making peg moves, and whichever player is left without a move loses. We calculate some simple nim-values and discuss when the game separates into a disjunctive sum of smaller games. In the version where a series of hops can be made in a single move, we show that neither the $\cal P$-positions nor the $\cal N$-positions (i.e. wins for the previous or next player) are described by a regular or context-free language.

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## Bibliographic Info

Paper provided by Santa Fe Institute in its series Working Papers with number 00-09-050.

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 Length: Date of creation: Sep 2000 Handle: RePEc:wop:safiwp:00-09-050 Contact details of provider: Postal: 1399 Hyde Park Road, Santa Fe, New Mexico 87501Web page: http://www.santafe.edu/sfi/publications/working-papers.htmlMore information through EDIRC

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