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Abstract:

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  -positions nor the ¡-positions (i.e. wins for the previous or next player) are described by a regular or context-free language. 1. Solitaire Peg Solitaire is a game for one player. Each move consists of hopping a peg over another one, which is removed. The goal is to reduce the board to a single peg. The best-known forms of the game take place on cross-shaped or triangular

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