Modelling and solving English Peg Solitaire

Modelling and solving English Peg Solitaire

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Article ID: iaor20072471
Country: United Kingdom
Volume: 33
Issue: 10
Start Page Number: 2935
End Page Number: 2959
Publication Date: Oct 2006
Journal: Computers and Operations Research
Authors: , , ,
Keywords: programming: integer, sports, programming: constraints
Abstract:

Peg Solitaire is a well known puzzle, which can prove difficult despite its simple rules. Pegs are arranged on a board such that at least one ‘hole’ remains. By making draughts/checkers-like moves, pegs are gradually removed until no further moves are possible or some goal configuration is achieved. This paper considers the English variant, consisting of a board in a cross shape with 33 holes. Modelling Peg Solitaire via constraint or integer programming techniques presents a considerable challenge and is examined in detail. The merits of the resulting models are discussed and they are compared empirically. The sequential nature of the puzzle naturally conforms to a planning problem, hence we also present an experimental comparison with several leading AI planning systems. Other variants of the puzzle, such as ‘Fool's Solitaire’ and ‘Long-hop’ Solitaire are also considered.

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