Modelling and solving English Peg Solitaire

  • Authors:

  • Christopher Jefferson;Angela Miguel;Ian Miguel;S. Armagan Tarim

  • Affiliations:

  • Department of Computer Science, Artificial Intelligence Group, University of York, Heslington, York, UK;Department of Computer Science, Artificial Intelligence Group, University of York, Heslington, York, UK;Department of Computer Science, Artificial Intelligence Group, University of York, Heslington, York, UK;Department of Management, Hacettepe University, Ankara, Turkey

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2006

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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.