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: | Tarim S. Armagan, Miguel Ian, Jefferson Christopher, Miguel Angela |
Keywords: | programming: integer, sports, programming: constraints |
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.