Modelling and solving English Peg Solitaire

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-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 CP or OR 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’ are also considered.