A Fresh Look at Peg Solitaire

Peg solitaire is a one-person game that is over 300 years old; most people are familiar with the puzzle on the “standard 33-hole board” in FIGURE 1. When I first saw this game, what struck me was the unusual shape of the board. How was this strange crossshaped board discovered and what is so special about it? While the history of the game is too fragmented to answer the question of the origin of this board, this paper will demonstrate that the special shape of the standard board can be derived from first principles. This board arises as a consequence of two very natural requirements: that of symmetry, and the ability to play from a board position with one peg missing to a single peg at the same location. We’ll show that in a certain well-defined sense, the shape of this board is unique.