A Peg Solitaire Font

Taishi Oikawa, Kazuaki Yamazaki, Tomoko Taniguchi and Ryuhei Uehara
Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
Pages 183–188 Regular Papers


Peg solitaire is one of the most popular classic puzzles around the world. It was proved that this puzzle was computationally intractable in general in 1990. The most common form of the puzzle consists of board with 33 holes and 32 pegs. A lot of solutions have been found by puzzle players by hand, and heuristic algorithms were developed in the 1990s. However, (super)computers running sophisticated algorithms can now enumerate all the solutions for this puzzle in a few minutes. That is, we can now completely solve certain peg solitaire puzzles of reasonable size. Using this technique, we design a “peg solitaire font” in the following way. We start with a peg solitaire puzzle on a board of size 5 × 7, which consists of 35 holes filled using 34 pegs placed in all holes except the central hole. Our algorithm running on a (super)computer generates all possible patterns reachable from the initial state. We find that there are 1,045,173,439 reachable patterns from the initial state. From these reachable patterns, we extract or “design” our font so that each of the characters in our font can be reached from the initial state. Readers are invited to solve the associated peg solitaire puzzle for each character.