Peg Solitaire

Peg Solitaire (also called Solo Noble or simply Solitaire in some European countries) is a single-player board game where the player removes pegs by jumping over them, similar to checkers captures. The goal is to remove all pegs except one, ideally ending with the last peg in the center of the board. The game is played on a cross-shaped or octagonal board with 33 or 37 holes, and every move must be a jump — there is no sliding or diagonal movement.

Rules

1. The board starts with pegs in every hole except the center, which is empty.
2. A peg may jump over an adjacent peg (horizontally or vertically, not diagonally) into an empty hole on the other side.
3. The jumped-over peg is removed from the board.
4. Only one peg may be jumped per move (though some positions allow a single peg to make consecutive jumps in one turn, like multi-jumps in checkers).
5. The game ends when no more jumps are possible.
6. A perfect solution leaves exactly one peg remaining, ideally in the center hole.

Board Variants

• English Board: Cross-shaped with 33 holes (most common).
• European Board: Octagonal/rounded cross with 37 holes.
• Triangular Board: 15 holes in a triangle (the "Cracker Barrel" version).
• Diamond Board: 41 holes in a diamond shape.

Strategies

• Work from the Edges Inward: Pegs on the outer edges are the hardest to remove later. Try to clear the perimeter first and consolidate pegs toward the center.
• Symmetry: Maintain symmetry in your moves when possible. Symmetric positions tend to have more solution paths available.
• Avoid Isolation: Do not leave single pegs stranded far from other pegs. An isolated peg with no adjacent peg to jump over is permanently stuck.
• Plan Chain Jumps: The most efficient moves involve a single peg making multiple consecutive jumps in one turn, clearing several pegs at once.
• Learn Known Solutions: For the standard 33-hole English board, optimal solutions have been fully enumerated. Learning a few key opening sequences makes it much easier to find a solution.
• Count Remaining Pegs: Keep track of how many pegs remain. A solvable game requires specific peg counts at various stages — if you notice you have too many pegs clustered in one area, reconsider your strategy.

Peg Solitaire is one of the oldest known single-player board games, with its origins shrouded in legend. According to popular tradition, the game was invented by a French nobleman imprisoned in the Bastille during the 17th century, who created it to pass the time. While this story is likely apocryphal, the game was certainly well-known in France by the late 1600s. The earliest reliable reference is an engraving from 1697 showing Princess de Soubise playing the game at the court of Louis XIV.

The game spread throughout Europe in the 18th century and became a popular parlor pastime. It attracted the attention of several mathematicians, including Gottfried Wilhelm Leibniz, who analyzed it in 1710, noting its connection to binary arithmetic and positional logic. The English cross-shaped board (33 holes) and the European octagonal board (37 holes) became the two standard formats, with each country favoring its own design.

In the 20th century, Peg Solitaire received rigorous mathematical treatment. In 1962, mathematician John Beasley applied the theory of "pagoda functions" to prove which starting and ending positions are solvable, settling long-standing questions about the game's combinatorics. The total number of possible board states has been computed to be over 187 million for the English board, of which only specific sequences lead to the single-peg solution.

The triangular 15-hole variant became an American cultural icon when the Cracker Barrel restaurant chain began placing wooden versions on every table in 1967. Millions of diners have attempted the puzzle while waiting for their meals, making it perhaps the most widely played physical version of any abstract puzzle in the United States. The game continues to be popular both as a physical wooden toy and in digital formats.