Peg solitaire

Peg solitaire is a game for one person.

You use a board with many small holes. You fill the holes with pegs or marbles. Most boards have one empty hole in the middle.

To play, you jump one peg over another. The jumped peg is then removed. You do this to clear the board.

Your goal is to leave only one peg. That last peg should stay in the center hole.

This game is very old. A princess played it a long time ago. It is a fun puzzle to solve.

Peg solitaire is a fun game for one person.

You play it on a board with many small holes. You fill these holes with pegs or marbles. Most games start with one empty hole in the center.

To play, you must make a jump. You jump one peg over an adjacent peg. The jumped peg must land in an empty hole. After the jump, you remove the peg you jumped over. Your goal is to clear the board. You want to leave only one single peg in the center hole.

This game has a long history. We see it in a picture from 1697. The image shows the Princess of Soubise playing the game.

There are two main types of boards. One is called the English board. The other is the European board. You can even play on a triangular board. Some people use a special move called a catalyst. This is one extra peg used to clear groups of three. It is a clever puzzle to solve.

Peg solitaire is a fascinating puzzle game designed for just one player.

You play it using small pegs or marbles on a board filled with holes. The main goal is to clear the board through clever movements. In most standard games, you start with one empty hole in the center. You must make valid moves until only one single peg remains. This final peg should end up sitting in that center hole. It is a game of skill and careful planning.

To play, you must follow a specific jumping rule. You pick up one peg and jump it over an adjacent peg. The moving peg must land in an empty hole two positions away. Once the jump is finished, you remove the peg you jumped over. This reduces the total number of pegs on the board. You can move pegs in straight lines, which are called orthogonal directions. Some players use a special tactic called a catalyst. This is one extra peg used to clear groups of three pegs at once.

This game has a very long and interesting history. The first evidence of the game comes from the court of Louis XIV. We can see it in a famous engraving from the year 1697. This artwork was made by Claude Auguste Berey. It shows Anne de Rohan-Chabot, the Princess of Soubise, with a puzzle by her side.

The August 1697 edition of the French magazine Mercure galant also describes the game. It gave readers the rules and sample problems to try at home.

There are two main types of traditional boards used today. The first is the English board, and the second is the European board. You can even play the game on a triangular board. On an English board, the shortest solution takes only 18 moves. This specific solution was found by Ernest Bergholt in 1912. Later, in 1964, John Beasley proved it was the shortest way possible. Scientists have also used computers to study the game deeply. In 1999, a computer used an exhaustive search to solve the game completely.

Peg solitaire connects to many different areas of math and science. Experts use a tool called a pagoda function to study the game. This helps them show if a certain puzzle is impossible to solve. The game is also linked to complex math problems called combinatorial optimization. Even though it looks like a simple pastime, it has many deep patterns. Some players enjoy finding new ways to start and end the game. It remains a popular way to test your brain and your logic.

Peg solitaire is a solo board game involving the movement of pegs or marbles across a board with holes.

Players aim to clear the board through strategic jumps. In the standard version, the board starts full except for one central hole. The ultimate objective is to make valid moves until only one solitary peg remains in that center hole. This game is known as solitaire in Britain, while Americans often call it peg solitaire to distinguish it from patience.

To play, you must follow a specific jumping mechanism. A valid move involves jumping a peg orthogonally, which means in a straight line, over an adjacent peg. The moving peg must land in an empty hole located two positions away. Once the jump is complete, you remove the jumped peg from the board. This process reduces the number of pegs with every turn. Some advanced players use a tactic called a catalyst. This is a single extra peg used to purge entire groups of three pegs at once.

There are two traditional board shapes used in the game: the English board and the European board. The English board is a common variant where the central hole is the starting point. The European board offers different challenges and different sets of alternative games. On a European board, players can start with a hole at one position and end with a peg in its mirrored position. Interestingly, if only orthogonal moves are permitted, there is no solution for the European board if the initial hole is centrally located.

History shows that the game has been cherished for centuries. The earliest evidence traces back to the court of Louis XIV in France. An engraving from 1697 by Claude Auguste Berey depicts Anne de Rohan-Chabot, the Princess of Soubise, with a puzzle by her side.

The August 1697 edition of the French magazine *Mercure galant* provided the first known written description of the rules and sample problems. This shows the game was a recognized pastime in high society long ago.

Mathematical analysis has revealed deep complexity within these simple moves. Researchers use a tool called a pagoda function to prove if certain problems are impossible to solve. In 1990, studies addressed generalized Hi-Q problems, which are equivalent to peg solitaire, showing they are NP-complete. By 1999, computers completely solved the game using exhaustive searches and symmetry. These digital studies show that only about 2.2% of all possible board positions can actually be reached starting from a center vacancy.

Specific records exist for the shortest possible solutions. For the standard English game, the shortest solution requires exactly 18 moves. Ernest Bergholt discovered this sequence in 1912. Later, in 1964, John Beasley provided the mathematical proof that it was the shortest possible way to finish.

On an English board, the final peg can only end up in specific spots that multiples of three permit. This mathematical constraint limits where a player can successfully finish a game.

Peg solitaire connects to several advanced fields of study. It is used to explore combinatorial optimization, which is the study of finding the best solution from many possibilities. In 1996, researchers discussed the properties of a "solitaire cone," which is a type of feasible region in math. The game also relates to abstract algebra, which helps prove there are only five fixed board positions where a game can successfully end with one peg. Whether played for fun or studied by scientists, the game remains a powerful model for logic and patterns.