Jump A Peg Wooden Games
Peg Solitaire Game Instructions

Peg Solitaire and Jumping Puzzles

Horse Race Game To play, you need a pair of dice, a deck of cards, and the Horse Race game board! From the deck of cards, discard the aces, kings, and jokers, leaving you with 44 cards. Shuffle and deal these cards. Each player will not necessarily receive the same amount of cards. Place the horses at the starting gate. Game Pieces: Each player chooses five pegs in a unique color. Winning: The first team or individual to have all of their pegs in the SAFE position wins the game. Dealing: Deal each player five cards. Player to the left of the dealer draws one. First player (or team) to have all their pegs in the HOME position wins the game! Players: 2 to 8 players. Each player uses 1 game paddle and selects a peg color. Pegs are placed in your START position to begin (Fig.

Peg Solitaire is a puzzle game for one person, thought to be at least 300 years old and of French origin. It is part of the Sequential Movement class of mechanical puzzles. It is related to the game Fox and Geese. (Also see the entry for Fox and Geese at the University of Waterloo's Elliott Avedon Virtual Museum of Games.)

In his 1985 book The Ins & Outs of Peg Solitaire, John D. Beasley states that the origins of Solitaire are unknown, and that the earliest clear evidence of the game he found is this portrait of Anne Chabot de RohanPrincesse de Soubise, who lived 1648-1709, engraved by Claude-Auguste Berey in 1697 - the French Wikipedia article on Berey says he lived circa 1660-1730.

Jump A Peg Wooden Games

Another very similar engraving by Antoine Trouvain entitled Dame de Qualité Joüant au Solitaire (A Woman of Quality, Playing Solitaire), from Figures du règne de Louis XIV, vol 1, fol 105, dates from 1695 - two years earlier than the Berey engraving.

Beasley says he regards 'the existence of Solitaire at the court of King Louis the XIV as adequately proven.'

Peg Solitaire Game Instructions

Beasley includes a quote from Gottfried Wilhelm Leibniz that appears in the 1710 Miscellanea Berolinensia I: 'Not so very long ago there became widespread an excellent kind of game, called Solitaire, where I play on my own, but as if with a friend as witness and referee to see that I play correctly.' (The Miscellanea Berolinensia (Berlin Miscellanea) was the primary journal of the Berlin Academy, and was published in seven volumes between 1710 and 1746.)

George Bell has done a lot of analysis of Peg Solitaire in its various forms. George's website offers all kinds of information and is definitely worth a visit! Also, at Alexander Bogomolny's Cut-the-Knot, there is a good explanation of the solution technique involving packages and purges, taken from Winning Ways for Your Mathematical Plays by Berlekamp, Conway, and Guy. Other statistics can be found at Jean-Charles Meyrignac's website euler.free.fr.

In their 2005 paper New Problems on Old Solitaire Boards (PDF), George Bell and John Beasley state that 'The game appears ... to have been the 'Rubik's Cube' of the court of Louis XIV.'

The game is played on a board having an arrangement of holes, with counters of some sort - typically pegs or marbles. The objective is to start with pegs in specific holes, and one or more vacant holes, then by legal jumping movements, remove pegs to achieve a goal configuration. A game where one must start with a full board save one empty hole, and end with one peg, is called a 'single vacancy to single survivor' problem. When the initial empty hole and the location of the final peg must be the same, it is called the 'complement problem.'

Typically, a legal move is to jump a peg over an adjacent peg, in a straight line, either horizontally or vertically in any direction but not diagonally. Depending on the variant being played, sometimes diagonal jumps are permitted, or jumps in certain directions are prohibited. In addition, the game can be played in reverse (as noted by Leibniz) - start with a single peg and then by 'reverse jumps' re-populate the board, with the objective of filling a specific field of holes.

The shape of the board and the arrangement of holes varies as well. Solitaire is usually played on a 33-hole cross-shaped board known as the 'English' board (though according to Beasley this board type probably appeared in Germany before appearing in England). A standard notation labeling the holes on the English board assigned the letters abcdefg to the columns and the digits 1-7 to the rows. The center hole is thus d4. The standard problem on the English board is to start with all holes filled save the central hole, and end with a lone peg there - this is called the Central Game, or the d4 complement problem. Modern readers may be more familiar with the side-5 triangular variant offering diversion at tables in Cracker Barrel and other restaurants.

The portrait shows the Princess with the 37-hole French board, but on this board it is impossible to start with the central hole vacant and end with the last peg there. Bell and Beasley explain, 'The unsolvability of the problem 'start by vacating the central hole, play to leave a single man in this hole' on the 37-hole board is a consequence of a property known as 'position class': the various positions possible on a Solitaire board can be divided into 16 different classes, and it is impossible to play from a position in one class to a position in another.' It is usually assumed that diagonal moves are prohibited, but it really isn't known definitvely whether or not diagonal moves were allowed when this was devised, and if they are, then the central game on the 37-hole French board is solvable in 13 moves.

Example Solitaire Board Types
(from the Wikipedia article)

1. European (or Continental) board, 17th century, 37 holes 2. J. C. Wiegleb, Germany 1779, 45 holes 3. Asymmetrical 3-3-2-2, 20th century	4. The English Board, 33 holes 5. Diamond, 41 holes 6. Triangular (side-5), 15 holes
Click here to open a window and run my Triangle Solitaire Solver.

A puzzler improves at Solitaire by at first achieving the objective of leaving but a single peg in the correct hole (rather than two or more pegs isolated across the board, or even one peg but in the wrong hole), and then by reducing the number of moves required for the task to its minimum. The number of jumps will always be equal to or less than the number of initial pegs minus one, since every jump eliminates one peg - but the number of moves can be less if we count the same peg jumping more than one other peg in succession to be a single move. For a given configuration, an interesting mathematical and computational challenge is to determine this minimum, and the correct sequence of moves - indeed, to determine if a solution exists at all for a given starting configuration and objective. The shortest solution to the central game on the English board requires 18 moves, shown by Ernest Bergholt in 1912 and proved in 1964.

Many versions of Peg Solitaire have been produced. One particularly well-known version called Hi-Q was offered by Kohner in the 1950s and 60s. According to this article by Richard Gottlieb, the Kohner brothers Frank, Paul, and Michael played a major role in shaping the modern toy industry. Frank Kohner died on Feb. 6 2011 at the age of 100.

Cafe Puzzle - 1978 Gordon Bros.
This is a vintage plastic peg solitaire set.

In the 1960's, Setko (aka the Set Screw and Mfg. Co. of Bartlett IL) offered a number of nice peg solitaire-type jumping and transposition puzzles.

Some were 'made for' Baekgaard & Butler - Glenview Ill.

Several of them were designed by a Calvin O. Brown.

Hoyle, Crestline, and even Skor-Mor offered similar sets.

Various box lid graphics, including a screw, crest, and alt. crest.

101 Cross
The classic - set up pegs in all holes except center. Jump in straight line horizontally or vertically, not diagonally, & remove jumped peg. End in center hole.

102 Tri-Puzzler
Walnut board, Oak board
Another classic, but on a side-6 grid rather than the side-5 at Cracker Barrel. Start with one hole anywhere, jump &

Peg Game Instructions