#Peg solitaire pegs left cracker
#Peg solitaire pegs left full

'The unsolvability of the problem 'start by vacating the central hole, play to leave a single man in this hole' on theģ7-hole board is a consequence of a property known as 'position class': the various positions possible on a Solitaireīoard can be divided into 16 different classes, and it is impossible to play from a position in one class to a position in 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

#Peg solitaire pegs left cracker

Modern readers may be more familiar with the side-5 triangular variant offering diversion at tables in Cracker Barrel and other restaurants. This is called the Central Game, or the d4 complement problem. 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. 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).Ī 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 shape of the board and the arrangement of holes varies as well. 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 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.ĭepending on the variant being played, sometimes diagonal jumps are permitted, or jumps in certain directions are prohibited. When the initial empty hole and the location of the final peg must be the same, it is called the ' complement problem.'

#Peg solitaire pegs left full

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.Ī 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. The game is played on a board having an arrangement of holes, with counters of some sort - typically pegs or marbles. to have been the 'Rubik's Cube' of the court of Louis XIV.' New Problems on Old Solitaire Boards (PDF), George Bell and John Beasley state that Other statistics can be found at Jean-Charles Meyrignac's website Taken from Winning Ways for Your Mathematical Plays by Berlekamp, Conway, and Guy. George's website offers all kinds of information and is definitely worth a visit!Īlso, at Alexander Bogomolny's Cut-the-Knot, there isĪ good explanation of the solution technique involving packages and purges, George Bell has done a lot of analysis of Peg Solitaire in its various forms. (The Miscellanea Berolinensia ( Berlin Miscellanea) was the primary journal of the Berlin Academy, and was published in seven volumes 'Not so very long ago there became widespread an excellent kind of game, called Solitaire, where I play on my own,īut as if with a friend as witness and referee to see that I play correctly.' King Louis the XIV as adequately proven.'īeasley includes a quote from Gottfried Wilhelm Leibniz that appears in the 1710 Miscellanea Berolinensia I: (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.īeasley says he regards 'the existence of Solitaire at the court of Beasley states that the origins of Solitaire are unknown, and that the earliestĪnne Chabot de Rohan Princesse de Soubise, who lived 1648-1709,įrench Wikipedia article on Berey says he lived circa 1660-1730.Īnother very similar engraving by Antoine Trouvain entitled In his 1985 book The Ins & Outs of Peg Solitaire, John D. It is part of the Sequential Movement class of mechanical puzzles. Peg Solitaire is a puzzle game for one person, thought to be at least 300 years old and of French origin.