Peg solitaire

Peg solitaire (or Solo Noble) is a board game for one player involving movement of pegs on a board with holes. Some sets use marbles in a board with indentations. The game is known simply as Solitaire in the United Kingdom where the card games are called Patience. It is also referred to as Brainvita (especially in India).

The first evidence of the game can be traced back to the court of Louis XIV, and the specific date of 1687, with an engraving made that year by Claude Auguste Berey of Anne de Rohan-Chabot, Princess of Soubise, with the puzzle by her side. The August 1687 edition of the French literary magazine Mercure galant contains a description of the board, rules and sample problems. This is the first known reference to the game in print.

The standard game fills the entire board with pegs except for the central hole. The objective is, making valid moves, to empty the entire board except for a solitary peg in the central hole.

There are two traditional boards ('.' as an initial peg, 'o' as an initial hole):

A valid move is to jump a peg orthogonally over an adjacent peg into a hole two positions away and then to remove the jumped peg.

In the diagrams which follow, · indicates a peg in a hole, * emboldened indicates the peg to be moved, and o indicates an empty hole. A blue ¤ is the hole the current peg moved from; a red * is the final position of that peg, a red o is the hole of the peg that was jumped and removed.

Thus valid moves in each of the four orthogonal directions are:

On an English board, the first three moves might be:

There are many different solutions to the standard problem, and one notation used to describe them assigns letters to the holes:

This mirror image notation is used, amongst other reasons, since on the European board, one set of alternative games is to start with a hole at some position and to end with a single peg in its mirrored position. On the English board the equivalent alternative games are to start with a hole and end with a peg at the same position.

There is no solution to the European board with the initial hole centrally located, if only orthogonal moves are permitted. This is easily seen as follows, by an argument from Hans Zantema. Divide the positions of the board into A, B and C positions as follows:

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