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Peg solitaire (or Solo Noble) is a board game from Madagascar 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

Wikipedia

If you need more detail on how to solve Peg Solitaire click here for an informative guide.