[Math Lair] Peg Solitaire

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Peg solitaire is a board game for one player. Its rules are pretty straightforward and so it's widely-played; there are millions of sets around, and it makes for a reasonably popular Christmas gift. However, solving the game is more complicated than it looks. While many different boards exist, the most common is played on a 33-hole board; a 37-hole board is also popular in continental Europe. Moves are made by jumping one peg over another horizontally or vertically (in some versions diagonal moves are allowed, but these versions are generally very easy), with the peg jumped over being removed. There are various variants, but the objective of the standard games is to remove all but one of the pegs. There is some mathematical interest to the game and whether certain positions can be solved or not.

Like other board games such as chess, the origins of peg solitaire are shrouded in obscurity. Unlike chess, however, there are no references to game scores in history, so the earliest reference to the game is in an engraving; Claude-Auguste Berey's "Madame la Princesse de Soubize jo¨ant au jeu de Solitaire". The earliest reference to the game in text was made by Leibniz, in 1710. The game is quite simple, however, and it's certainly possible that the game, or a variant thereof, could have been played well before the year 1700 or so.