Proposed by Chris Jefferson, Angela Miguel, Ian Miguel, Armagan Tarim

Peg Solitaire (also known as Hi-Q) is played on a board with a number of holes. In the English version of the game, the board is in the shape of a cross with 33 holes:

  OOO
OOO
OOOOOOO
OOOOOOO
OOOOOOO
OOO
OOO


Pegs (‘X’s here) are arranged on the board so that at least one hole remains. A number of different problems arise from Solitaire, e.g. finding a path from the initial to a goal state, or finding the shortest number of moves to a state where no more moves are possible.

Moves are draughts/checkers-like and are horizontal or vertical:

XXO -> OOX


The following is the classic ‘central’ version of the game:

 Start:     Goal:
XXX        OOO
XXX        OOO
XXXXXXX    OOOOOOO
XXXOXXX -> OOOXOOO
XXXXXXX    OOOOOOO
XXX        OOO
XXX        OOO


The French version of the game has four extra holes:

  OOO
OOOOO
OOOOOOO
OOOOOOO
OOOOOOO
OOOOO
OOO


The french version of solitaire cannot be completed starting with one hole in the middle, and ending with one peg in the center, without adding one extra peg during play (the player gets to decide where and when to place the extra peg).

Other board types, such as the Solitaire Triangle, also exist.