chapter
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A Solitaire Game and Its Relation to a Finite Field

The game we are about to discuss is played by one person who uses a board with 33 holes in it as pictured in Figure 1. In the initial position there is a peg in all but one of the holes in the board; usually, the empty hole is in the center of the board. The object of the puzzle is to obtain, by means of a sequence of moves, a position on which only one peg remains on the board. Sometimes it is required that the remaining peg should be in the hole in the center of the board. There is only one type of move, and it consists of jumping one peg over another into an empty hole, and at the same time the peg that has been jumped over is removed from the board. Jumping is allowed both horizontally and vertically, so in every move three consecutive holes in a row of holes in the board are involved.