Notes on solving and playing peg solitaire on a computer

Details Notes on solving and playing peg solitaire on a computer Notes on solving and playing peg solitaire on a computer

2009-03-23

arxiv.org/abs/0903.3696v3

Mathematics

Combinatorics

21 pages, 9 figures, 6 tables. Added text and a program to count the number of solutions

Scientific paper

We consider the one-person game of peg solitaire played on a computer. Two popular board shapes are the 33-hole cross-shaped board, and the 15-hole triangular board - we use them as examples throughout. The basic game begins from a full board with one peg missing and finishes at a board position with one peg. First, we discuss ways to solve the basic game on a computer. Then we consider the problem of quickly distinguishing boards positions that can be reduced to one peg ("winning" board positions) from those that cannot ("losing" board positions). This enables a computer to alert the player if a jump under consideration leads to a dead end. On the 15-hole triangular board, it is possible to identify all winning board positions (from any single vacancy start) by storing a key set of 437 board positions. For the "central game" on the 33-hole cross-shaped board, we can identify all winning board positions by storing 839,536 board positions. Using these winning board positions, we calculate that the total number of solutions to the central game is 40,861,647,040,079,968.

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