9x9 Peg Solitaire
Last Modified August 24, 2005|
Copyright © 2005 by George I. Bell
Extended version of this page [Not available online]
This web page documents some interesting properties and solutions for peg solitaire on the square 9x9 board.
In 1962, Robin Merson found an elegant argument which gives a lower bound
for the length of a solution on the 6x6 board.
This argument can be generalized to any square (or even rectangular) null class
board, but on an n x n board the bound is not very tight
if n is odd.
The complement problem from a corner must use at least
On the 9x9 board the lower bound indicates that any solution must have at least 24 moves. The best solution I have seen was constructed by Alain Maye, by hand, and has 34 moves. It is likely it can be done in fewer than 34 moves, but I doubt the minimum length solution is under 28 moves.
The solution below answers this question. After 8 jumps (or 6 moves) the board position becomes square symmetric (shown in red). The next 60 jumps come in sets of 4 moves that are rotational copies of one another, so every 4 moves you pass through a position with rotational symmetry (shown in green). Then the final 11 jumps (or 6 moves) finish at the center. The final solution has 8+60+11=79 jumps (or 72 moves) and passes through 16 positions with rotational symmetry, 5 of them being square symmetric. It is not possible to go through more than 16 positions with rotational symmetry, because one cannot be reached in under 8 jumps from either end.