The Cracker Barrel Peg Puzzle

I am planning to write a C/C++ program to solve the "Peg Puzzle" which is present on the dining tables at the Cracker Barrel restuarants. The puzzle is as follows

The puzzle consists of a triangular block of wood containing 15 holes, 14 of which have golf tees (aka pegs) in them. The game consists of jumping pegs over one another and removing the jumped-over peg, in a similar manner to checkers. The object is to end up with as few pegs as possible, hopefully one.