The Figure shows the handy little 3-purge , our most popular package. Since the peg and the space on either side of the head are essential to the package, but are restored to their original state, we call them the catalyst. In the Figure below, a dark dot indicates a peg to be purged, a hollow one a space to be filled, and crosses XX indicate catalyst places of which one must be full and the other empty. You should check that every purge has a catalyst it needs. Peg Solitaire Painlessly Packaged.
Picture pops prior problems.
First, take care of the middle 3-purge. What remains consists of two symmetrical configurations that can be removed by steps 5,6,7, and 8 from the upper left diagram. Reference E.R.Berlekamp, J.H.Conway, R.K.Guy, Winning Ways for Your Mathematical Plays , v2, Academic Press, 1982. An admirable implementation of the game by Jeff Holst is available on-line . Another one by Pascal Glauser employs a genetic algorithm to find a solution for you.