For the classic, "perfect win", you must end up with a single peg in the center hole. This configuration is the complement of the starting position, in which there are pegs in every hole *except* the center. An interesting (and useful) observation is that a valid move (a jump) is the same running backwards and forwards if you complement the board: X X O -> O O X Complement and time-reverse: O O X <- X X O This means that if you write a solution finger that searches for solutions, keeping track of configurations it's seen, you can stop at the halfway point. When you reach that point, simply see if you've encountered the complement of the position. If so, you can piece the two together to form a complete solution. I coded this back in the mid-80s, and even with the speed and memory limitations of the time, it was able to solve it very quickly (there are many, many solutions). Tom James Propp writes:
I bought a vintage Hi-Q set for my family a few weeks ago:
https://en.wikipedia.org/wiki/Peg_solitaire
Now that I'll be spending lots of time at home with my kids, I'm thinking that there should be some good activities we could do with it.
Any ideas?
I know that Berlekamp-Conway-Guy has a section on this, and maybe it even explains how to win, but I don't want to just see the answer; I'd like a "curriculum" that'll Socratically guide me and my kids towards the solution. (Or is it the sort of puzzle where you basically need to use a brute-force approach?)
I kind of like the fact that I don't know the solution; it puts me and my kids more on the same level.
Jim Propp