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Is this an interesting aspect of peg solitaire?

Asked by LostInParadise (29150points) July 17th, 2021

In peg solitaire you have a a board with holes containing pegs. The usual problem is to start with all holes filled except the one in the center and to remove pegs by jumping over them until there is one peg left, which is in the center. See for example over here

What I discovered was that if you have a solution, you get a second solution by making the same moves in reverse order. To see that this might be true, realize that the first move will be a jump to the center, which means that going in the reverse direction the last jump will be into the center. Still, I don’t think that it is obviously true. I can prove it, and while the proof is not difficult, I would say it is at least a step up from being trivial.

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