Reverse Solitaire

Reverse Solitaire is very much like Peg Solitaire except the moves now are in reverse: a jump over an empty square magically fills it with a peg. The goal of the game is to get the starting position of the Solitaire whereas now you start with its ending position. In principle, the puzzle should be as easy (or as difficult) as its original counterpart. However, I have discovered that to me, as far as the theory goes, it's much easier to visualize full packages than the empty ones. Try playing the game before reading further.


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Following is an excerpt from
E.R.Berlekamp,J.H.Conway,R.K.Guy,
Winning Ways for your Mathematical Plays, v2.

"The game called Solitaire pleases me much. I take it in reverse order. That is to say that instead of making a configuration according to the rules of the game, which is to jump to an empty place and remove the piece which one has jumped, I thought it was better to reconstruct what had been demolished, by filling an empty hole over which one has leaped."

Leibniz

The famous philosopher plainly thought that playing Solitaire backwards was different from playing it forwards, but really it's exactly the same! For let's see what happens when he makes one of his backward moves. Leibniz regards this as jumping piece t into hole r and filling the empty hole s over which he has leaped, but the diagram shows that we can regard him as jumping the hole at r over the hole at s into the piece at t and removing the hole over which he has jumped. (Of course to remove a hole he inserts a piece!)

Do you agree with that?

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