Alice has been trying to solve a puzzle lately, and today she sent Bob this text message:

I finally found it! I've got the solution! It's pretty simple actually: 5-17, 12-10, 3-11, 18-6, 30-18, 27-25, 24-26, 13-27-25, 9-11, 7-9, 22-24-26-12-10-8, 31-23, 16-28, 33-31-23, 21-7-9, 1-3-11-25, 4-16-28-30-18-16, 15-17

A few minutes later Bob texted her back:

You probably made a mistake somewhere. It doesn't work for me.

But when Alice tried the solution again, it worked perfectly!

To which puzzle is this the solution? And why does it work for Alice, but not for Bob?

up vote 9 down vote accepted

Alice has described

a solution to "English" peg-solitaire (number the spaces on the board in the "obvious" way with 1 at, say, top left; x-y-z means jump a peg from x to y and thence to z, removing the two pegs jumped over in the process)

but Bob has

a solitaire board of a different shape, perhaps the "European" which has four extra pegs.

All credit to Rosie F whose answer

suggested the things-jumping-over-other-things mechanic to me

and I would urge anyone inclined to upvote or accept this answer to upvote hers too.

  • +1 Neat! I have seen various notations for peg solitaire but had not seen that one before. – Rosie F Sep 21 '16 at 12:33

International (10x10) checkers/draughts? Bob had assumed 8x8, but that doesn't work, for one thing because some of the notation represents illegal moves, and for another because there are 33s, but notation for 8x8 checkers/draughts doesn't use numbers greater than 32, because only 32 squares are used.

  • Maybe I don't understand how the notation works for 10x10, but 12-10 doesn't look like a legal move to me. – Gareth McCaughan Sep 21 '16 at 11:58

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