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Google didn't come up with a result: https://www.google.com/search?q=cracker+barrel+peg+game+solvability+in+higher+dimensions

The Cracker Barrel Peg Game consists of a triangular board with 15 holes for pegs. 14 pegs go in to the holes with one empty. A peg can jump over one other peg into an empty hole to remove the peg jumped over. Solution: https://youtube.com/watch?v=ILKXEnX_YGM

Came to mind when I walked in to a TV show and saw the game on the screen. A friend after I asked in a Discord gave me this: http://mtweb.mtsu.edu/cc2013/Beeler.pdf but it seems to be generalized to two dimensional graphs.

For example, in the third dimension you would be a tetrahedron consisting of layers of 1, 3, 6, 10, and 15 pegs with one peg open. In the fourth dimension you would have tetrahedron layers of size 1, 4, 10, 20, and 35 pegs.

Is this puzzle solvable in higher dimensions? And why?

Aly
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    There are lots of similar puzzles with slightly different shapes, sizes, and rules that all go under the name "peg solitaire" so you should specify exactly which you mean. – Ted Aug 28 '17 at 04:00
  • Possibly combine graph theory and vector spaces to show how we can transcend a proof from $R^2$ to $R^3$ or even $R^n$? – Stone Sep 16 '17 at 15:04
  • That's what I would like to see, but I'm not that knowledgeable in either of those subjects. – Aly Sep 16 '17 at 17:41

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