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Cracker Barrel Restaurants place a puzzle called “Jump All But One Game” at each table. The puzzle starts with golf tees arranged in a triangle as in Figure 5.29a where the presence of a tee is noted with a solid dot and the absence is noted with a hollow dot. A move can be made if a tee jump over one adjacent tee and land on an empty space. When a move is made, the tee that is jumped over is removed. A possible first move is shown in Figure 5.29b. The goal is to have just one remaining tee. Use the Klein 4-group to show that no matter what sequence of (legal) moves you make, the last remaining tee cannot be in a bottom corner position. enter image description here

I don't know how to apply the Klein 4-group into this problem. Please give me some hints.

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  • $\begingroup$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. $\endgroup$
    – Community Bot
    Commented May 4 at 12:03
  • $\begingroup$ I don't really see how the Klein 4 group applies either. The usual proof involves 3-colouring the holes such that any three-in-a-row contains all three colours. Then every move will increment or decrement the number of pegs in each colour. A simple parity argument then tells you what colour hole the final peg must be in. $\endgroup$
    – Jaap Scherphuis
    Commented May 8 at 8:52

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