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 Pegless Painting Plummets! (2) (Posted on 2006-06-02)
It is strongly recommended that you try this one first.

Can you hang a painting from three pegs such that the removal of any single peg causes the painting to fall?

 Submitted by Tristan Rating: 4.0000 (1 votes) Solution: (Hide) Call the pegs, from left to right, A, B, and C. I will denote the string's path by using capital letters whenever it goes over the corresponding peg, and small letters whenever it goes under the peg. For example, the solution to the original "Pegless Painting Plummets!" would be denoted as AbBAaB When, for example, peg B is removed, all 'b's and 'B's are removed, leaving AAa. Consecutive pairs like AA are removed because they signify a backtracking in the string's path. We are left with just the sequence a, which signifies that the painting has plummeted. This notation is necessary because the solution to this problem is much longer. This is the solution that Jer came up with. I hope you have lots of string. AbBAaBcCBaABbAabC If we remove all 'a's and 'A's, we are left with bBBcCBBbbC which reduces to bc If we remove all 'b's and 'B's, we are left with AAacCaAAaC which reduces to ac If we remove all 'c's and 'C's, we are left with AbBAaBBaABbAab which reduces to ab Jer has posted an ascii illustration, as well as a general solution for n pegs here.

 Subject Author Date solution without string Robby Goetschalckx 2006-06-09 04:39:40 re: This works brianjn 2006-06-06 02:16:10 re: This works Salil 2006-06-05 22:56:41 This works Jer 2006-06-05 13:16:59 here's an idea macgyver08 2006-06-03 03:52:48 a try Salil 2006-06-03 00:50:24

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