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Pegless Painting Plummets! (2) (Posted on 2006-06-02) Difficulty: 5 of 5
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

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.


If we remove all 'a's and 'A's, we are left with
which reduces to

If we remove all 'b's and 'B's, we are left with
which reduces to

If we remove all 'c's and 'C's, we are left with
which reduces to

Jer has posted an ascii illustration, as well as a general solution for n pegs here.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Solutionsolution without stringRobby Goetschalckx2006-06-09 04:39:40
re: This worksbrianjn2006-06-06 02:16:10
re: This worksSalil2006-06-05 22:56:41
SolutionThis worksJer2006-06-05 13:16:59
here's an ideamacgyver082006-06-03 03:52:48
a trySalil2006-06-03 00:50:24
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