Picture-Hanging Puzzles

Details Picture-Hanging Puzzles Picture-Hanging Puzzles

2012-03-16

arxiv.org/abs/1203.3602v1

Computer Science

Data Structures and Algorithms

17 pages, 7 figures, 11 puzzles. Full version of FUN 2012 paper

Scientific paper

We show how to hang a picture by wrapping rope around n nails, making a polynomial number of twists, such that the picture falls whenever any k out of the n nails get removed, and the picture remains hanging when fewer than k nails get removed. This construction makes for some fun mathematical magic performances. More generally, we characterize the possible Boolean functions characterizing when the picture falls in terms of which nails get removed as all monotone Boolean functions. This construction requires an exponential number of twists in the worst case, but exponential complexity is almost always necessary for general functions.

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