Picture-Hanging Puzzles

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...

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Bibliographic Details
Published inTheory of computing systems Vol. 54; no. 4; pp. 531 - 550
Main Authors Demaine, Erik D., Demaine, Martin L., Minsky, Yair N., Mitchell, Joseph S. B., Rivest, Ronald L., Pǎtraşcu, Mihai
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.05.2014
Springer Nature B.V
Subjects
Algorithms
Analysis
Applied mathematics
Boolean
Boolean functions
Computer Science
Construction
Magic & magicians
Mathematical analysis
Mathematical models
Nails
Pictures
Polynomials
Puzzles
Studies
Theory of Computation
Topological manifolds
Wrapping
Algorithms
Topology
Monotone functions
Free group
Magic
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-013-9501-0