Picture-Hanging Puzzles

  • Erik D. Demaine
  • Martin L. Demaine
  • Yair N. Minsky
  • Joseph S. B. Mitchell
  • Ronald L. Rivest
  • Mihai Pǎtraşcu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7288)


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.


Boolean Function Sorting Network Borromean Ring Monotone Boolean Function Borromean Link 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • Martin L. Demaine
    • 1
  • Yair N. Minsky
    • 2
  • Joseph S. B. Mitchell
    • 3
  • Ronald L. Rivest
    • 1
  • Mihai Pǎtraşcu
    • 4
  1. 1.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA
  2. 2.Department of MathematicsYale UniversityNew HavenUSA
  3. 3.Department of Applied Mathematics and StatisticsState University of New YorkStony BrookUSA
  4. 4.AT&T Labs–ResearchFlorham ParkUSA

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