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Picture-Hanging Puzzles

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Fun with Algorithms (FUN 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7288))

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Abstract

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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Author information

Authors and Affiliations

  1. MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, MA, 02139, USA

    Erik D. Demaine, Martin L. Demaine & Ronald L. Rivest

  2. Department of Mathematics, Yale University, 10 Hillhouse Ave., New Haven, CT, 06520, USA

    Yair N. Minsky

  3. Department of Applied Mathematics and Statistics, State University of New York, Stony Brook, NY, 11794-3600, USA

    Joseph S. B. Mitchell

  4. AT&T Labs–Research, 180 Park Ave., Florham Park, NJ, USA, 07932

    Mihai Pǎtraşcu

Authors
  1. Erik D. Demaine
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  2. Martin L. Demaine
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  3. Yair N. Minsky
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  4. Joseph S. B. Mitchell
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  5. Ronald L. Rivest
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  6. Mihai Pǎtraşcu
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Col. By Dr., K1S 5B6, Ottawa, ON, Canada

    Evangelos Kranakis

  2. Department of Mathematics and Computer Science, Wesleyan University, 06459, Middleton, CT, USA

    Danny Krizanc

  3. Dipartimento di Scienze Ambientali, Informatica e Statistica, Università Ca’ Foscari, Via Torino 155, 30172, Mestre (Ve), Italy

    Flaminia Luccio

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© 2012 Springer-Verlag Berlin Heidelberg

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Demaine, E.D., Demaine, M.L., Minsky, Y.N., Mitchell, J.S.B., Rivest, R.L., Pǎtraşcu, M. (2012). Picture-Hanging Puzzles. In: Kranakis, E., Krizanc, D., Luccio, F. (eds) Fun with Algorithms. FUN 2012. Lecture Notes in Computer Science, vol 7288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30347-0_11

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  • DOI: https://doi.org/10.1007/978-3-642-30347-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30346-3

  • Online ISBN: 978-3-642-30347-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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