Skip to main content
Springer Nature Link
Log in

Picture-Hanging Puzzles

  • Conference paper
Fun with Algorithms (FUN 2012)

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

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Brunn, H.: Über Verkettung. Sitzungsberichte der Bayerische Akad. Wiss. 22, 77–99 (1892)

    Google Scholar 

  2. Demaine, E.D., Demaine, M.L., Uehara, R.: Any monotone Boolean function can be realized by interlocked polygons. In: CCCG 2010, pp. 139–142 (2010)

    Google Scholar 

  3. Ellul, K., Krawetz, B., Shallit, J., Wang, M.: Regular expressions: new results and open problems. J. Autom. Lang. Comb. 9(2-3), 233–256 (2005)

    MathSciNet  Google Scholar 

  4. Makanin, G.S.: Decidability of the universal and positive theories of a free group. Mathematics of the USSR-Izvestiya 25(1), 75–88 (1985)

    Article  MathSciNet  Google Scholar 

  5. Pegg Jr., E.: http://www.mathpuzzle.com/hangingpicture.htm

  6. Rolfsen, D.: Knots and Links. Publish or Perish, Inc., Houston (1976)

    MATH  Google Scholar 

  7. Sillke, T.: http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/quantum/B201

  8. Sloane, N.J.A.: Sequence A073121. In: On-Line Encyclopedia of Integer Sequences (August 2002), http://www.research.att.com/projects/OEIS?Anum=A073121

  9. Spivak, A.: Brainteasers B 201: Strange painting. Quantum, 13 (May/June 1997)

    Google Scholar 

  10. Stanford, T.: Brunnian braids and some of their generalizations. Bull. Lond. Math. Soc. To appear arXiv:math.GT/9907072, http://arXiv.org/abs/math/9907072

  11. Tait, P.G.: On knots. Trans. Royal Society of Edinburgh 28, 145–190 (1876)

    Google Scholar 

  12. vos Savant, M.: Ask Marilyn. PARADE (2001) (Posed June 10 and solved June 17)

    Google Scholar 

Download references

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martin L. Demaine
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yair N. Minsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Joseph S. B. Mitchell
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ronald L. Rivest
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Mihai Pǎtraşcu
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

  • 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)

Publish with us

Policies and ethics