Picture-hanging puzzles
Name
Rivest_Picture-hanging puzzles.pdf
Size
668.22 KB
Format
Adobe PDF
Checksum (MD5)
75b3186d74b2e44fd265a1d23cf9eb86
Author(s)
Demaine, Erik D.
Demaine, Martin L.
Minsky, Yair N.
Mitchell, Joseph S. B.
Rivest, Ronald L.
Patrascu, Mihai
Date Issued
2012
Journal
Fun With Algorithms
Publisher
Springer-Verlag
Citation
Demaine, Erik D. et al. “Picture-Hanging Puzzles.” Fun with Algorithms. Ed. Evangelos Kranakis, Danny Krizanc, & Flaminia Luccio. (Lecture Notes in Computer Science ; Vol. 7288) Berlin: Springer Berlin Heidelberg, 2012. pp.81–93. Web.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/978-3-642-30347-0_11
