Picture-Hanging Puzzles
Name
1203.3602.pdf
Description
Submitted version
Size
2.11 MB
Format
Adobe PDF
Checksum (MD5)
a61ab057947d2ccee1d104f7da5209e0
Author(s)
Demaine, Erik D
Demaine, Martin L
Minsky, Yair N.
Mitchell, Joseph S. B.
Rivest, Ronald L
Pǎtraşcu, Mihai
Date Issued
September 2013
Journal
Theory of Computing Systems
Publisher
Springer Science and Business Media LLC
Citation
Demaine, Erik D. et al. "Picture-Hanging Puzzles." Theory of Computing Systems (September 2013): 531–550 © 2013 Springer Science+Business Media New York
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
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00224-013-9501-0
