Picture-Hanging Puzzles
Data Structures and Algorithms
2014-04-29 v2 General Topology
Group Theory
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.
Cite
@article{arxiv.1203.3602,
title = {Picture-Hanging Puzzles},
author = {Erik D. Demaine and Martin L. Demaine and Yair N. Minsky and Joseph S. B. Mitchell and Ronald L. Rivest and Mihai Patrascu},
journal= {arXiv preprint arXiv:1203.3602},
year = {2014}
}
Comments
18 pages, 8 figures, 11 puzzles. Journal version of FUN 2012 paper