# Picture-Hanging Puzzles

• Published in 2012
In the collections
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.

## Other information

arxivId
1203.3602
isbn
9783642303470
pages
17

### BibTeX entry

@article{Demaine2012,
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.},
archivePrefix = {arXiv},
arxivId = {1203.3602},
author = {Demaine, Erik D. and Demaine, Martin L. and Minsky, Yair N. and Mitchell, Joseph S. B. and Rivest, Ronald L. and Patrascu, Mihai},
eprint = {1203.3602},
isbn = 9783642303470,
month = {mar},
pages = 17,
title = {Picture-Hanging Puzzles},
url = {http://arxiv.org/abs/1203.3602 http://arxiv.org/pdf/1203.3602v2},
year = 2012,
primaryClass = {cs.DS},
urldate = {2012-11-03},
collections = {Puzzles,Easily explained}
}