Picture-Hanging Puzzles

• Published in 2012
• Added on 2012-11-03

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.

Links

• http://arxiv.org/abs/1203.3602
• http://arxiv.org/pdf/1203.3602v2

Other information

BibTeX entry

@article{Demaine2012,
	key = {Demaine2012},
	type = {article},
	title = {Picture-Hanging Puzzles},
	author = {Demaine, Erik D. and Demaine, Martin L. and Minsky, Yair N. and Mitchell, Joseph S. B. and Rivest, Ronald L. and Patrascu, Mihai},
	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.},
	comment = {},
	date_added = {2012-11-03},
	date_published = {2012-03-01},
	urls = {http://arxiv.org/abs/1203.3602,http://arxiv.org/pdf/1203.3602v2},
	collections = {easily-explained,puzzles,the-groups-group},
	url = {http://arxiv.org/abs/1203.3602 http://arxiv.org/pdf/1203.3602v2},
	urldate = {2012-11-03},
	year = 2012,
	archivePrefix = {arXiv},
	arxivId = {1203.3602},
	eprint = {1203.3602},
	isbn = 9783642303470,
	month = {mar},
	pages = 17,
	primaryClass = {cs.DS}
}