Faulty picture-hanging improved
Discrete Mathematics
2021-02-02 v1 Combinatorics
Abstract
A picture-hanging puzzle is the task of hanging a framed picture with a wire around a set of nails in such a way that it can remain hanging on certain specified sets of nails, but will fall if any more are removed. The classical brain teaser asks us to hang a picture on two nails in such a way that it falls when any one is detached. Demaine et al (2012) proved that all reasonable puzzles of this kind are solvable, and that for the -out-of- problem, the size of a solution can be bounded by a polynomial in . We give simplified proofs of these facts, for the latter leading to a reasonable exponent in the polynomial bound.
Cite
@article{arxiv.2102.00984,
title = {Faulty picture-hanging improved},
author = {Johan Wästlund},
journal= {arXiv preprint arXiv:2102.00984},
year = {2021}
}
Comments
14 pages, 3 figures