English

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 kk-out-of-nn problem, the size of a solution can be bounded by a polynomial in nn. 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

R2 v1 2026-06-23T22:43:56.416Z