{
  "id": "2102.00984",
  "version": "v1",
  "published": "2021-02-01T17:07:59.000Z",
  "updated": "2021-02-01T17:07:59.000Z",
  "title": "Faulty picture-hanging improved",
  "authors": [
    "Johan Wästlund"
  ],
  "comment": "14 pages, 3 figures",
  "categories": [
    "cs.DM",
    "math.CO"
  ],
  "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 $k$-out-of-$n$ problem, the size of a solution can be bounded by a polynomial in $n$. We give simplified proofs of these facts, for the latter leading to a reasonable exponent in the polynomial bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-01T17:07:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "G.2.1",
      "G.3"
    ],
    "keywords": [
      "faulty picture-hanging",
      "classical brain teaser asks",
      "polynomial bound",
      "specified sets",
      "framed picture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}