Faulty picture-hanging improved

02/01/2021

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by   Johan Wästlund, et al.

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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.