Author(s)Demaine, Erik D.; Demaine, Martin L.; Minsky, Yair N.; Mitchell, Joseph S. B.; Rivest, Ronald L.; Patrascu, Mihai; ... Show more Show less
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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.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Fun With Algorithms
Demaine, Erik D. et al. “Picture-Hanging Puzzles.” Fun with Algorithms. Ed. Evangelos Kranakis, Danny Krizanc, & Flaminia Luccio. (Lecture Notes in Computer Science ; Vol. 7288) Berlin: Springer Berlin Heidelberg, 2012. pp.81–93. Web.
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