@article{DDMMx12y,
  author = 	 { Erik D. Demaine and Martin L. Demaine and Yair N. Minsky and Joseph S. B. Mitchell and Ronald L. Rivest
                   and Mihai P{\u{a}}tra{\c{s}}cu },
  title = 	 { Picture-Hanging Puzzles },
  pages = 	 { 531--550 },
  journal =      { Theory of Computing Systems },
  date =         { 2014-04 },                  
  OPTyear = 	 { 2014 },
  OPTmonth = 	 { May, },
  volume = 	 { 54 },
  number =       { 4 },                  
  abstract =     { 
                  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.  
                 },                  
}