TY - GEN
T1 - Picture-hanging puzzles
AU - Demaine, Erik D.
AU - Demaine, Martin L.
AU - Minsky, Yair N.
AU - Mitchell, Joseph S.B.
AU - Rivest, Ronald L.
AU - Pǎtraşcu, Mihai
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/84861994581
U2 - 10.1007/978-3-642-30347-0_11
DO - 10.1007/978-3-642-30347-0_11
M3 - Conference contribution
AN - SCOPUS:84861994581
SN - 9783642303463
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 81
EP - 93
BT - Fun with Algorithms - 6th International Conference, FUN 2012, Proceedings
T2 - 6th International Conference on Fun with Algorithms, FUN 2012
Y2 - 4 June 2012 through 6 June 2012
ER -