Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Picture-Hanging Puzzles   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.

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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org