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Hypercube orientations with only two in-degrees
We consider the problem of orienting the edges of the -dimensional
hypercube so only two different in-degrees and occur. We show that this
can be done, for two specified in-degrees, if and only if an obvious necessary
condition holds. Namely, there exist non-negative integers and so that
and . This is connected to a question arising from
constructing a strategy for a "hat puzzle."Comment: 9 pages, 4 figure
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