We consider the problem of orienting the edges of the n-dimensional
hypercube so only two different in-degrees a and b 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 s and t so that
s+t=2n and as+bt=n2n−1. This is connected to a question arising from
constructing a strategy for a "hat puzzle."Comment: 9 pages, 4 figure