Hypercube orientations with only two in-degrees

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 = n2. This is connected to a question arising from constructing a strategy for a “hat puzzle.” AMS 2010 subject classification: 05C20; 00A08; 94B05