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 obvious necessary conditions hold. Namely, we need 0⩽a,b⩽n and also there exist non-negative integers s and t so that s+t=n2 and as+bt=n2n−1. This is connected to a question arising from constructing a strategy for a “hat puzzle”.