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 = 2 n and a s + b t = n 2 n − 1 . This is connected to a question arising from constructing a strategy for a “hat puzzle”.