  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
$s+t=2^n$ and $as+bt=n2^{n-1}$. This is connected to a question arising from
constructing a strategy for a "hat puzzle."
