\indent We show that it is possible to orient the edges of the $n$-dimensional cube so that only the in-degrees $a$ and $b$ occur if and only if the two obvious necessary conditions hold, namely there are nonnegative 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 strategies for a type of hat game with $n$ players so that regardless of placements the number of correct guesses is $a$ or $b$. Joint work with Joe Buhler, Ron Graham and Eric Tressler