  The Hales numbered $n$-dimensional hypercube and the corresponding adjacency
matrix exhibit interesting recursive structures in $n$. These structures lead
to a very simple proof of the well-known bandwidth formula for hypercube, whose
proof was thought to be surprisingly difficult. A related problem called
hypercube antibandwidth, for which Harper proposed an algorithm, is also
reexamined in the light of the above recursive structures, and a close form
solution is found.
