Let *A* be a solid *a*×*b*×*c* rectangular
brick in three dimensions, where *a*, *b*, *c* > 0. Let
*B* be the set of all points which are a distance at most one from
some point in *A* (in particular, *B* contains *A*).
Express the volume of *B* as a polynomial in *a*, *b*, and
*c*.

Source: Putnam Competition, 1984