  We prove that a particular pushing-blocks puzzle is intractable in 3D. The
puzzle, inspired by the game PushPush, consists of unit square blocks on an
integer lattice. An agent may push blocks (but never pull them) in attempting
to move between given start and goal positions. In the PushPush version, the
agent can only push one block at a time, and moreover, each block, when pushed,
slides the maximal extent of its free range. We prove this version is NP-hard
in 3D by reduction from SAT. The corresponding problem in 2D remains open.
