  Budach's Mouse-in-an-Octant Problem (attributed to Lothar Budach in a 1980
article by van Emde Boas and Karpinski) concerns the behaviour of a very simple
finite-state machine ("the mouse") moving on the integer two-dimensional grid.
Its decidability is apparently still open. This note sketches a proof that an
extended version of the problem (a super-mouse) is undecidable.
