  If a flat, horizontal, plate settles onto a flat surface, it is known that
the gap $h$ decreases with time $t$ as a power-law: $h\sim t^{-1/2}$. We
consider what happens if the plate is not initially horizontal, and/or the
centre of mass is not symmetrically positioned: does one edge contact the
surface in finite time, or does the plate approach the horizontal without
making contact? The dynamics of this system is analysed and shown to be
remarkably complex.
