I wrote:

<<
> PUZZLE:
> Given a rhombus tiling of a 2n-gon (so that each polygon edge is a rhombus
> edge), show that the number of rhombi is determined by n.
>>

As Michael Kleber and George Hart have (perhaps inadvertently) pointed out, I neglected to mention (except in the Subject line) that the 2n-gon is supposed to be regular.

For a straightforward generalization to parallelograms, one need only assume that the 2n-gon is convex and has n pairs of parallel sides.

--Dan