Nick Baxter asks for references to the Colllege Board question:

<<
  Problem:
    Given an equilateral pyramid (square base), glue two regular
    tetrahedrons (same edge length) to two non-adjacent triangular faces.
    How many faces does the resulting polyhedron have?
>>

I may be wrong, but as I recall it, the problem was to glue a regular tetrahedron to a regular octahedron along one common face.

--Dan