Some unit cubes are assembled to form a larger cube. Some of the faces of the larger cube are then painted. The cube is taken apart and it is found that 217 of the unit cubes have paint on them. What is the total number of unit cubes?
(In reply to Another way of looking at it.
I like your way, Charlie... much cleaner than what I suggested... (which was pretty much raw brute force)...
but it was a very easy problem to do by plowing through it (and I was in a hurry!).