Breaking a larger cube into a smaller one I would appreciate ideas on solving the following problem:


  
    A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2.How many of smaller cubes have paint on exactly 2 side ?
Here's my hint: Stare at that for a sufficiently long time, and the solution will come up.



and if that doesn't help, try this:
Imagine a Rubik's cube. There are 6 corners, each 3 colored, then 8 edges that have only 2 colors, and finally there are 6 centre faces that have only one color. So if its all painted the same color then obviously you'll have 8 such cubies...