Picture a Rubik Cube. Now drop it into paint so that is completly covered. When the paint is dry, imagine smashing it on the floor and breaking it into smaller cubes. How many of the cubes have one face painted. How many cubes has 2 faces covered in paint? How many have three faces covered in paint? How many have 0 faces covered in paint. How could you predict the above for any Rubki cube. What about 4x4x4, 5x5x5, 6x6x6? NXNXN?
