A wooden cube with side length 3 inches is painted red. It is then cut, by cuts parallel to its faces, into 27 cubes of side length 1 inch. After it is cut:
- How many of the 1 × 1 × 1 cubes would have three red faces? Two? One? None?
- If a 4 × 4 × 4 cube were painted and then cut into 64 1 × 1 × 1 cubes, how many cubes would have three/two/one/no red faces?
- How many cubes would have three/two/one/no red faces if a cube with side length n was cut into cubes of side length 1?