With three differently colored paints, in how many ways can the faces of a rectangular box can be painted so that the color changes occur only at each corner?
I was trying to solve this by principle of inclusion and exclusion, but I am unable to enumerate the number of ways to color the rectangular box( without any restrictions) because there are some distinct faces(adjacent faces) and some are non distinct faces(opposite faces).
Please help
Edit: The colorings which differ by rotation/s are considered to be same.