The six faces of a cube are painted in such a manner that no two adjacent faces have the same colour. The three colours used are red, white and black. The cube is then cut into 36 smaller cubes in such a manner that 32 cubes are of one size and the rest are of a bigger size, and each of the bigger cubes has no red coloured face. Answer the questions by considering the smaller cubes of both the sizes.
How many smaller cubes have only two of their faces painted?