Question

The six faces of a cube are painted in a manner that no two adjacent faces have the same colour. The three colour used in the painting are red, blue and green. The cube is then cut into 64 equal cubical parts. Answer the following question.
How many cubes in all have three sides painted?
Options:
(a) 2 4
(b) 16
(c) 10
(d) 8​

Answer 1

8 small cubes with one vertex of original cube

Answer 2

8

Step-by-step explanation:

Six faced cube is painted in a manner such that no adjacent faces are of same color. The total number of colors used to paint the cubes are 3 which are red, blue and green.

With these two statement we can judge that the opposite faces are of similar color. As the cube is painted and then cut into 64 equal cubical pieces then only 8 pieces will be of the type which are painted from three sides. As only the corner of bigger cubes will have three sides painted.

As an example I have attached a image below in which we can see that the if cube is cut in equal parts only the corner of cube will have three sides painted. And in cube we have only 8 such corners.