If a cube is painted yellow on all faces and cut into 27 small cubes of equal size, then which of the following are correct?
A. Six cubes are painted on one face only.
B. There is only one cube which is not painted on any face.
C. There are six cubes which have two faces painted.
D. There are eight cubes which have three faces painted.

A cube is initially painted yellow on all its six sides and then divided into 27 smaller cubes of equal size. This results in an arrangement similar to a Rubik’s cube. There is one cube located at the center of the cube (at the intersection of the three axes: longitudinal, lateral, and vertical) which remains unpainted. Each of the six sides of the cube has a smaller cube at the center that is painted on just one face. The cube has eight corners, and the cubes situated there are painted on three surfaces. The remaining twelve cubes are painted on only two sides. Consequently, only six small cubes on the cube are painted on one face.

So, we can say statements A,B and D are correct.

Statement C is wrong as there are 12 cubes which have two faces painted.