Question

Three adjacent face of one cube is painted in pink, one adjacent pair of faces is painted in black and the remaining faces are Painted in violet. The cube is the cut into 216 identical cubelets.

How many the cubelets have exactly two painted surface in two different colors?

• A. 36
• B. 32
• C. 48
• D. 38

Answer 1

The correct option is B 32

Cube is cut in $6\times 6\times 6=216$ cubelets

Pattern of painting is an follows.



Let us analysis the color combination

Corners	Edges	Faces
PPP- 1, BBP =1 PPB -2, BBV = 1 PPV-1, PVB =2	PP = 3, PB = 4 BB =1, PV = 2 BV =2	P = 3 B =2 V =1

In this question there is a restriction on the number of painted surface. The paint should be only on two faces only. Hence we'll not consider cubelets from corner. Hence only 32 cubelets.