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 smaller cubes or cubelets have exactly two colors on them?

• A. 32
• B. 36
• C. 37
• D. 42

Answer 1

The correct option is B 36

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

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

The cubelets with exactly two colors are found at corners and along the edges having different colors on either side = 5 corner pieces + 8 edges $\times (6-2)=37$ cubelets.