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 cubelets do not have pink color on them?

• A. 120
• B. 100
• C. 150
• D. 125

Answer 1

The correct option is D 125

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

The number of cubelets with no pink color = 216 - (36 from one pink surface + 30 from second + 25 from third) = 125 cubelets.