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 of the cubelets have exactly one painted surface of exactly one color?

• A. 84
• B. 108
• C. 96
• D. 102

Answer 1

The correct option is C 96

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 only the cubelets from middle of faces of cube will be considered

$=6\times (6-2{)}^2=96$ cubelets.