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 color on them?

• A. 107
• B. 109
• C. 96
• D. 113

Answer 1

The correct option is D 113

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 cubelets with exactly one color are

One exactly at corner (PPP) = 1

At the three edges each of PP category = 3 (6 - 2) = 12

At the one edge of BB category = 1(6 - 2) =4

At the middle of each of the six faces $=6\times (6-2)=96$

So total cubelets with exactly one colour are

$1+12+4+96=113$