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 smaller cubes have only pink and black colors on them?

• A. 16
• B. 18
• C. 19
• D. 24

Answer 1

The correct option is C 19

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 only pink and black are found at corners and along the edges PB

= 2 PPB cubelets + 1 BBP cubelet + 4 P edges $\times$ (6 -2) = 19 cubelets.