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 cubelets will have all three colors on them?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

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

Pattern of painting is as 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 small pieces with three color will form corners. Only 2-such diagonal opposite y cubelets are possible.