Question

A solid cube has been painted yellow, blue and black on pairs of opposite faces. The cube is then cut into 36 smaller cubes such that 32 cubes are of the same size while 4 others are of bigger sizes. Also no faces of any of the bigger cubes is painted blue.

How many cubes do not have any of their faces painted yellow?

• A. 0
• B. 4
• C. 8
• D. 16

Answer 1

The correct option is D 16

In the given statement, there are $36$ cubes, $32$ of which are of the same size and $4$ other sure of bigger size. Clearly, each side of bigger cubes is twice as large as that of similar cubes. Also, since no face of any of the larger cubes is painted blue, so each one of the larger cubes has one face painted red, one is black and all other faces are unpainted.
The cubes having atleast one face painted yellow are the $10$ cubes along the top surface and $10$ cubes along the bottom surface i.e. $20$ cubes having atleast one face painted yellow.

Thus, the number of cubes having none of their faces painted yellow are

$36-20=16$.