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 have only two faces painted ?

• A. $24$
• B. $20$
• C. $16$
• D. $8$

Answer 1

The correct option is B $20$

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.
Leaving the $4$ central cubes on each of the blue surface and $8$ cubes at the edges of the block, all the rest have two faces painted. Thus, the cubes having only two faces painted are $8$ cubes on each of the blue surfaces and $4$ larger cubes i.e. there are $(8\times 2)+4=20$ such cubes.