Question

A cube is cut into two equal parts along a plane parallel to one of it the faces. One piece is coloured orange on the two largest faces and yellow on the remaining. The other piece is coloured yellow on two smaller adjacent faces and orange on the remaining. Each is then cut into $32$ cubes of the same size. These $64$ cubes are mixed up. Then, how many cubes have no coloured face at all?

• A. $0$
• B. $4$
• C. $8$
• D. $16$

Answer 1

Answer: (A)

$0$

The bigger cube is made up of 4 layers each of which has 16 smaller cubes.

When the cube is cut in half, each piece will have 2 layers of 16 smaller cubes each. Therefore all 64 smaller cubes has atleast one face exposed.

Since all the sides of the two pieces are painted (either yellow or orange), no small cube has any sde which is not coloured.

Option A is correct.