Question

How many small cubes are there which have no coloured faces?

• A. $0$
• B. $4$
• C. $8$
• D. $16$

Answer 1

The correct option is C $8$

For the sake of simplicity, let’s assume you painted and cut a $4cm\times 4cm\times 4cmcube$.

Cutting the 4x4x4 cube into 4 cubes would create $64\times 1\times 1\times 1$ cubes.

Removing the top and bottom layers of cubes would remove $2$cm from the height and make the stack $4\times 4\times 2$.

Removing the left and right layers of cubes would remove $2$ cm from the width and make the stack $4\times 2\times 2$.

Removing the front and back layers would remove $2$ cm from the length and make the stack $2\times 2\times 2$.

a $2\times 2\times 2$cube would be made of $8\times 1\times 1\times 1$cubes.

So, you would have $8$ cubes that are not painted.