Hard
A cube painted yellow on all faces is cut into 27 small cubes of equal size. How many small cubes are there which have no face painted at all?
Explanation
Explanation
Step 1: A small cube with no face painted at all must be completely hidden inside the large cube, not touching any of its outer surfaces. Step 2: In a 3×3×3 cube, only the single small cube sitting exactly at the centre, one layer in from every face, meets this condition. So there is 1 small cube with no face painted.
PRO TIP
Re-check your working by substituting the answer back into the original question.