Hard
A cube painted yellow on all faces is cut into 27 small cubes of equal size. How many small cubes are there painted on atleast 3 faces?
Explanation
Explanation
Step 1: In a 3×3×3 cube, the maximum number of painted faces any small cube can have is 3, and these are exactly the small cubes sitting at the corners of the large cube. Step 2: A cube has 8 corners, so there are 8 small cubes with 3 painted faces, and none has more than 3. So 8 small cubes are painted on at least 3 faces.
PRO TIP
Re-check your working by substituting the answer back into the original question.