Question

A cube painted yellow on all faces is cut into 27 small cubes of each size. How many small cubes are painted on one face only?

Answer 1

Answer:

6

Step-by-step explanation:

The small cubes fall into 4 different types:

1. The centre small cube.  1 of these.  Not painted at all.
2. Centre of each face.  6 of these as there's one on each face.  Painted on one face only.
3. Middle of each edge.  12 of these as there's one on each edge.  Painted on two faces.
4. Corner.  8 of these as there's one at each corner.  Painted on three faces.

Notice this accounts for all 1+6+12+8 = 27 small cubes.

The 6 of type 2 are the ones that are painted on one face only.