Directions: A cube of side 10 cm is coloured red with a 2 cm wide green strip…

For a cube whose outer surface is painted and then sliced into an n × n × n grid of identical smaller cubes, every small cube's set of painted faces is fixed purely by its position in the grid: the 8 corner cubes each expose 3 faces, the cubes lying along an edge (excluding corners) each expose 2 faces, the cubes at the centre of a face expose exactly 1 face, and the cubes strictly inside the block expose none. When two colours are used — a border strip running around every face and a plain interior — every exposed face that touches any edge of the big cube takes the border colour, and only a face whose exposed square sits away from every edge keeps the interior colour.

1. Side = 10 cm, cut into 125 = 53 smaller cubes, so each small cube has side 10 / 5 = 2 cm — exactly the width of the green strip. So the green strip is exactly one layer of small cubes deep along every edge of every face.

2. Classify the 125 small cubes by position: 8 corner cubes (3 exposed faces each), 12 edges × 3 middle cubes = 36 edge cubes (2 exposed faces each), 6 faces × 3 × 3 = 54 face-centre cubes (1 exposed face each), and 3 × 3 × 3 = 27 fully interior cubes (0 exposed faces). Check: 8 + 36 + 54 + 27 = 125.

3. A corner cube's three exposed faces each lie in the outermost layer along both directions of that face, so all three faces fall inside the green border — each corner cube has 3 green faces.

4. An edge cube's two exposed faces each still lie in the outermost layer along one of the two directions of that face (because the cube sits on an edge), so both exposed faces fall inside the green border too — each edge cube has 2 green faces.

5. A face-centre cube's single exposed face lies entirely in the inner 6 cm × 6 cm square of that face, away from every edge, so that face is red, not green — 0 green faces. Interior cubes expose no face at all — 0 green faces.

6. “At least two green faces” is satisfied only by the corner cubes and the edge cubes: 8 + 36 = 44.

Cross-check by complementary counting: total pieces minus the pieces that do NOT qualify = 125 − 54 (face-centre) − 27 (interior) = 44, matching the direct count.

So 44 cubes have at least two green faces each.