A solid, four-inch cube of wood is coated with blue paint on all six sides. Then the cube is cut into smaller one-inch cubes.These new one-inch cubes will have either three blue sides, two blue sides, one blue side, or no blue sides. How many of each will there be with no sides colored?

When a 4-inch cube is painted on all six sides and cut into 1-inch cubes, the interior cubes have no paint. The 4x4x4 cube has 64 total cubes. The outer layer consists of cubes with at least one painted face. The interior is a 2x2x2 cube (since we remove one layer from each side: 4-2=2). So 2x2x2 = 8 cubes have zero painted sides. The distractor counts (4, 12, 24) correspond to cubes with 3, 2, and 1 painted sides respectively.