Question

The surface of a cube is painted red and blue, 3 sides of each color. the cube is then cut into 27 equal sized smaller cubes.

A: How many cubes have at least 2 sides painted blue?

B: How many cubes have at least 1 side painted red?

Answer 1

A: it depends how the cube is painted. If the 3 blue sides of the original cube share a common corner then 7 of the smaller cubes have at least 2 sides that are blue. If 2 opposite faces of the original cube are blue then 6 of the 27 have at least 2 faces that are blue.

B: 19 or 21, again depending on how the original cube is painted.