Question

The surface of a cube is painted red and blue, 3 sides of each. The cube is cut into 27 equal sized smaller cubes. Find both answers to the question, "How many cubes have at least 2 sides painted blue?" and "How many cubes have at least 1 side painted red?"

I have no idea how to do this at all what so ever.

Answer 1

Pick up a real cube and draw a 3x3 grid one each face.

Fill in the grids on 3 faces with R and 3 with B.

The very center cubelet has no painted faces.

Now count the others and total up the various color combinations.

Make sure that it makes no difference how the two colors are arranged on the cube.