posted by Neil on .
Each cube below is made up of smaller cubes, but the large cubes are not solid. They had tunnels through them.
• The first cube originally had 27 small cubes, but the tunnel removed 3 cubes.
• The second cube originally had 64 small cubes, but two straight tunnels, 4 cubes deep, removed some cubes.
• The third cube, which originally had 125 small cubes, has 3 straight tunnels, five cubes deep from face to face.
The outside surfaces of these cube constructions have been painted including inside the tunnels and on the bottom. For each construction, how many small cubes have paint on 4 faces? 3 faces? 2 faces? 1 face? 0 face?