Question

You have a 10×10×10 inch cube that is made up of 1×1×1 inch cubes. You paint the outside of the big cube red. How many of the little cubes have paint on at least one of their sides?

Answer 1

The total amount of little cubes on the surface is 600, since there is 100 cubes on one face and there are 6 faces (6 times 100). But, there is overlap because the cubes on the edges are painted on more than one edge. There are 12 edges, and every edge has 10 that need to be subtracted. So that’s a total of 120 that need subtracting, and 600-120 is 480.