Question

A cube with edge of length 10 is painted. The cube is then divided into 1000 unit cubes. Among these small cubes, how many cubes which have one or two painted faces?

Answer 1

The numbers of small cubes which have exactly one painted face is 8²=64 on each of the 6 faces, i.e. 64×6=384 cubes.  Also, the number of small cubes which have exactly two painted face is 8 on each of the 12 edges, i.e. 8×12=96 cubes.  Hence there are 384+96=480 cubes