A wooden block 5 cm long, 4 cm deep and 2 cm high is painted on all six faces and then cut into 1 cm cubes. How many cubes have paint on exactly two faces?

The block is only 2 cubes high, so the four upright edges are made of corner cubes only. Along each of the 4 long edges there are $5-2=3$ non-corner cubes, and along each of the 4 depth edges $4-2=2$. Total $4\times 3+4\times 2=20$.