Each face of two cubes is labeled with a single digit from 0 to 9. It is possible to show any date from 01 to 31 on the front faces. The problem is to determine the sum of the digits that cannot be seen.[more]
See the details for a hint.[less]
Each cube must have faces with 0, 1, and 2, leaving six faces with 3, 4, 5, 6, 7, 8; the face with 6 can be turned upside down to be 9.
 M. Gardner, The Colossal Book of Short Puzzles and Problems, New York: W. W. Norton, 2006 pp. 4, 18.