Two-Cube Calendar

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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.


See the details for a hint.


Contributed by: Izidor Hafner (August 2013)
Open content licensed under CC BY-NC-SA



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.


[1] M. Gardner, The Colossal Book of Short Puzzles and Problems, New York: W. W. Norton, 2006 pp. 4, 18.

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