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Nets for a Two-Cube Calendar

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This Demonstration shows nets for a two-cube calendar. Each cube face is labeled with a single digit from 0 to 9. It is possible to show any date from 01 to 31 on the two front faces. You can do this by manually rotating each cube into the proper orientation. The problem is to determine the sum of the digits that cannot be seen.

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See the Details for a hint.

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Contributed by: Izidor Hafner and Mateja Budin (July 2017)
Open content licensed under CC BY-NC-SA

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Details

Two cubes have a total of 12 faces. Because we must be able to show the dates 11 and 22, each cube must have faces 1 and 2. There are nine dates 01 to 09, so each cube must also have the face 0. That leaves six faces for the seven remaining numbers 3, 4, 5, 6, 7, 8, 9. But the face with 6 can be turned upside down to show a 9.

Reference

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

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