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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.
See the Details for a hint.
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