Cube Calendar

Logic Level 2

Peter uses two cubes to show the days of the months. On each face of a cube, there is a digit displayed. For example, in the image above, he is showing day 03 of the month.

The cubes can be rotated, and have their positions swapped. Furthermore, the face with a value of 6 can be flipped upside-down to obtain the value of 9. This allows us to display all 31 days of the month.

In the image above, what is the sum of the numbers on the 4 hidden faces of the green cube?

Problem from OBMEP 2011.

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