Posted by **Anonymous** on Wednesday, October 2, 2013 at 3:38pm.

How many distinct ways are there to label the faces of a cube with distinct numbers from 1 to 6, such that there is at least one pair of opposite faces which do not sum to 7?

Rotations (which preserve orientation) are considered the same way.

Reflections (which do not preserve orientation) are considered distinct.

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