# Non-standard dice

**Discrete Mathematics**Level 4

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 \(7\)?

**Details and assumptions**

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

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