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- Can you place the numbers 1-8 at the corners of a cube, such
that each face has the same sum (of its four adjacent corners)?
In how many ways can this be done?
- Can you place different numbers (preferably consecutive) at the corners
of a cube such that the six faces have different sums? Consecutive sums?
- Can you place different numbers (preferably consecutive) on the sides
of a cube such that the eight corners have different sums (of their
three adjacent faces)? Consecutive sums?