Question: (a) In how many ways can we 3-color the vertices of a regular hexagon that is free to move in space? (b) Give a combinatorial

(a) In how many ways can we 3-color the vertices of a regular hexagon that is free to move in space?
(b) Give a combinatorial argument to show that for all m ∈ Z+, (m6 + 2m + 2m2 + 4m3 + 3m4) is divisible by 12.

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