Question: (a) In how many ways can we 5-color the vertices of a regular hexagon that is free to move in two dimensions? (b) Answer part

(a) In how many ways can we 5-color the vertices of a regular hexagon that is free to move in two dimensions?
(b) Answer part (a) if the hexagon is free to move in three dimensions.
(c) Find two 5-colorings that are equivalent for case (b) but distinct for case (a).

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