Two people take turns coloring a convex polyhedron
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Rachel and Beatrice take turns coloring the faces of a convex polyhedron red and blue, respectively. A player wins if she gets her color on three faces that share a common vertex. If Rachel goes first and both players use their optimal strategies, who wins the game? I don't really understand where to start. I tried playing the game but that didn't help much for me because I couldn't think of any ideas. I know that for a tetrahedron, the game results in a tie. I know that for a cube the first person wins if they pick something adjacent to their first move. After this, I am not sure with a pentagon because if it is a square-based-pyramid, the first person wins if the pick the square but if it is a triangular prism, it results in a tie.
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