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Problem 6 (Six-Point Problem)

We start with six points in the plane such that no three of them are on the same line. Two players play a game where they take turns connecting any two points with a line. Once two points are connected, they cannot be joined a second time. The players continue to play until one player is forced to connect points resulting in the formation of a triangle. This player is the loser. Show that the person who makes the opening move will always will if he/she plays skillfully.

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Last modified on Tuesday, January 12, 1999