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10 games

From concerned reader: if I am reading the question correctly, the answer of 10 games submitted is not accurate. However, let me clarify the question first. I believe that we are asking how many games must be played in total to determine one, and only one, winner of the entire tournament. Given that this is the correct interpretation of the question, the correct answer is that 19 games must be played to determine a singular winner of the tournament.

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