Mad Marchness\text{Mad Marchness}

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The NCAA basketball tournament is currently set up as a single elimination tournament made up of sixty-three games, played by sixty-four teams each spring. This means that once a team loses, they are eliminated.

However, this method is not conducive to identifying a true third or fourth place team. One way to fix this is to change the tournament style from single elimination to double elimination. In a double elimination tournament, each team must lose twice in order to be eliminated.

If the tournament was now played in a double elimination style, what is the maximum number of games necessary to determine a third place winner?

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