# geometry

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Stupid logic problem: At the state basketball tournament, 42 basketball games are played to determine the winner of the tournament. After each game, the loser is eliminated from the tournament. How many teams are in the tournament?

• geometry -

work backwards ....

final game: 2 teams , 1 game
semi's : 4 teams , 2 game, total = 3 games
quarters: 8 teams, 4 games, total = 7 games
round before: 16 teams, 8 games, total = 15 games
before that : 32 teams, 16 gaMES, total = 31 games
before that: 64 teams, 32 games, total = 63 games

In a loser-elimination tournament, there cannot be a total of 42 games, unless some teams had byes.
Data seems flawed.
e.g.
for 32 teams there would be 31 games,
for 64 teams there would be 63 games
notice the the total number of teams must be a power of 2 and the total number of games is 1 less than the number of teams.

Check my thinking.

• geometry -

e.g. look at the draw for the men's singles at the
current US Open Tennis tournament

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