1024 players participate in a tennis tournament in a direct elimination format. Each match eliminates exactly one player. How many games must be played to determine the champion?
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The elimination tournament
In a tournament like this, following the table game by game is more distracting than it helps. The question becomes clearer when you look at what really changes after each encounter.
Hints
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- No cuentes rondas: cuenta eliminados.
- Each match elimina exactly a jugador.
Solution
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Answer: 1023 matches are needed. Explanation: Each match eliminates exactly one player. At the beginning there are 1024 players and at the end there should only be 1 champion left. Therefore we must eliminate
$$ 1024-1=1023 $$
players, and that requires exactly 1023 games. No further formula is needed: a knockout tournament ends when all but one have fallen.
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