Consider a knock-out women's badminton singles tournament where there are no ties. The loser in each game is eliminated from the tournament. Every player plays until she is defeated or remains the last undefeated player. The last undefeated player is declared the winner of the tournament. If there are players in the beginning of the tournament, how many games should be played in total to declare the winner of the tournament?
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Answer: C
In any single-elimination (knock-out) tournament, the following principle applies:
- Each game played results in exactly one loser, who is immediately eliminated from the tournament.
- To determine a single undefeated winner from a starting pool of players, exactly players must be eliminated.
Since each elimination requires exactly one game, the total number of games needed is:
Given that the tournament starts with players:
Thus, games must be played to declare the winner.
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