Discussion
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 64 players in the beginning of the tournament, how many games should be played in total to declare the winner of the tournament?
Answer: C
63 games are needed.
Every game eliminates exactly one player, and the tournament ends when exactly one player, the winner, is left undefeated. Starting from 64 players, 63 players must be eliminated, so 63 games are played.
Counting round by round gives the same total: 32 + 16 + 8 + 4 + 2 + 1 = 63.
64 counts one game per player, but the winner never loses. 32 is only the first round, and 127 is the number of games for a draw of 128 players.
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