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The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner ?
  • a)
    15
  • b)
    29
  • c)
    61
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The 30 members of a club decided to play a badminton singles tournamen...
Clearly, every member except one (i.e. the winner) must lose one game to decide the winner. Thus, minimum number of matches to be played = 30 - 1 = 29.
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Most Upvoted Answer
The 30 members of a club decided to play a badminton singles tournamen...
Problem Analysis:
In a singles tournament, each match eliminates one player. Therefore, to determine the winner, there must be one player remaining who has not been eliminated. Let's analyze the given options.

Options Analysis:
a) 15: If there are 15 matches, then 15 players will be eliminated, and there will be 15 players remaining. However, this is not sufficient to determine the winner, as there can be multiple players with the same number of wins.

b) 29: If there are 29 matches, then 29 players will be eliminated, and there will be only 1 player remaining. This player will be the winner, as there are no other players left to play against.

c) 61: If there are 61 matches, then 61 players will be eliminated, and there will be no players remaining. This means that there cannot be a winner, as all players have been eliminated.

d) None of these: This option is incorrect, as we have already determined that option b) is the correct answer.

Therefore, the minimum number of matches that must be played to determine the winner is 29, which is option b).

Conclusion:
To determine the winner in a badminton singles tournament with 30 members, a minimum of 29 matches must be played. This ensures that all but one player have been eliminated, leaving the remaining player as the winner.
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The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner ?a)15b)29c)61d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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