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How many matches?

51 teams are there and they are to play basketball matches. A team is out of the tournament if it looses 2 games. What is the maximum number of games to be played to decide one winner?

SOLUTION : A team is out as soon it looses 2 matches. In a match, one team definitely looses. So, for 51 teams, the number of matches in which all of them will be eliminated is atmost 102. There cannot be more than 102 matches. But if there are 102 matches, no team will be winner. So, answer is less than 102.

For a team to be a winner, remaining teams have to be eliminated, which can only be done if all of those 50 teams lose 2 matches. So, a minimum of 100 matches have to be played.

So, the answer can be 100 or 101. Answer would be 100 when the winning team has lost no match. Answer will be 101 when winning team has lost 1 match. So, maximum games to be played to decide 1 winner is 101.

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