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Problem #302

Tennis Tournament

In a tennis tournament, N = 1234567890 people participate.

The organizing committee numbered all the people as {1,2,3,.....,N} based on their abilities (ability of participant 1 > ability of participant 2 > ability of participant 3 > … > ability of participant N).

Every participant has the same number (say M) of friends in the tournament. A participant calls himself \textbf{superior} if his ability is greater than more than half of his friends.

For example, if M = 13, then a participant will consider himself superior if his ability is greater than 6 of his friends, for M = 14, a participant will be superior if his ability is greater than 7 of his friends.

Find the maximum possible number of participants that can consider themselves as \textbf{superior}.

Contributed by Ashutosh Singh

Solved by 2 users

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