If There's a Loser, Everyone Else is Popular

Discrete Mathematics Level 5

In a class of \(2015\) kids, any set of \(3\) kids contains at least one pair of friends. It turns out that in any possible arrangement, the most popular kid will have at least \(k\) friends. Find \(k\).

Details and Assumptions

  • Friendship is a mutual relation.
  • The most popular kid is the kid with the most friends.
  • If two people tie for most number of friends, then randomly select one of them to be the most popular.
  • This problem is not original.

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