olymmath

CL-MO 2012 Problem 3

    A person enters the social network facebook. He befriends at least one person a day for the first 3030 days. At the end of those 3030 days, it has been exactly 4545 friends. Prove that there is a sequence of consecutive days where made exactly 1414 friends.

    Dataset text AI-MO AoPS. Quoted with source.

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