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2022 USAMO Problems/Problem 6

Revision as of 13:41, 27 March 2022 by Shihan (talk | contribs) (Created page with "==Problem== There are <math>2022</math> users on a social network called Mathbook, and some of them are Mathbook-friends. (On Mathbook, friendship is always mutual and permane...")
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Problem

There are $2022$ users on a social network called Mathbook, and some of them are Mathbook-friends. (On Mathbook, friendship is always mutual and permanent.)

Starting now, Mathbook will only allow a new friendship to be formed between two users if they have at least two friends in common. What is the minimum number of friendships that must already exist so that every user could eventually become friends with every other user?

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