2022 USAMO Problems/Problem 6

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?

See also

2022 USAMO (ProblemsResources)
Preceded by
Problem 5
Followed by
Last Problem
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All USAMO Problems and Solutions

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