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MathNet 2020 — Math Olympiad Vault — Part 01 Question 132

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 01

Question 132

There are $19,998$ people on a social media platform, where any pair of them may or may not be friends. For any group of $9,999$ people, there are at least $9,999$ pairs of them that are friends. What is the least number of friendships, that is, the least number of pairs of people that are friends, that must be among the $19,998$ people?