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Found problems: 1

2024 Auckland Mathematical Olympiad, 9
$100$ students came to a party. The students who did not have friends among other students left the party first. Then those with one friend among remaining students left. Then those with $2,3, \ldots 99$ friends among remaining students left. What is the maximal number of students that can still remain at the party after that? (If $A$ is a friend of $B$, then $B$ is a friend of $A$).
party algebra