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School Clubs

Author: mathforces
Problem has been solved: 3 times

Русский язык | English Language

The school has 2020 students and there are various clubs in this school such that there are no two different clubs with the same sets of members. If two students are in a club together, they know each other. However, it turned out that if a student is not a member of a club, then she does not know at least one member of this club. Let $N$ be the largest possible number of clubs in this school. Find the last 5 digits of $N$. (If person $A$ knows person $B$ than person $B$ knows person $A$.)

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