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Subsets of 3 without exactly one common element

Source: 2023 Bulgaria JBMO TST Problem 4

May 7, 2023
combinatoricssetSubset

Problem Statement

Given is a set of n≥5n\ge5 people and mm commissions with 33 persons in each. Let all the commissions be nice if there are no two commissions AA and BB, such that ∣A∩B∣=1\mid A\cap B\mid=1. Find the biggest possible mm (as a function of nn).
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