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"Family" of subsets

Source: Indonesia TST Round 1-Combinatorics

March 3, 2024
TststcombinatoricsSubset

Problem Statement

Let AA be a set with 10001000 members and F=\mathcal F ={A1,A2,…,AnA_1,A_2,\ldots,A_n} a family of subsets of A such that (a) Each element in F\mathcal F consists of 3 members (b) For every five elements in F\mathcal F, the union of them all will have at least 1212 members Find the largest value of nn
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