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About the subsets of S

Source: Turkey EGMO TST 2019 #1

July 15, 2020
combinatoricscombinatorics proposed

Problem Statement

A1,A2,...,AnA_1, A_2, ..., A_n are the subsets of ∣S∣=2019|S|=2019 such that union of any three of them gives SS but if we combine two of subsets it doesn't give us SS. Find the maximum value of nn.
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