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A classic extremal combi on sets and memberships

Source: Indonesia TST 2016 Round 3

March 24, 2024
combinatoricsSetsExtremal combinatorics

Problem Statement

Let {E1,E2,…,Em}\{E_1, E_2, \dots, E_m\} be a collection of sets such that Ei⊆X={1,2,…,100}E_i \subseteq X = \{1, 2, \dots, 100\}, Ei≠XE_i \neq X, i=1,2,…,mi = 1, 2, \dots, m. It is known that every two elements of XX is contained together in exactly one EiE_i for some ii. Determine the minimum value of mm.
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