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Maximal number of sets

Source: Korean Summer Program Practice Test 2016 5

August 17, 2016
combinatoricsset

Problem Statement

Find the maximal possible nn, where A1,…,An⊆{1,2,…,2016}A_1, \dots, A_n \subseteq \{1, 2, \dots, 2016\} satisfy the following properties. - For each 1≤i≤n1 \le i \le n, ∣Ai∣=4\lvert A_i \rvert = 4. - For each 1≤i<j≤n1 \le i < j \le n, ∣Ai∩Aj∣\lvert A_i \cap A_j \rvert is even.
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