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5-element subsets

Source: 69 Polish MO 2018 Second Round - Problem 5

April 28, 2018
combinatoricsset theorypigeonhole principlePolandcounting

Problem Statement

Let A1,A2,...,AkA_1, A_2, ..., A_k be 55-element subsets of set {1,2,...,23}\{1, 2, ..., 23\} such that, for all 1≤i<j≤k1 \le i < j \le k set Ai∩AjA_i \cap A_j has at most three elements. Show that k≤2018k \le 2018.
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