MathDB

5

Part of 2018 Poland - Second Round

Problems(1)

5-element subsets

Source: 69 Polish MO 2018 Second Round - Problem 5

4/28/2018
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.
combinatoricsset theorypigeonhole principlePolandcounting