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subsets of a set with m elements, related

Source: 1986 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p4

November 21, 2022
combinatoricsSubsets

Problem Statement

Given the finite set MM with mm elements and 19861986 further sets M1,M2,M3,...,M1986M_1,M_2,M_3,...,M_{1986}, each of which contains more than m2\frac{m}{2} elements from MM . Show that no more than ten elements need to be marked in order for any set MiM_i (i=1,2,3,...,1986i =1, 2, 3,..., 1986) contains at least one marked element.
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