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intressting comb problem

Source: Romania TST for BMO 1994,P3

September 6, 2017
combinatoricsalgebra

Problem Statement

Let M1,M2,...,M11M_1, M_2, . . ., M_{11} be 5−5-element sets such that M_i \cap M_j \neq {\O} for all i,j∈{1,...,11}i, j \in \{1, . . ., 11\}. Determine the minimum possible value of the greatest number of the given sets that have nonempty intersection.
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