IMO 2008 Shortlist C6
For n ≥ 2, let S1,S2,...,S2n be 2n subsets of A = {1,2,3,...,2n+1 } that satisfy the following property: There do not ex...
Category: Combinatorics
Problem
For n ≥ 2, let S1,S2,...,S2n be 2n subsets of A = {1,2,3,...,2n+1 } that satisfy the following property: There do not exist indices a and b with a < b and elements x,y,z ∈ A with x < y < z such that y,z ∈ Sa and x,z ∈ Sb. Prove that at least one of the sets S1,S2,...,S2n contains no more than 4n elements.