IMO 2007 Shortlist C7
Let α < 3 − √ be a positive real number. Prove that there exist positive integers n and p > α · 2n for which one can sel...
Category: Combinatorics
Problem
Let α < 3 − √ be a positive real number. Prove that there exist positive integers n and p > α · 2n for which one can select 2p pairwise distinct subsets S1, ..., Sp, T1, ..., Tp of the set {1,2,...,n} such that Si ∩ Tj 6= ∅ for all 1 ≤ i,j ≤ p. (Austria)