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14th Philippine Mathematical Olympiad 2011-National Stage #5

Source:

October 13, 2014
combinatorics unsolvedcombinatorics

Problem Statement

There are exactly 120120 Twitter subscribers from National Science High School. Statistics show that each of 1010 given celebrities has at least 8585 followers from National Science High School. Prove that there must be two students such that each of the 1010 celebrities is being followed in Twitter by at least one of these students.