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Regional Olympiad - Republic of Srpska 2004 Grade 9 Problem 4

Source: Regional Olympiad - Republic of Srpska 2004

September 19, 2018
SetscombinatoricsDivisiondisjointSubset

Problem Statement

Set S={1,2,...,n}S=\{1,2,...,n\} is firstly divided on mm disjoint nonempty subsets, and then on m2m^2 disjoint nonempty subsets. Prove that some mm elements of set SS were after first division in same set, and after the second division were in mm different sets
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