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Weights in sets

Source: Bosnia and Herzegovina TST 2015 day 2 problem 2

May 18, 2015
weightssetcombinatoricspartition

Problem Statement

Let NN be a positive integer. It is given set of weights which satisfies following conditions: i)i) Every weight from set has some weight from 1,2,...,N1,2,...,N; ii)ii) For every iāˆˆ1,2,...,Ni\in {1,2,...,N} in given set there exists weight ii; iii)iii) Sum of all weights from given set is even positive integer. Prove that set can be partitioned into two disjoint sets which have equal weight
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