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subset of {1,2, 3,... , 2014}, with 12 elements, with numbers of sum = 2015

Source: INAMO Shortlist 2015 C7

May 14, 2019
combinatoricsSumSubset

Problem Statement

Show that there is a subset of AA from {1,2,3,...,2014}\{1,2, 3,... , 2014\} such that : (i) ∣A∣=12|A| = 12 (ii) for each coloring number in AA with red or white , we can always find some numbers colored in AA whose sum is 20152015.
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