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Bosnia and Herzegovina JBMO TST 2017 Problem 2

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2017

September 16, 2018
combinatoricsSetsSubsets

Problem Statement

Let AA be a set A={1,2,3,...,2017}A=\{1,2,3,...,2017\}. Subset SS of set AA is good if for all xāˆˆAx\in A sum of remaining elements of set SS has same last digit as xx. Prove that good subset with 405405 elements is not possible.
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