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Regional Olympiad - FBH 2015 Grade 12 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2015

September 23, 2018
combinatoricsSets

Problem Statement

It is given set A={1,2,3,...,2n−1}A=\{1,2,3,...,2n-1\}. From set AA, at least n−1n-1 numbers are expelled such that: a)a) if number a∈Aa \in A is expelled, and if 2a∈A2a \in A then 2a2a must be expelled b)b) if a,b∈Aa,b \in A are expelled, and a+b∈Aa+b \in A then a+ba+b must be also expelled Which numbers must be expelled such that sum of numbers remaining in set stays minimal
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