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Regional Olympiad - FBH 2013 Grade 11 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2013

September 24, 2018
combinatoricsset

Problem Statement

If A={1,2,...,4s−1,4s}A=\{1,2,...,4s-1,4s\} and S⊆AS \subseteq A such that ∣S∣=2s+2\mid S \mid =2s+2, prove that in SS we can find three distinct numbers xx, yy and zz such that x+y=2zx+y=2z
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