MathDB
Nice pigeonhole problem

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July 5, 2020
geometric inequalitycombinatoricspigeonholepigeonhole principle

Problem Statement

Consider 16 16 pairwise distinct natural numbers smaller than 1597. 1597. a) Prove that among these, there are three numbers having the property that the sum of any two of them is bigger than the third. b) If one of these numbers is 1597, 1597, is still true the fact from subpoint a)?
Teodor Radu