Problem #PRU-116873

Problems Methods Extremal principle Extremal principle (other) Mathematical induction Mathematical induction (other) Algebraic methods Partitions into pairs and groups; bijections Pigeonhole principle Pigeonhole principle (other)
 14–15  4.0

Problem

We are given \(n+1\) different natural numbers, which are less than \(2n\) (\(n>1\)). Prove that among them there will always be three numbers, where the sum of two of them is equal to the third.