ISL 2021 A1

Let $n$ be an integer, and let $A$ be a subset of $\left\{0,1,2,3, \ldots, 5^{n}\right\}$ consisting of $4 n+2$ numbers. Prove that there exist $a, b, c \in A$ such that $a<b<c$ and $c+2 a>3 b$ .

Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.

Official text: IMO 2021 Shortlist booklet, page 5.

Solutions

Official solution Solution 1 by the IMO Problem Selection Committee

The terms of the source let olymmath link to this solution but not copy it. Read the solution (IMO official site).

Locator isl/2021/a1 · Tag BNKDTAFRDJ · Edit this page on GitHub · Keys: j next, k previous