IMC 2024 · Problem 6

Day 231st IMC · Blagoevgrad, Bulgaria

Statement

Prove that for any function $f \colon \mathbb{Q} \to \mathbb{Z}$ , there exist $a, b, c \in \mathbb{Q}$ such that $a < b < c$ , $f(b) \ge f(a)$ , and $f(b) \ge f(c)$ .

Official solution

Hidden so you can work on the problem first.

Proposed by Mehdi Golafshan & Markus A. Whiteland, University of Li`ege, Li`ege.