Circle inequality
Source: Ukrainian Mathematical Olympiad 2024. Day 1, Problem 9.3
March 19, 2024
algebrainequalities
Problem Statement
positive real numbers with sum are arranged on a circle. It is known that any two adjacent numbers differ at least in times. For each pair of adjacent numbers, the smaller one was subtracted from the larger one, and then all these differences were added together. What is the smallest possible value of this resulting sum?Proposed by Oleksiy Masalitin