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Minimum value

Source: 2024 imocsl A2 (idependent quiz P3)

August 8, 2024
algebraIMOCminimum valueinequalitiesabsolute value

Problem Statement

Given integer n≥3n \geq 3 and x1x_1, x2x_2, …, xnx_n be nn real numbers satisfying ∣x1∣+∣x2∣+…+∣xn∣=1|x_1|+|x_2|+…+|x_n|=1. Find the minimum of ∣x1+x2∣+∣x2+x3∣+…+∣xn−1+xn∣+∣xn+x1∣.|x_1+x_2|+|x_2+x_3|+…+|x_{n-1}+x_n|+|x_n+x_1|. Proposed by snap7822
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