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Maximum of min(a1-a1a2,a2-a2a3,...) where a_n in [0,1]

Source: 2001 Moldova MO Grade 8 P2

April 12, 2021
Inequalityoptimizationinequalities

Problem Statement

If n∈Nn\in\mathbb N and a1,a2,…,ana_1,a_2,\ldots,a_n are arbitrary numbers in the interval [0,1][0,1], find the maximum possible value of the smallest among the numbers a1−a1a2,a2−a2a3,…,an−ana1a_1-a_1a_2,a_2-a_2a_3,\ldots,a_n-a_na_1.
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