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min f(x) = sum |x-a_i| , n even

Source: Czech and Slovak Olympiad 1980, National Round, Problem 4

September 13, 2024
algebrainequalities

Problem Statement

Let a1<a2<...<ana_1 < a_2< ...< a_n are real numbers, f(x)=∑i=1n∣x−ai∣,f(x) = \sum_{i=1}^n|x-a_i|, for nn even. Find the minimum of this function.
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