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min sum |x-a_i|

Source: Polish MO Finals 1969 p2

August 22, 2024
algebrainequalities

Problem Statement

Given distinct real numbers a1,a2,...,ana_1,a_2,...,a_n, find the minimum value of the function y=∣x−a1∣+∣x−a2∣+...+∣x−an∣,   x∈R.y = |x-a_1|+|x-a_2|+...+|x-a_n|, \,\,\, x \in R.
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