Problem #PRU-116994

Problems Calculus Functions of one variable. Continuity Intermediate value theorem. Connectedness.
 14–16  3.0

Problem

Let x1,x2,…,xn be some numbers belonging to the interval [0,1]. Prove that on this segment there is a number x such that 1n(|x−x1|+|x−x2|+⋯+|x−xn|)=1/2.