IMO 1982 LL AUS3

Origin: AUS

Problem

Given n points X1, X2, . . . , Xn in the interval 0 \leqXi \leq1, i = 1, 2, . . . , n, show that there is a point y, 0 \leqy \leq1, such that n n  i=1 |y −Xi| = 1 2.