THE 68th NMO SELECTION TESTS FOR THE JUNIOR BALKAN MATHEMATICAL OLYMPIAD

Question

Given x_1, x_2, , x_n real numbers, prove that there exists a real number y such that y - x_1 + y - x_2 + + y - x_n n-12.

Accepted Answer

As a + -a 1, a R (with equality if a is not an integer), we have _1 i j n x_i - x_j n(n-1)2,