ASU 410 All Soviet Union MO 1985 sum of |a_i - b_i| = n^2
Source:
August 5, 2019
algebrasetabsolute value
Problem Statement
Numbers 1,2,3,...,2n are divided onto two equal groups. Let a1,a2,...,an be the first group numbers in the increasing order, and b1,b2,...,bn -- the second group numbers in the decreasing order. Prove that ∣a1−b1∣+∣a2−b2∣+...+∣an−bn∣=n2