21th British Mathematical Olympiad 1985 Problems

21th British Mathematical Olympiad 1985 Problems1.  Prove that ∑1n ∑1n | xi - xj | ≤ n2 for all real xi such that 0 ≤ xi ≤ 2. When does equality hold? 2.  (1) The incircle of the triangle ABC touches BC at L. LM is a diameter of the incircle. The ray AM meets BC at N. Show that | NL | = | AB - AC |.