30th International Mathematical Olympiad 1989 Problems & Solutions

A1.  Prove that the set {1, 2, ... , 1989} can be expressed as the disjoint union of subsets A1, A2, ... , A117 in such a way that each Ai contains 17 elements and the sum of the elements in each Ai is the same. A2.  In an acute-angled triangle ABC, the internal bisector of angle A meets the circumcircle again at A1. Points B1 and C1 are defined similarly. Let A0 be the point of