11th Asian Pacific Mathematics Olympiad 1999 Problems

11th Asian Pacific Mathematics Olympiad 1999 ProblemsA1.  Find the smallest positive integer n such that no arithmetic progression of 1999 reals contains just n integers. A2.  The real numbers x1, x2, x3, ... satisfy xi+j ≤ xi + xj for all i, j. Prove that x1 + x2/2 + ... + xn/n ≥ xn.