36th Polish Mathematical Olympiad Problems 1985

36th Polish Mathematical Olympiad Problems 1985A1.  Find the largest k such that for every positive integer n we can find at least k numbers in the set {n+1, n+2, ... , n+16} which are coprime with n(n+17).A2.  Given a square side 1 and 2n positive reals a1, b1, ... , an, bn each ≤ 1 and satisfying ∑ aibi ≥ 100. Show that the square can be covered with