25th All Soviet Union Mathematical Olympiad Problems 1991

1.  Find all integers a, b, c, d such that ab - 2cd = 3, ac + bd = 1. 2.  n numbers are written on a blackboard. Someone then repeatedly erases two numbers and writes half their arithmetic mean instead, until only a single number remains. If all the original numbers were 1, show that the final number is not less than 1/n. 3.  Four lines in the plane