6th All Soviet Union Mathematical Olympiad 1972 Problems & Solutions

1.  ABCD is a rectangle. M is the midpoint of AD and N is the midpoint of BC. P is a point on the ray CD on the opposite side of D to C. The ray PM intersects AC at Q. Show that MN bisects the angle PNQ. 2.  Given 50 segments on a line show that you can always find either 8 segments which are disjoint or 8 segments with a common point. 3.  Find the largest integer