24th All Soviet Union Mathematical Olympiad Problems 1990

1.  Show that x4 > x - 1/2 for all real x. 2.  The line joining the midpoints of two opposite sides of a convex quadrilateral makes equal angles with the diagonals. Show that the diagonals are equal. 3.  A graph has 30 points and each point has 6 edges. Find the total number of triples such that each pair of points is joined or each pair of points is