Thursday, November 11, 2010
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
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