Mathematical Olympiads 2000-2001: Problems and Solutions from Around the World
Titu Andreescu, Zuming Feng, George Lee, Jr
MAA, Oct 16, 2003 - Mathematics - 282 pages
This book is a continuation of Mathematical Olympiads 1999-2000: Problems and Solutions From Around the World, published by the Mathematical Association of America. It contains solutions to the problems from 27 national and regional contests featured in the earlier book, together with selected problems (without solutions) from national and regional contests given during 2001. In many cases multiple solutions are provided in order to encourage students to compare different problem-solving strategies. The editors have tried to present a wide variety of problems, especially from those countries that have often done well at the IMO. The problems themselves should provide much enjoyment for all those fascinated by solving challenging mathematics questions.
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Classification of Problems
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adjacent an+i angle bisector Angle Bisector Theorem assume balls bisector of angle cards circle circumcenter circumcircle of triangle claim coins collinear color completes the proof concyclic congruent contains convex hull convex polygon convex quadrilateral coprime cyclic defined denote desired directed angles distinct divides divisible edges elements equal equation exactly exists function given graph Hence homothety implying incircle inequality intersection point isosceles lattice points Law of Sines least lemma lies line BC midpoint modulo multisets natural numbers nine-point circle nonnegative orthocenter pairs parallel partition permutation perpendicular Pigeonhole Principle plane polygon polynomial positive integers Problem 3 Let Prove quadratic residue quadrilateral ABCD radical axis real numbers rectangles recursively relatively prime respectively sake of contradiction satisfying segments sequence sides Similarly Solution square subsets Suppose tangent Theorem Titu Andreescu triangle ABC vertex vertices ZABC