International Mathematical Olympiad, Volume 2The famed International Mathematical Olympiad has been challenging students worldwide for over 40 years. Since the first competition in Romania in 1959 - with only seven countries participating - it has expanded to attract competitors from over 80 countries, representing all five continents. This third volume features every question from 1991-2004, along with comprehensive solutions and multiple answers where applicable. A fantastic selection of mathematical puzzles, this fully updated three-volume series will be of interest to serious mathematicians and enthusiasts alike. Istvan Reiman's compilation of logic puzzles and questions will tease the intellect of all those with a mathematical mind. Istvan Reiman was formerly Leader of the Chair of Geometry at the Budapest University of Technology. He has been guiding the Youth Mathematical Circle of the J Bolyai Mathematical Society and directing the preparation of Hungarian students for the annual International Maths Olympiad for 40 years. |
Contents
Section 1 | 1 |
Section 2 | 3 |
Section 3 | 21 |
Section 4 | 52 |
Section 5 | 60 |
Section 6 | 71 |
Section 7 | 89 |
Section 8 | 95 |
Section 10 | 124 |
Section 11 | 129 |
Section 12 | 138 |
Section 13 | 140 |
Section 14 | 143 |
Section 15 | 144 |
Section 16 | 158 |
Section 9 | 101 |
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Common terms and phrases
A₁ a˛+b˛ An+1 angle arbitrary assume b₁ bicentric polygons bisector C₁ centre choose circle circle k circumcircle circumradius coefficients collinear colour consecutive contains contradiction convex coprime denote diagonals digits distance divides divisor edges elements equality holds equation Euler line Figure finite fixed points graph hence implies incentre incircle inequality International Mathematical Olympiad isosceles k₁ lattice least least common multiple Lemma length midpoint n-tuples n₁ notations orthocentre P₁ pair pairwise parallel parallelepiped pedal triangle permutations perpendicular plane Pn(x point of intersection polygonal path polynomial positive integer prime problem proof quadrangle quadrilateral radius real numbers Remark respectively right triangle rotation Second solution segments sequence sides Similarly square subsets tangent tetrahedron theorem Third solution triangle ABC values vectors vertex vertices