International Mathematical Olympiad, 1959-1999
A fantastic selection of mathematical puzzles for all age groups. This book represents a compilation of questions set for the famed International Maths Olympiads. A book of logic puzzles and questions that will tease the minds of all those with a mathematical mind. - Features all questions from the annual Olympiad, from 1959 to date - Includes solutions to every question - with multiple answers where applicable - Of interest to serious mathematicians and enthusiasts alike
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ABCD altitude arbitrary assume centre circle circumcircle coefficients collinear colour complete graph consecutive Consider construction contains contradiction convex hull coprime cyclic quadrilateral Determine diagonal digits distance divides divisible divisor edges elements equality holds equation Euler line excircle Figure fixed point function given graph hand side hence hypotenuse implies incentre incircle induction inequality infinitely interval isosceles triangle labelled least lemma length locus midpoint monochromatic triangle n-gon nonnegative notations orthogonal pair parallel permutations perpendicular bisector plane point of intersection polygon polygonal path polynomial positive integers possible values prime problem proof Prove radius ratio real numbers rectangle relatively prime Remark respectively right triangle Second solution segments sequence Similarly square statement subsets symmetric tangent tetrahedron theorem Third solution trapezium triangle ABC triangle inequality vector vertex vertices yields zero