The Colorado Mathematical Olympiad and Further Explorations : From the Mountains of Colorado to the Peaks of Mathematics This book presents the 20 year account of the Colorado Mathematical Olympiad — its dreams and rewards hard work and conflict. It features more than just original wonderful problems and their ingenious solutions; it tells a compelling story involving the lives of those who have been part of the Olympiad. The reader will meet Olympians and follow their paths as professionals. In the vast field of competition books this book is unique for it builds bridges between Olympiads and “real” mathematics by demonstrating through 20 “Further Explorations ” the trains of mathematical thought showing how a solved Olympiad problem gives birth to deeper problems and leads to the forefront of mathematical research full of striking results and open problems. Like Gauss Alexander Soifer would not hesitate to inject Eureka! at the right moment. Like van der Waerden he can transform a dispassionate exercise in logic into a compelling account of sudden insights and ultimate triumph. — Cecil Rousseau Chair USA Mathematical Olympiad Committee ... this book is not so much mathematical literature as it is literature built around mathematics… with the Further Explorations sections anyone so inclined could spend a lifetime on the mathematics sprouting from this volume. —Peter D. Johnson Jr. Auburn University I finished reading the book in one sitting – I just could not put it down. Professor Soifer has indebted us all by first making the effort to organize the Colorado Mathematical Olympiads and then making the additional effort to tell us about it in such an engaging and useful way. —Branko Grünbaum University of Washington A delightful feature of the book is that in the second part more related problems are discussed. Some of them are still unsolved. —Paul Erdős The book is a gold mine of brilliant reasoning with special emphasis on the power and beauty of coloring proofs. Strongly recommended to both serious and recreational mathematicians on all levels of expertise. —Martin Gardner. Preface Olympiad History: What it is and How it Started Three Celebrated Ideas Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Further Explorations Rooks in Space Chromatic Number of the Plane Polygons in a Colored Circle Polyhedra in a colored Sphere How Does one Cut a Triangle Points in Convex Figures Triangles in a Colored Plane Rectangles in a Colored Plane Colored Polygons Infinite Finite Schur Theorem Bibliography Year 11 Year 12 Year 13 Year 14 Year 15 Year 16 Year 17 Year 18 Year 19 Year 20 Further Explorations Chromatic Number of a Grid Stone Age Entertainment The Erdös Problem Squares in a Square Washington Recangles Olde Victorian Map Colouring More Stone Age Entertainment The 1 10 100 Problem King Arthur and the Knights of the Round Table A Map Coloring Game Bibliography.