The Colorado Mathematical Olympiad and Further Explorations

by Soifer, Alexander; Engel, Philip L.; Erdos, Paul; Gardner, Martin; Grunbaum, Branko

• ISBN13: 9780387754710
• ISBN10: 0387754717
• Format: Paperback
• Copyright: 2011-04-13
• Publisher: Springer Verlag

Summary

Over the past two decades, the once small local Colorado Springs Mathematics Olympiad, founded by the author himself, has now become an annual state-wide competition, hosting over one-thousand high school contenders each year.This updated printing of the first edition of Colorado Mathematical Olympiad: the First Twenty Years and Further Explorations offers an interesting history of the competition as well as an outline of all the problems and solutions that have been a part of the contest over the years. Many of the essay problems were inspired by Russian mathematical folklore and written to suit the young audience; for example, the 1989 Sugar problem was written as a pleasant Lewis Carroll-like story. Some other entertaining problems involve olde Victorian map colorings, King Authur and the knights of the round table, rooks in space, Santa Claus and his elves painting planes, football for 23, and even the Colorado Springs subway system.The book is more than just problems, their solutions, and event statistics; it tells a compelling story involving the lives of those who have been part of the Olympiad from every perspective.

Author Biography

Alexander Soifer has published around 100 articles and four other books entitled, Mathematics as Problem-Solving, 2/e How Does one Cut a Triangle? 2/e Mathematical Coloring Book, and Geometric Etudes in Combinatorial Mathematics. The 2nd ed. of Mathematical Coloring Book (forthcoming with Spenser). We are publishing 2nd ed. of the other three books. Soifer is renowned for creating significant problems and conjectures, and this book could be helpful to others thinking about organizing an olympiad. Soifer is at Princeton and Colorado. Author confirms sales of 3000 copies of all three books listed above, (excluding Mathematical Coloring Book) all self-sold by author.  These three books are out of stock.

Table of Contents

Forewords to The Colorado Mathematical Olympiad and Further Explorations	p. vi
Foreword	p. vi
Foreword	p. viii
Foreword	p. x
Forewords to Colorado Mathematical Olympiad	p. xiii
Foreword	p. xiii
Foreword	p. xv
Foreword	p. xvii
Foreword	p. xviii
Foreword	p. xx
Greetings to the Reader: Preface to The Colorado Mathematical Olympiad and Further Explorations	p. xxix
Preface to Colorado Mathematical Olympiad	p. xxxvi
The First Ten Years Colorado Mathematical Olympiad: How it Started and What it has Become	p. 3
Three Celebrated Ideas	p. 11
First Colorado Mathematical Olympiad April27,1984	p. 13
Historical Notes 1	p. 13
Problems 1	p. 18
Solutions 1	p. 19
Second Colorado Mathematical Olympiad April 19,1985	p. 27
Historical Notes 2	p. 27
Problems 2	p. 31
Solutions 2	p. 32
Third Colorado Mathematical Olympiad April 18,1986	p. 35
Historical Notes 3	p. 35
Problems 3	p. 39
Solutions 3	p. 39
Fourth Colorado Mathematical Olympiad Aprill7,1987	p. 45
Historical Notes 4	p. 45
Problems 4	p. 47
Solutions 4	p. 48
Fifth Colorado Mathematical Olympiad April 22,1988	p. 53
Historical Notes 5	p. 53
Problems 5	p. 62
Solutions 5	p. 63
The Sixth Colorado Mathematical Olympiad April 21,1989	p. 71
Historical Notes 6	p. 71
Problems 6	p. 76
Solutions 6	p. 77
Seventh Colorado Mathematical Olympiad April 27,1990	p. 83
Historical Notes 7	p. 83
Problems 7	p. 86
Solutions 7	p. 87
Eighth Colorado Mathematical Olympiad April 26, 1991	p. 95
Historical Notes 8	p. 95
Problems 8	p. 100
Solutions 8	p. 101
Ninth Colorado Mathematical Olympiad April 24,1992	p. 107
Historical Notes 9	p. 107
Problems 9	p. 111
Solutions 9	p. 113
Tenth Colorado Mathematical Olympiad April 23,1993	p. 121
Historical Notes 10	p. 121
Problems 10	p. 124
Solutions 10	p. 126
Further Explorations Introduction to Part II	p. 141
Rooks In Space	p. 143
Chromatic Number of the Plane (My Favorite Open Problem)	p. 145
Polygons in a Colored Circle, Polyhedra in a Colored Sphere	p. 151
How Does One Cut a Triangle?	p. 153
Points in Convex Figures	p. 155
Triangles in a Colored Plane	p. 159
Rectangles in a Colored Plane	p. 165
Colored Polygons	p. 167
Infinite-Finite	p. 171
The Schur Theorem	p. 173
The Second Decade The Olympiad: How It has Continued and What It has Become	p. 181
Eleventh Colorado Mathematical Olympiad April 22, 1994	p. 183
Historical Notes 11	p. 183
Problems 11	p. 187
Solutions 11	p. 188
Twelfth Colorado Mathematical Olympiad April 28, 1995	p. 197
Historical Notes 12	p. 197
Problems 12	p. 200
Solutions 12	p. 202
Thirteenth Colorado Mathematical Olympiad April 19, 1996	p. 207
Historical Notes 13	p. 207
Problems 13	p. 209
tSolutions 13	p. 211
Fourteenth Colorado Mathematical Olympiad April 25, 1997	p. 217
Historical Notes 14	p. 217
Problems 14	p. 220
Solutions 14	p. 221
Fifteenth Colorado Mathematical Olympiad April24, 1998	p. 229
Historical Notes 15	p. 229
Problems 15	p. 235
Solutions 15	p. 237
Sixteenth Colorado Mathematical Olympiad April 23, 1999	p. 243
Historical Notes 16	p. 243
Problems 16	p. 249
Solutions 16	p. 250
Seventeenth Colorado Mathematical Olympiad April21, 2000	p. 259
Historical Notes 17	p. 259
Problems 17	p. 262
Solutions 17	p. 263
Eighteenth Colorado Mathematical Olympiad April 20, 2001	p. 271
Historical Notes 18	p. 271
Problems 18	p. 279
Solutions 18	p. 280
Nineteenth Colorado Mathematical Olympiad April 19, 2002	p. 289
Historical Notes 19	p. 289
Problems 19	p. 293
Solutions 19	p. 294
Twentieth Colorado Mathematical Olympiad Aprill8, 2003	p. 303
Historical Notes 20	p. 303
Problems 20	p. 310
Solutions 20	p. 311
Further Explorations of the Second Decade How I Envision Mathematics Education: Introduction to Part IV	p. 323
Chromatic Number of a Grid	p. 325
Stone Age Entertainment	p. 327
The Erdos Train Station	p. 333
Squares in Square: The 1932 Erdo's Conjecture	p. 337
From Squares in a Square to Clones in Convex Figures	p. 345
Olde Victorian Map Colouring	p. 351
Achievement Games: Is Snaky a Loser?	p. 357
Finite Sets of Infinite Fun: Three Classic Problems	p. 361
From King Arthur to Mysteries of Hamiltonian Graphs	p. 365
Exploring Map Coloring	p. 367
Winners Speak: Reminiscences in Eight Parts Introduction to Part V	p. 371
Reminiscences in Eight Parts	p. 373
Gazette-Telegraph	p. 373
Matt Fackelman	p. 374
Brian Becker	p. 376
Charlie O'Keefe	p. 377
David Hunter	p. 379
Gideon Yaffe	p. 381
Aaron Parsons	p. 383
Matthew Kahle	p. 385
Farewell to the Reader	p. 391
References	p. 395
Index of Names	p. 401
Index of Terms	p. 407
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