For more than 50 years, the Mathematical Association of America has been engaged in the construction and administration of challenging contests for students in American and Canadian high schools. The problems on these contests are constructed in the hope that all high school students interested in mathematics will have the opportunity to participate in the contests and will find the experience mathematically enriching. These contests are intended for students at all levels, from the average student at a typical school who enjoys mathematics to the very best students at the most special school.

In the year 2000, the Mathematical Association of America initiated the American Mathematics Competitions 10 (AMC 10) for students up to grade 10. *The Contest Problem Book VIII* is the first collection of problems from that competition covering the years 2001–2007. J. Douglas Faires and David Wells were the joint directors of the AMC 10 and AMC 12 during that period, and have assembled this book of problems and solutions.

There are 350 problems from the first 14 contests included in this collection. A Problem Index at the back of the book classifies the problems into the following major subject areas: Algebra and Arithmetic, Sequences and Series, Triangle Geometry, Circle Geometry, Quadrilateral Geometry, Polygon Geometry, Counting Coordinate Geometry, Solid Geometry, Discrete Probability, Statistics, Number Theory, and Logic. The major subject areas are then broken down into subcategories for ease of reference. The Problems are cross-referenced when they represent several subject areas.

### Table of Contents

Preface

Problems

2000 AMC 10 Problems

2001 AMC 10 Problems

2002 AMC 10A Problems

2002 AMC 10B Problems

2003 AMC 10A Problems

2003 AMC 10B Problems

2004 AMC 10A Problems

2004 AMC 10B Problems

2005 AMC 10A Problems

2005 AMC 10B Problems

2006 AMC 10A Problems

2006 AMC 10B Problems

2007 AMC 10A Problems

2007 AMC 10B Problems

Solutions

2000 AMC 10 Solutions

2001 AMC 10 Solutions

2002 AMC 10A Solutions

2002 AMC 10B Solutions

2003 AMC 10A Solutions

2003 AMC 10B Solutions

2004 AMC 10A Solutions

2004 AMC 10B Solutions

2005 AMC 10A Solutions

2005 AMC 10B Solutions

2006 AMC 10A Solutions

2006 AMC 10B Solutions

2007 AMC 10A Solutions

2007 AMC 10B Solutions

Index of Problems

About the Editors

### About the Editors

**J. Douglas Faires** received his BS in mathematics from Youngstown State University in 1963, and earned his PhD in mathematics from the University of South Carolina in 1970. He has been a Professor at Youngstown State University since 1980, and has been actively involved in the MAA for many years. For example, he was Chair of the Ohio Section in 1981-1982 and Governor from 1997-2000. He is currently a member of the MAA’s Undergraduate Research and Undergraduate Student Activities Committees and he was the National Director of the AMC 10 Competition of the American Mathematics Competitions until 2007.

Faires is a past President of Pi Mu Epsilon and he was a member of their Council for many years. Faires has been the recipient of many awards and honors. He was named the Outstanding College-University Teacher of Mathematics by the Ohio Section of the MAA in 1996; he has also received five Distinguished Professorship awards from Youngstown State University, and an honorary Doctorate of Science Degree in May 2006. Faires has authored and coauthored numerous books including *Numerical Analysis* (now in its eight edition!), *Numerical Methods* (third edition), *PreCalculus* (fourth edition), and *First Steps for Math Olympians*, a book in the MAA Problem Book Series.

**David Wells** received a PhD in mathematics from the University of Pittsburgh in 1973. He taught at Ohio Dominican University for six years and has been at the New Kensington campus of Penn State University since 1979. During his career at Penn State he has received both the Teresa Cohen Service Award from the Department of Mathematics and the Excellence in Teaching Award from the New Kensington Campus. He has been a member of the MAA since 1974, holding several sectional and national positions during that time. He served as Governor of the Allegheny Mountain Section from 1996 to 1999 and has recently been appointed as Chair of the MAA Committee on the American Mathematics Competitions. He has chaired the AMC 12 Contest Committee since 2001. Dr. Wells received the Meritorious Service Award from the Allegheny Mountain Section of the MAA in 2005. His non-mathematical interests include hiking and songwriting.