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The William Lowell Putnam Mathematical Competition Problems and Solutions 1965-1984

The William Lowell Putnam Mathematical Competition Problems and Solutions 1965-1984

Gerald L. Alexanderson, Leonard F. Klosinski, and Loren C. Larson, Editors

Print ISBN: 978-0-88385-463-1
168 pp., Paperbound, 1985
List Price: $36.00
MAA Member: $27.00
Series: Problem Books

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Since 1928, the Putnam Competition has been providing a challenge to gifted college mathematics students. This book, the second of the Putnam Competition volumes, contains problems with their solutions for the years 1965-1984. Additional solutions are presented for many of the problems. Included is an essay on recollections of the first Putnam Exam by Herbert Robbins, as well as appendices listing the winning teams and students from 1965 through 1984. This volume offers the problem solver an enticing sample of challenging problems and their solutions.

In 1980, the MAA published the first William Lowell Putnam Mathematical Competition book, covering the contests from 1938 to 1964. In 2002 the third of the Putnam books appeared, covering the years 1985 through 2000. All three of these books belong on the bookshelves of students, teachers, and all interested in problem solving.

Table of Contents

Recollections of the First Putnam Examination by Herbert Robbins
List of Problems
Solutions to the Problems in the Various Competitions
Index of Problems


Let us make clear from the start that we have not tried with this collection to imitate the scholarly and extensive treatment of the first twenty-five contests by Gleason, Greenwood, and Kelly (The William Lowell Putnam Mathematical Competition/Problems and Solutions: 1938-1964. Washington: MAA, 1980). That splendid volume shows the years of work spent in following up on problems, compiling better solutions, and tracing effects of some of the problems in subsequent work.

We have done none of that here. We have compiled material essentially already available in The American Mathematical Monthly and Mathematics Magazine, correcting in several cases solutions where errors had crept in. The present volume is mainly an attempt to put together in convenient form existing material. A volume comparable to the Gleason, Greenwood, Kelly book will have to wait for another time. We hope that in the meantime the present collection will benefit students interested in preparing for the Competition, faculty who wish to organize problem seminars. Or any others just interested in problems.

For information about the history of the Putnam Competition, we refer the reader to the excellent articles by Garrett Birkhoff and L. E. Bush in the earlier collection. These articles also appeared in the Monthly in 1965. We are happy to have in the present collection a further bit of information about the origins of the Competition, an essay on the first contest by Herbert Robbins as told to Alan Tucker.

We have summarized lists of winning teams and individual participants; more extensive information on winners and teams appeared in annual reports in the Monthly.

Our work would have been much more difficult had we not had the reports of the Competition carefully prepared by former directors of the Competition, James H. McKay (Oakland University) and Abraham P. Hillman (University of New Mexico). We wish especially to thank them for their many contributions over the years and specifically for their excellent reports. They are largely responsible for the presentation of solutions that have appeared in the Monthly during their directorships, though, of course, they had the benefit of having the solutions given them by members of the Questions Committees over those years. And, of course, had the members of the Questions Committee not provided the questions (and in many cases solutions) there would have been no Competition. We therefore wish to thank the members of the Questions Committee: H. S. M. Coxeter (University of Toronto), Adriano M. Garsia (California Institute of Technology), Robert E. Greenwood (University of Texas, Austin), Nicholas D. Kazarinoff (University of Michigan, Ann Arbor), Leo Master (University of Alberta), Albert Wilansky (Lehigh University), Warren S. Loud (University of Minnesota, Minneapolis), Murray S. Klamkin (Ford Scientific Laboratories), Nathan S. Mendelsohn (University of Manitoba), Donald J. Newman (Yeshiva University), J. Ian Richards (University of Minnesota, Minneapolis), Gulbank D. Chakerian (University of California, Davis), Joseph D. E. Konhauser (Macalester College), Richard J. Bumby (Rutgers University, New Brunswick), Lawrence A. Zalcman (University of Maryland, College Park), Edward J. Barbeau, Jr. (University of Toronto), Kenneth B. Stolarsky (University of Illimois, Urbana-Champaign), Joel H. Spencer (State University of New York, Stony Brook), William J. Firey (Oregon State University), Douglas A. Hensley (Texas A & M University), Melvin Hochster (University of Michigan, Ann Arbor), Bruce A. Reznik (University of Illinois, Urbana-Champaign), and Richard P. Stanley (Massachusetts Insitutes of Technology).

We would further like to thank Alan Tucker, Chairman of the Publications Committee of the MAA, A. B. Wilcox, Executive Director, and Beverly Joy Ruedi of the Editorial Office of the MAA.

Gerald L. Alexanderson
Leonard F. Klosinski
Loren C. Larson

March, 1985


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