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Library of Congress Cataloging-in-Publication Data:
DeTemple, Duane W.
Solutions manual to accompany combinatorial reasoning : an introduction to the art
of counting / Duane DeTemple, William Webb.
pages cm
ISBN 978-1-118-83078-9 (pbk.)
1. Combinatorial analysis–Textbooks. 2. Mathematical analysis–Textbooks. I. Webb, William, 1944- II. Title.
QA164.D48 2013
511′.6–dc23
2013035522
This manual provides the statements and complete solutions to all of the odd numbered problems in the textbook Combinatorial Reasoning: An Introduction to the Art of Counting. The definitions, theorems, figures, and other problems referenced in the solutions contained in this manual are to that book.
The most important thing to remember is that you should not turn to any solution in this manual without first attempting to solve the problem on your own. Many of the problems are subtle or complex and therefore require considerable thought—and time!—before you can expect to find a correct method of solution. You will learn best by trying to solve a problem on your own, even if you are unsuccessful. We hope that most often you will consult this manual simply to confirm your own answer. Often your answer will be the same as ours, but sometimes you may have found a different method of solution that is not only correct, but may even be better than ours (if so, please send us your alternative solution at the address below). If the answer to a problem eludes you even after a good effort, then take a look at the solution offered here. Even in this case, it is best only to read the beginning of the solution and see if you can continue to solve the problem on your own.
Many students wonder how to go about attacking nonroutine problems. We have listed some suggestions below that may be helpful for solving combinatorial problems and more generally for solving problems in any branch of mathematics.
For a more complete discussion of mathematical problem solving, you are encouraged to consult How to Solve It, the classic, but still useful, book of George Pólya.
DUANE DETEMPLE
WILLIAM WEBB
Washington State University, Pullman, WA
detemple@wsu.edu and webb@math.wsu.edu