# Problem Solving Through Recreational Mathematics

## Bonnie Averbach; Orin Chein

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Many of the most important mathematical concepts were developed from recreational problems. This book uses problems, puzzles, and games to teach students how to think critically. It emphasizes active participation in problem solving, with emphasis on logic, number and graph theory, games of strategy, and much more. Includes answers to selected problems. Index. 1980 edition.

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Contenuti:

Preface; To the Reader; Acknowledgments 1. Following the Clues; Sample problems; Which chart or Diagram to Choose; Presenting a Solution; Some Steps in Problem Solving; Tree Diagrams; The Multiplication Principle; Simplification; The Chapter in Retrospect; Exercises 2. Solve It With Logic; Sample Problems; Statements; Variables and Connectives; Negation; “And”—Conjunction; “Or”—Disjunction; Conditional and Biconditional Statements; Drawing Conclusions; Compound Statements; Logical Implication and Equivalence; Arguments and Validity; The Chapter in Retrospect; Exercises 3. From Words to Equations: Algebraic Recreations; Sample Problems; Introducing Variables; The Chapter in Retrospect; Exercises 4. Solve It With Integers, Some Topics from Number Theory; Sample Problems; Diophantine Equations; Divisibility; Prime Numbers; The Infinitude of Primes; The Sieve of Eratosthenes; More About Primes; Linear Diophantine Equations; Division With Remainders; Congruence; Casting Out Nines; Solving Linear Congruences; Solving Linear Diophantine Equations; The Chapter in Retrospect; Exercises 5. More About Numbers: Bases and Cryptarithmetic; Sample Problems; Positional Notation; Changing Bases; Addition and Multiplication in Other Bases; Cryptarithmetic; The Chapter in Retrospect; Exercises 6. Solve It With Networks: An Introduction to Graph Theory; Sample Problems; Graphs; Eulerian Paths and Circuits; Odd and Even Vertices; More Than Two Odd Vertices; Directed Graphs; Hamiltonian Circuits; The Knight’s Tour; Other Applications; Coloring Graphs and Maps; The Chapter in Retrospect; Exercises 7. Games of Strategy for Two Players; Sample problems; Chance-Free Decisionmaking; Games of Perfect Information; Finiteness; The Existence of Winning Strategies; Position--State of the Game; The State Diagram of a Game; How Do We Find a Winning Strategy?; Finding a Winning Strategy by Working Backward; Finding Winning Strategies by Simplifying a Game; Finding Winning Strategies With a Frontal Assault; How Many Possibilities Need Be Considered?; Symmetry as a Limiting Factor; Déjà Vu—We’ve Seen it Before; The Game of Nim; Pairing Strategies; Variations of a Game; The Chapter in Retrospect; Exercises 8. Solitaire Games and Puzzles; Sample Problems; The Tower of Brahma; Dissection Problems; Polyominoes; Soma; Peg Solitaire; The Fifteen Puzzle; Even and Odd Permutations; Coloring and the 15 Puzzle--A Second Approach; Colored Cubes; Colored Cubes--A Second Approach; The Chapter in Retrospect; Exercises 9. Potpourri; Decimation; Coin Weighing; Shunting; Syllogisms; Grab Bag; The Book in Retrospect Appendix A. Some Basic Algebraic Techniques Appendix B. Mathematical Induction Appendix C. Probability Bibliography; Hints and Solutions; Answers to Selected Problems; Index

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Book by Averbach Bonnie

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## 1.Problem Solving Through Recreational Mathematics (Paperback)

Editore: Dover Publications Inc., United States (2003)
ISBN 10: 0486409171 ISBN 13: 9780486409177
Nuovi Paperback Quantità: 10
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Descrizione libro Dover Publications Inc., United States, 2003. Paperback. Condizione libro: New. 229 x 165 mm. Language: English . Brand New Book. Historically, many of the most important mathematical concepts arose from problems that were recreational in origin. This book takes advantage of that fact, using recreational mathematics problems, puzzles and games to teach students how to think critically. Encouraging active participation rather than just observation, the book focuses less on mathematical results than on how these results can be applied to thinking about problems and solving them. Each chapter contains a diverse array of problems in such areas as logic, number and graph theory, two-player games of strategy, solitaire games and puzzles, and much more. Sample problems (solved in the text) whet readers appetites and motivate discussions; practice problems solidify their grasp of mathematical ideas; and exercises challenge them, fostering problem-solving ability. Appendixes contain information on basic algebraic techniques and mathematical inductions, and other helpful addenda include hints and solutions, plus answers to selected problems. An extensive appendix on probability is new to this Dover edition. Codice libro della libreria AA99780486409177

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## 2.Problem Solving Through Recreational Mathematics (Paperback)

Editore: Dover Publications Inc., United States (2003)
ISBN 10: 0486409171 ISBN 13: 9780486409177
Nuovi Paperback Quantità: 10
Da
The Book Depository
(London, Regno Unito)
Valutazione libreria

Descrizione libro Dover Publications Inc., United States, 2003. Paperback. Condizione libro: New. 229 x 165 mm. Language: English . Brand New Book. Historically, many of the most important mathematical concepts arose from problems that were recreational in origin. This book takes advantage of that fact, using recreational mathematics problems, puzzles and games to teach students how to think critically. Encouraging active participation rather than just observation, the book focuses less on mathematical results than on how these results can be applied to thinking about problems and solving them. Each chapter contains a diverse array of problems in such areas as logic, number and graph theory, two-player games of strategy, solitaire games and puzzles, and much more. Sample problems (solved in the text) whet readers appetites and motivate discussions; practice problems solidify their grasp of mathematical ideas; and exercises challenge them, fostering problem-solving ability. Appendixes contain information on basic algebraic techniques and mathematical inductions, and other helpful addenda include hints and solutions, plus answers to selected problems. An extensive appendix on probability is new to this Dover edition. Codice libro della libreria AA99780486409177

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Editore: Dover Publications Inc. (2003)
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Descrizione libro Dover Publications Inc., 2003. PAP. Condizione libro: New. New Book.Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria IB-9780486409177

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## 6.Problem Solving Through Recreational Mathematics (Dover Books on Mathematics)

Editore: Dover Publications (1999)
ISBN 10: 0486409171 ISBN 13: 9780486409177
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Descrizione libro Dover Publications, 1999. Paperback. Condizione libro: New. Codice libro della libreria 0486409171

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## 7.Problem Solving Through Recreational Mathematics

Editore: Dover Publications Inc. (1999)
ISBN 10: 0486409171 ISBN 13: 9780486409177
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Descrizione libro Dover Publications Inc., 1999. Condizione libro: New. Series: Dover Books on Mathematics. Num Pages: 480 pages, illustrations. BIC Classification: PB. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 166 x 234 x 24. Weight in Grams: 658. . 1999. Paperback. . . . . . Codice libro della libreria V9780486409177

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## 8.Problem Solving Through Recreational Mathematics (Dover Books on Mathematics)

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ISBN 10: 0486409171 ISBN 13: 9780486409177
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Descrizione libro Dover Publications. PAPERBACK. Condizione libro: New. 0486409171 Brand New Book. Ships from the United States. 30 Day Satisfaction Guarantee!. Codice libro della libreria 4786319

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## 9.Problem Solving Through Recreational Mathematics (Paperback)

ISBN 10: 0486409171 ISBN 13: 9780486409177
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Descrizione libro 2000. Paperback. Condizione libro: New. 165mm x 23mm x 233mm. Paperback. Many of the most important mathematical concepts were developed from recreational problems. This book uses problems, puzzles, and games to teach students how to think critically. It emphas.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 480 pages. 0.680. Codice libro della libreria 9780486409177

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## 10.Problem Solving Through Recreational Mathematics

Editore: Dover Publications Inc.
ISBN 10: 0486409171 ISBN 13: 9780486409177
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Descrizione libro Dover Publications Inc. Condizione libro: New. Series: Dover Books on Mathematics. Num Pages: 480 pages, illustrations. BIC Classification: PB. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 166 x 234 x 24. Weight in Grams: 658. . 1999. Paperback. . . . . Books ship from the US and Ireland. Codice libro della libreria V9780486409177

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