Problem solving through recreational mathematics

Problem solving through recreational mathematics

Bonnie Averbach, 1933-

Book - 2000

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Subjects
Mathematics.
Mathematical recreations.
Problem solving.
Published
Mineola, N.Y. : Dover 2000.
Language
English
Main Author
Bonnie Averbach, 1933- (-)
Other Authors
Orin Chein, 1943- (-)
Item Description
Originally published: Mathematics. San Francisco : W. H. Freeman, c1980.
Physical Description
458 p. : ill. ; 24 cm
Bibliography
Includes bibliographical references and index.
ISBN
9780486409177
  • 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
  • Deja 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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