Table of Contents

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