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