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; ChanceFree Decisionmaking; Games of Perfect Information; Finiteness; The Existence of Winning Strategies; PositionState 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 PuzzleA Second Approach; Colored Cubes; Colored CubesA 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 

