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One of life's most exhilarating experiences is the "aha!" moment that comes from pondering a mathematical problem and then seeing the way to an elegant solution. Try your hand at these: Can you cut a sheet of typing paper with scissors into only one piece so that an elephant can step through it? What is the first time after noon at which the hour and minute hands meet? Seventeen pennies are on a table. Two players take turns removing 1, 2, 3, or 4 pennies. The last to make a legal move wins. Is there a winning strategy? How fast can you find the sum of the numbers 1 + 2 + 3 up to 100?

Contains:

1. Problems versus Exercises
2. Strategies and Tactics
3. The Problem Solver's Mind-Set
4. Searching for Patterns
5. Closing the Deal—Proofs and Tools
6. Pictures, Recasting, and Points of View
7. The Great Simplifier—Parity
8. The Great Unifier—Symmetry
9. Symmetry Wins Games!
10. Contemplate Extreme Values
11. The Culture of Problem Solving
12. Recasting Integers Geometrically
13. Recasting Integers with Counting and Series
14. Things in Categories—The Pigeonhole Tactic
15. The Greatest Unifier of All—Invariants
16. Squarer Is Better—Optimizing 3s and 2s
17. Using Physical Intuition—and Imagination
18. Geometry and the Transformation Tactic
19. Building from Simple to Complex with Induction
20. Induction on a Grand Scale
21. Recasting Numbers as Polynomials—Weird Dice
22. A Relentless Tactic Solves a Very Hard Problem
23. Genius and Conway's Infinite Checkers Problem
24. How versus Why—The Final Frontier