The Art and Craft of Problem Solving

4 CHAPTER 1 WHAT THIS BOOK IS ABOUT AND HOW TO READ IT As we climb a mountain, we may encounter obstacles. Some of these obstacl ...

choice of notation can be critical. 2 THE THREE LEVELS OF PROBLEM SOLVING 5 Perhaps we should focus on the conclusion: how do ...

6 CHAPTER 1 WHAT THIS BOOK IS ABOUT AND HOW TO READ IT We have shown that f(n) is one less than a perfect square for all integer ...

1.3 A PROBLEM SAMPLER 7 recreational problem will help you later with more mathematically sophisticated prob­ lems. The Census-T ...

8 CHAPTER^1 WHAT THIS BOOK IS ABOUT AND HOW TO READ IT of the problems are quite challenging and interesting, roughly comparable ...

1.3 A PROBLEM SAMPLER 9 1.3.7 (AIME 19 94) Find the positive integer n for which llog 2 1j + llog 2 2j + llog 2 3j + ... + llog ...

10 CHAPTER 1 WHAT THIS BOOK IS ABOUT AND HOW TO READ IT solutions are always OK, even if you know that the problem you are worki ...

1.4 HOW TO READ THIS BOOK 11 in two directions: tiling ells in more elaborate shapes, tiling shapes with things other than ells. ...

12 CHAPTER 1 WHAT THIS BOOK IS ABOUT AND HOW TO READ IT use the "Halmos" symbol, a filled-in square.^8 We used a Halmos at the e ...

Chapter 2 Strategies for Investigating Problems As we've seen, solving a problem is not unlike climbing a mountain. And for inex ...

14 CHAPTER 2 STRATEGIES FOR INVESTIGATING PROBLEMS 2.1 Psychological Strategies Effective problem solvers stand out from the cro ...

2.1 PSYCHOLOGICAL STRATEGIES 15 It isn't hard to acquire a modest amount of mental toughness. As a beginner, you most likely lac ...

16 CHAPTER 2 STRATEGIES FOR INVESTIGATING PROBLEMS tempts should you try to prove impossibility. If you cannot do so, then do no ...

2.1 PSYCHOLOGICAL STRATEGIES 17 There is a moral to the story, of course. Most people, when confronted with this problem, immedi ...

18 CHAPTER^2 STRATEGIES FOR INVESTIGATING PROBLEMS it." Sometimes, in fact, seeing a creative solution can be inhibiting, for ev ...

2.1 PSYCHOLOGICAL STRATEGIES 19 boundary, it is pretty easy. Let the first line join three points, and make sure that each new l ...

20 CHAPTER 2 STRATEGIES FOR INVESTIGATING PROBLEMS The sequence that is left over is, of course, the Fibonacci numbers (Problem ...

2.1 PSYCHOLOGICAL STRATEGIES 21 cated than the monk problem, it too possesses a very brief and imaginative "one-liner" solution. ...

22 CHAPTER 2 STRATEGIES FOR INVESTIGATING PROBLEMS karate expert break a board with seemingly effortless power. But once you mas ...

(a) If English is your mother tongue, try work­ ing on word puzzles. Many daily newspapers carry the Jumble puzzle, in which you ...