TABLE OF CONTENTS

Preface

Acknowledgements

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IX

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XU!

CHAPTER 1: Basic Concepts

Introductory Remarks

A First Problem

How to Count

The Use of Induction

Problems of Logic

Issues of Parity

Exercises

CHAPTER 2: A Deeper Look at Geometry

Classical Planar Geometry

Analytic Geometry

Miscellaneous and Exotic Geometry Problems

Solid Geometry

Exercises

CHAPTER 3: Problems Involving Counting

Elementary Problems in Probability

More Sophisticated Problems in Probability

More on Counting

The Classical Marriage Problem and Related Ideas

CHAPTER 4: Problems of Logic

Straight Logic

Games

Tracing Routes, and Learning from Parity

Mysterious Arithmetic Problems

Surprises

CHAPTER 5: Recreational Math

Magic Squares and Related Ideas

Problems Involving Weighings

CHAPTER 6: Algebra and Analysis

A Little Algebra

Inequalities

Trigonometry and Related Ideas

CHAPTER 7: A Miscellany

Crossing the River and Similar Exercises

Things That Are Impossible

CHAPTER 8: Real Life

Introductory Remarks

Everyday Objects

Some Case Studies

Statistics