Counting

Welcome to the Math All Star series books! These books are for middle/high school students who are motivated to compete in various math competitions (e.g. MathCounts, AMC, AIME etc). Their coaches may also find these books useful. Its website, www.mathallstar.com, has more information, such as table of contents, practice problems and so on. Counting You think everybody can count? Take a look at some competition problems, or just try those practice mentioned above, you will think differently. Counting problems appear in math competitions at all levels. It is one type of problems that senior students or even adults may not outperform well trained junior students. This is because counting usually does not involve complex theorems or formulas. Instead, it demands a systematic way to analyze and approach problems. This is why a structured training is very important. This book is written to serve such need. The book first teaches essential counting principles and formulas by going over easy-to-follow examples. It also points out hidden pitfalls, common misunderstanding and explains how to avoid them. Second half of the book expands into various well established patterns of counting problems and related techniques for each pattern. Mastering these is very powerful and effective in improving problem solving skills. Each section of the book starts with examples, progresses with inspiring questions and detailed step by step reasoning. It emphasizes on enabling students to understand why and how to reach solutions, not just simply remembering the results or formulas. Multiple solutions are also presented when appropriate to help students build insights into the nature of these problems, as the differences and/or similarities of these solutions are fully examined and discussed. Each section has practice problems for which full solution is provided at the end of the book. Upon completing this book, students will be able to: analyze and approach problems like trained pros watch out embedded catches identify patterns and apply appropriate techniques