Counting: Math for Gifted Students

Welcome to the Math All Star series These books are for middle school and high school students who are motivated to participate in math competitions such as MathCounts, AMC, and AIME. Their coaches may also find these books useful.

The website, www.mathallstar.org, provides extra practice problems and serves as a highly recommended supplemental learning resource.

Counting

You think everybody can count? Take a look at some counting problems available on the aforementioned website, and you might just think differently.

Counting problems appear in all levels of math competitions. It is one type of problems that senior students and even adults may not necessarily do better on than well-trained junior students. This is because counting problems usually do not involve complex theorems or formulas. Rather, they demand a systematic and analytical approach, which can be mastered with the structured training that this book offers.

The first half of the book teaches essential counting principles and formulas by going over easy-to-follow examples. After identifying hidden pitfalls and common misunderstandings, this book offers tips on how to avoid those traps. The second half covers well-established patterns in counting problems and introduces different ways to tackle each type. Mastering these techniques has proven to be very powerful and effective in improving problem solving skills.

Each chapter starts with examples and progresses with inspiring questions, followed by detailed, step-by-step reasoning. When there are multiple solutions, their similarities and differences are examined to provide students with greater insights. Each chapter contains practice problems with full solutions provided at the end of the book.

Upon completing this book, students will be able to:

• Analyze and approach problems like trained pros
• Identify common pitfalls in problem solving, and
• Recognize frequently used patterns and apply appropriate techniques