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This open hall contains a collection of individual lessons. They are accessible by everyone. You can simply login in as a guest and enjoy the pleasure of learning. Notwithstanding that, logging in as a registered user provides additional benefits such as automatic progress tracking.

Contents are grouped into three categories:

General Topics

This category includes a series of videos which are not related to a specific course. Each video addresses a point that may benefit some interested audiences.

Sample Lessons

These are actual lessons extracted from various courses. The purpose is to provide prospect students a taste of what are being taught. Meanwhile, some lessons are part of to-be-released courses. Therefore they can also be served as previews of those up-coming courses.

Battle Fields

Here, we demonstrate how to apply those learned in various courses to the real world. Each lesson solves a typical problem many of which are from recent competitions.

Everybody can count 1, 2, 3. But solving competition counting problems is not easy. Counting related problems appear in various contents at all levels from AMC8 to IMO. For example, 2015 AIME I has 3 such questions of 15 in total. That is 20% of the total score!

Counting does not involve lots of complex formulas. With that said, to be good at counting will require systematic training. Knowing how to analyze and approach a problem is far more important than just remembering some formulas.

Course contents

This course can be divided into two parts: the basics and the techniques.

The basic part covers the following topics:

- Three fundamental Counting principles
- the addition principle
- the multiplication principle
- the inclusion-exclusion principle (Venn's diagram)
- The permutation and combination formulas
- Elementary probability

In addition to basic knowledge and formulas, pitfalls and cautions when working on competition problems are also emphasized. Collectively, these should provide students with solid foundation for further study.

The techniques part focuses on those patterns and solutions that can be directly employed to solve actual problems in an effective way. The vast majority of competition problems are based on well-known patterns. Therefore a strong contender should be familiar with them in order to avoiding spending time on inventing individualized solution during the contest.

If knowing basic knowledge and formulas is similar to knowing how a chess piece can move, mastering patterns is similar to mastering all these opening, tactics and so on. While many courses and books on the market stop at teaching formulas, this course will provide you with unique opportunity to learn and help improve competition performance in a meaningful way.

As an increasingly popular topic in recent competitions, geometric probability is also covered at the end of the course. Upon completing, students should be able to immediately recognize and effectively solve such problems. An example of geometric probability question is 2015 AMC10A #25 / AMC12A #23.

Course format

The online course is organized into several sections. Each section contains a series of lessons. Each lesson comes with a video lecture, instant questions, and homework assignment. A video lecture may also embed interactive quizzes to ensure leaner's engagement. All homework will be reviewed and commented in time. The instructor will be happy to answer questions and provide suggestions. (

Reference book

Reference book can be found here.


Grade 6 or above.

Course Layout

To enroll into this course, please register and login using your own account.

Indeterminate equations is a popular subject in math competitions at all levels, from AMC 8 to IMO. For example, the second question in 2015 IMO is an indeterminate equation. So is the first question in 2015 USAMO. In addition, AIME and AMC12/10/8 also have various related questions every year.

Despite its popularity, how to solve indeterminate equations is rarely discussed in classrooms. Consequently, many students are lack of necessary knowledge and skills to tackle such problems. When coming across indeterminate equations in competitions, they tend to either skip or take a try-my-luck approach by making wild guesses. However, most indeterminate equations in these tests have well known structured solutions. Hence there are obvious rooms for skill improvement.

This course provides a comprehensive coverage for solving indeterminate equation which is both appropriate and sufficient for middle school and high school students. Upon completing this course, students should be able to recognize various types of indeterminate equations and apply proper solving techniques accordingly.

Reference and Material

The following book can be used as an excellent reference while taking this course. Meanwhile, its table of contents also provides an overview of the course coverage.

Indeterminate Equation, by Xing Zhou

This book is available on Amazon (click the image above).

Click here to view its table of contents.


These problems are not the most challenging ones, but are typical. Each question represents one type of indeterminate equation or involves one typical solving technique. Students are encouraged to try them before starting the courses.

Course Structure

To enroll into this course, please register and login using your own account.