Combinatorics Overview

Counting and using the basic principles of probability are two basic skills any student learns in school, but they are the gateway to the mathematical field of combinatorics. On Brilliant, the combinatorics topic area is a varied mix of counting, probability, games, graph theory, and more. Whether you're looking for quick practice problems that strengthen your abstract reasoning skills or for advanced, open-ended challenges, we have something here for you. The collection of Brilliant problems and articles is large and growing.

Within combinatorics, you can learn about wide-ranging topics such as the following:

Brilliant's article collection is expanding to cover every topic you might encounter in any pre-collegiate math program. In most topic areas, we cover the content in much more depth than traditional grade-school standards, with a focus on real understanding instead of memorization.

The most popular introductory combinatorics topics on Brilliant are as follows:

Our goal is to be able to challenge any student in the world with math that stretches their skills. The topics below are at the collegiate level or beyond, including some math topics that you likely wouldn't see in school unless you majored in math.

Whether you're just beginning to study for your first math competition, or if you're a pro aiming for a perfect score, Brilliant is a resource for every trick and topic that you might be looking for. The competitions and exams that Brilliant can help you study for include the following:

International Math Competitions

• IMO
• IMC
• Mathematical Kangaroo

USA Math Exams and Competitions

• AIME
• AMC8 / AMC10 / AMC12
• AP Exams (AB Calculus, BC Calculus)
• ARML
• MATHCOUNTS
• MOEMS
• SAT
• USAMO
• USAJMO
• USAMTS

Indian Math Exams and Competitions

• RMO
• KVPY
• IIT JEE