Who Should Take This Course

This course is for students who are looking for a fun, challenging, and systematic introduction to the fascinating world of Combinatorics, which is not covered in depth in most school curricula, but which appears throughout middle and high school math competitions. This course will give you the main tools you need, in one month. To take this course, students should have successfully completed our Module 1: Algebra Basics course, or have skipped over it due to prior background.

This course will be understandable by anyone with a solid background in Pre-Algebra, and the willingness to concentrate on a single math problem for several minutes. At the same time, even high school students (who have not yet taken classes outside of school in Combinatorics) will learn a significant amount. Not recommended for students who can already score 17+ on AMC 8. Still not sure if this is the right course? Feel free to contact us at course-consulting@poshenloh.com to discuss.


Course curriculum

  • 02
  • 03
    Day 2 Challenge: Venn Diagram
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    • Day 2: Something to Think About
    • Day 2: Challenge Explanation
    • Day 2: Your Turn
    • Day 2: Your Turn Explanation
  • 04
    Day 3 Challenge: Overlapping Worlds
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    • Day 3: Something to Think About
    • Day 3: Challenge Explanation
    • Day 3: Your Turn
    • Day 3: Your Turn Explanation
  • 05
    Day 4 Challenge: Careful Casework
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    • Day 4: Something to Think About
    • Day 4: Challenge Explanation
    • Day 4: Your Turn
    • Day 4: Your Turn Explanation
  • 06
    Week 1 Challenge
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    • Week 1 Challenge: Try Your New Skills
  • 07
    Course Survey
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    • Week 1: Help Us Learn More About Your Learning Experience
  • 08
    Day 5 Challenge: Arranging Repeated Digits
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    • Day 5: Something to Think About
    • Day 5: Challenge Explanation
    • Day 5: Your Turn
    • Day 5: Your Turn Explanation
  • 09
    Day 6 Challenge: Comparing Choices
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    • Day 6: Something to Think About
    • Day 6: Challenge Explanation
    • Day 6: Your Turn
    • Day 6: Your Turn Explanation
  • 10
    Day 7 Challenge: Pascal's Patterns
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    • Day 7: Something to Think About
    • Day 7: Challenge Explanation
    • Day 7: Your Turn
    • Day 7: Your Turn Explanation
  • 11
    Day 8 Challenge: Distributing Grades
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    • Day 8: Something to Think About
    • Day 8: Challenge Explanation
    • Day 8: Your Turn
    • Day 8: Your Turn Explanation
  • 12
    Week 2 Challenge
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    • Week 2 Challenge: Try Your New Skills
  • 13
    Course Survey
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    • Week 2: Help Us Learn More About Your Learning Experience
  • 14
    Day 9 Challenge: Counting Paths
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    • Day 9: Something to Think About
    • Day 9: Challenge Explanation
    • Day 9: Your Turn
    • Day 9: Your Turn Explanation
  • 15
    Day 10 Challenge: Tiling Strips
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    • Day 10: Something to Think About
    • Day 10: Challenge Explanation
    • Day 10: Your Turn
    • Day 10: Your Turn Explanation
  • 16
    Day 11 Challenge: Avoiding Repeats
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    • Day 11: Something to Think About
    • Day 11: Challenge Explanation
    • Day 11: Your Turn
    • Day 11: Your Turn Explanation
  • 17
    Day 12 Challenge: Counting Colorings
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    • Day 12: Something to Think About
    • Day 12: Challenge Explanation
    • Day 12: Your Turn
    • Day 12: Your Turn Explanation
  • 18
    Week 3 Challenge
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    • Week 3 Challenge: Try Your New Skills
  • 19
    Course Survey
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    • Week 3: Help Us Learn More About Your Learning Experience
  • 20
    Day 13 Challenge: Counting Orderings
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    • Day 13: Something to Think About
    • Day 13: Challenge Explanation
    • Day 13: Your Turn
    • Day 13: Your Turn Explanation
  • 21
    Day 14 Challenge: Matchings
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    • Day 14: Something to Think About
    • Day 14: Challenge Explanation
    • Day 14: Your Turn
    • Day 14: Your Turn Explanation
  • 22
    Day 15 Challenge: Pouring Buckets
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    • Day 15: Something to Think About
    • Day 15: Challenge Explanation
    • Day 15: Your Turn
    • Day 15: Your Turn Explanation
  • 23
    Day 16 Challenge: Polyhedra
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    • Day 16: Something to Think About
    • Day 16: Challenge Explanation
    • Day 16: Your Turn
    • Day 16: Your Turn Explanation
  • 24
    Week 4 Challenge
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    • Week 4 Challenge: Try Your New Skills
  • 25
    What's Next
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    • Congratulations on Completing This Course!
    • Week 4: Help Us Learn More About Your Learning Experience

How To Use This Course

The best way to build creative thinking skills is to play with challenging new problems every day, especially those for which you don’t know how to start. This course, which can be finished in 1 month, constitutes of 16 Daily Challenges and Weekly Challenges. Each Daily Challenge has two related math problems and their explanations. Don’t worry if they look unfamiliar. Just use the whole time during the problem videos (and hints) to think. You’ll get to invent your own strategies, which is the fun part!

Even if you figure out how to do a problem yourself, watching its explanation video is still very beneficial. It will show multiple interesting ways to do the problem, and introduce deeper ideas in math using everyday language. This brings advanced math down to earth.

There is only one practice problem in each Daily Challenge (the “Your Turn” problem), and there aren’t any homework problems. This is because the way to learn how to solve the widest variety of problems is to learn how to invent your own solution methods! So, we encourage you to solve new problems all on your own instead of working on repetitive exercises. You’ll spend the same time on fewer problems, every one of which needs fresh creativity.

After every four Daily Challenges, we revisit the topics (with some twists), through a Weekly Challenge problem set that lets you focus uninterrupted for 40 minutes, on a variety of specially designed questions. After doing the problems, please read the explanations, even for the problems you solved. There are a lot of fun math coincidences and insights hidden in the problems.

We recommend pacing the course so that you can play with this flavor of mathematical thinking for a bit of time almost every day. 

The standard pace is to pick four days each week for four Daily Challenges, plus one hour on the weekend for the Weekly Challenge. If you think this pace is not challenging enough, feel free to double the pace, so that you can finish eight Daily Challenges and two Weekly Challenge each week.

  • Instructor

    Po-Shen Loh is a social entrepreneur, working across the full spectrum of mathematics and education, all around the world. He is the founder of the free personalized learning platform expii.com, an education technology social enterprise which algorithmically curates openly licensed math/science lessons and problems contributed by the world. Sales of these online courses support the development of these social initiatives.

    Loh draws from his experience as a mathematics professor at Carnegie Mellon University, and also as the national coach of the USA International Mathematical Olympiad team. His research and educational outreach takes him to cities across the world, reaching over 10,000 people annually through public lectures and in-person events, and he has featured in or co-created videos totaling over 5 million YouTube views.

    He has been continually involved in math competitions since he was a contestant in the late 1990's: when he ranked 3rd at the National MATHCOUNTS competition, and won a silver medal for the United States of America as a contestant at the International Mathematical Olympiad. He can be followed on Instagram (@poshenloh), Twitter (@poshenloh), WeChat (罗博深数学), and Weibo (poshenloh / 罗博深).

    Po-Shen Loh

    Math Professor

    Po-Shen Loh