Low barrier
Many excellent problems begin with nothing more than careful counting and a clear diagram.
About
A serious competition, open by design.
The Combinatorics Open is a free online combinatorics competition for pre-university students anywhere in the world.
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What is the Combinatorics Open?
It is an individual competition: one student, one paper, and ninety focused minutes. Students can begin at any time inside a 48-hour worldwide window, making the same problem set accessible across time zones.
The first edition takes place on November 14–15, 2026. It consists of 20 short-answer problems, arranged to begin accessibly and build toward substantial challenge.
Our mission
Give any student with a pencil and internet connection access to a serious combinatorics competition.
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Free to enter.
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Available worldwide.
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Built around original problems.
Why combinatorics
Elementary questions. Unexpected depth.
Combinatorics rewards the habit of looking closely at structure—and then finding the one observation that changes the problem.
High ceiling
The same elementary language leads to some of the deepest and most beautiful ideas in mathematics.
Creative work
Progress comes from finding structure, not from recalling a long list of formulas.
Wide reach
Counting and discrete structure appear throughout mathematics, algorithms, probability, and computer science.
The 2026 paper