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.
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What is combinatorics?
Combinatorics is the mathematics of discrete structure. It asks how objects can be arranged, selected, connected, or constrained: how many configurations are possible, whether a pattern must exist, and what changes when one condition is added.
Its problems often need little more than arithmetic, a diagram, and patience. The challenge is not recalling a formula. It is finding the useful viewpoint: an invariant, a graph, a recurrence, a clever way to count the same set twice, or a small case that reveals the whole structure.
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.
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Why we built the Open.
Combinatorics is unusually approachable and unusually deep, yet students often meet it only in scattered olympiad problems or advanced courses. We created the Combinatorics Open to give the subject a focused stage of its own.
The competition is free, online, and available across time zones so access does not depend on geography or a school budget. The paper is designed to reward careful reasoning and original insight, then remain available as a permanent collection for students and teachers after contest day.
The 2026 paper