Original problems
Every official problem is written for the competition.
Combinatorics Open 2026
A combinatorics competition
open to everyone.
The Combinatorics Open is a free online competition for pre-university students anywhere in the world.
November 14–15, 2026
Edition 01combinatoricsopen.org
20Short-answer problems
90 minOne sitting
48 hrWorldwide window
$0Always free
Current waitlist
Already taking shape worldwide.
Students are already gathering for the first Combinatorics Open—from established olympiad communities to places building something new.
Students on the waitlist
Countries represented
Country-level data only. No individual locations are shown.- United States: 25 on the waitlist
- China: 10 on the waitlist
- India: 9 on the waitlist
- Canada: 7 on the waitlist
- Vietnam: 7 on the waitlist
- South Korea: 6 on the waitlist
- Romania: 5 on the waitlist
- Taiwan: 5 on the waitlist
- Japan: 5 on the waitlist
- Poland: 4 on the waitlist
- Bulgaria: 4 on the waitlist
- Türkiye: 4 on the waitlist
- Hungary: 3 on the waitlist
- Serbia: 3 on the waitlist
- United Kingdom: 3 on the waitlist
- Germany: 3 on the waitlist
- Singapore: 3 on the waitlist
- Israel: 2 on the waitlist
- Australia: 2 on the waitlist
- Mexico: 2 on the waitlist
- Brazil: 2 on the waitlist
- Indonesia: 2 on the waitlist
- Philippines: 1 on the waitlist
View all 23 countries
United States25
China10
India9
Canada7
Vietnam7
South Korea6
Romania5
Taiwan5
Japan5
Poland4
Bulgaria4
Türkiye4
Hungary3
Serbia3
United Kingdom3
Germany3
Singapore3
Israel2
Australia2
Mexico2
Brazil2
Indonesia2
Philippines1
01
Combinatorics is simple to enter.
Hard to master.
Combinatorics begins with a question anyone can understand: how many ways? Its prerequisites are light, but its strongest ideas reach deep into olympiad mathematics, computer science, and the study of structure.
The Open gives students a serious, accessible way to test themselves through counting, probability, graphs, invariants, extremal arguments, games, recursion, and related combinatorial ideas.
Why the Open exists02
Try a problem.
No memorized formula is the point. Look for the structure, make a small observation, and count carefully.
A student draws three distinct diagonals of a regular octagon, choosing each diagonal so that all three pass through the center. How many different sets of three diagonals are possible?
The format
One paper. Twenty problems.
A focused individual contest, built to reward insight at every level of the paper.
01
Individual competition
02
20 short-answer problems
03
90 minutes
04
Answers below 1,000,000,000
05
One point per problem
06
No penalty for wrong answers
07
Start any time in the 48-hour window
08
Pen and paper · English · Honor code
Difficulty progression
1–8Foundations
9–15Advanced
16–20Challenge
2026 schedule
A clear path to contest day.
All dates use Coordinated Universal Time, so the same window applies wherever you are.
01October 1
Registration opens
02November 13
Registration closes
12:00 UTC03November 14
Competition opens
00:00 UTC04November 15
Competition closes
23:59 UTC05November 17
Problems & solutions
06November 19
Preliminary results
07November 24
Final results
Your 90-minute timer begins only when you start the contest.
Awards
Recognition that rewards performance.
Achievement is recognized across the overall field, junior division, and participating countries.
01
Gold, Silver & Bronze
Medal designations based on competition performance.
02
Junior Ranking
A separate ranking for grade 10 and below, or equivalent.
03
Country Top Scorer
For countries with at least five official participants.
04
Digital Certificates
For all participants.
Medal designations are guaranteed; physical medals are not. Any physical gold medals will depend on confirmed sponsor support.
Problem process
Built around problem integrity.
Independent verification
Answers are checked through separate methods.
Blind test-solving
Test-solvers review difficulty and ambiguity before the contest.
Faculty review
The final set receives faculty review.
Open worldwide
Wherever you are,
you can compete.
Anyone who has not completed secondary school can compete officially, regardless of country or grade.
Undergraduates and adults are welcome to participate unofficially.
Check eligibilityThe subject
Many ideas. One way of thinking.
The paper ranges across the language of discrete structure, with every problem designed to stand on its own.
01
Counting
02
Probability
03
Graph Theory
04
Pigeonhole Principle
05
Extremal Arguments
06
Games
07
Invariants
08
Recursion
Permanent archive
Built to last beyond contest day.
Problems, solutions, and official results will remain publicly available after each edition.
Explore the archive2026 Problems
Available November 17
Scheduled2026 Solutions
Available November 17
Scheduled2026 Results
Available November 24
ScheduledGet involved
Take your place in the Open.
Compete
Take the 2026 Open from anywhere in the world.
RegisterSchool coordinators
Help students at your school participate with a clear local point of contact.
Become a coordinatorSponsor
Support books, subscriptions, prizes, or medals through in-kind sponsorship.
Partner with usBacked and supported by
Sponsors supporting the 2026 Combinatorics Open.
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