Get better at Olympiad maths. One hard problem at a time.
You don't need more problems. You need the right problems, in the right order. Build a route from the level you can solve today to AMC, AIME, BMO, USAMO, the IMO, or wherever you are trying to get next.
- 1,964
- problems on the track, in order
- 14,000
- more in the searchable library
- 335
- competitions covered
- 43
- countries they were set in
The right problem is just beyond what you can already do.
Collecting ever bigger folders of hard questions does not make you better. Too easy and you repeat what you already know. Too hard and you spend three hours reading a solution you were never going to find. What you want is the problem you can almost solve, and then the next one. That is all the ordering is for.
What are you aiming for?
Start with one of these goals, or build a route around your own. We'll show you the stages, problems and training time needed to get there.
Qualify for AIME
You are comfortable with most of an AMC 10, or a UK Senior Maths Challenge. Now build the range, and the speed, to break through.
- Stages
- 3–5
- Problems
- 1,000
- Time
- 6 mo
- Per week
- 11h
Make USAMO
AMC 12 no longer worries you and AIME is familiar. The next jump is deeper problems, and writing mathematics rather than finding answers.
- Stages
- 4–7
- Problems
- 1,440
- Time
- 1 yr
- Per week
- 13h
Reach BMO Round 2
You have time on your side. Build from Senior Maths Challenge level to full Olympiad proofs without rushing it.
- Stages
- 3–7
- Problems
- 1,700
- Time
- 2 yr
- Per week
- 7h
From BMO to the squad
You have made a second round already. From here almost everything is a proof, and very little comes quickly.
- Stages
- 6–9
- Problems
- 932
- Time
- 18 mo
- Per week
- 10h
Train at the hardest end
No preliminaries and no routine exercises. Only problems that may take an afternoon.
- Stages
- 7–10
- Problems
- 564
- Time
- 1 yr
- Per week
- 13h
Your goal isn't here?
Choose your starting level, your target, your topics and your deadline.
- Stages
- any
- Problems
- yours
- Time
- yours
- Per week
- yours
Olympiad maths is a ladder.
The mathematics changes as you climb. At first, success is about seeing the right idea. Higher up, it is about persistence, proof, and staying with a problem long after the obvious approaches have run out.
| Stage | What it asks of you | Roughly this paper | Problems |
|---|---|---|---|
| 3 | Spot the idea. | AMC 10/12 early · UK Senior Maths Challenge | 260 |
| 4 | Connect ideas that do not obviously belong together. | AMC 12 late · AIME early | 340 |
| 5 | Keep going when the first approach fails. | AIME late | 400 |
| 6 | Turn an answer into a proof. | BMO Round 1 · national Olympiad first round | 400 |
| 7 | Find the structure the problem is trying to hide. | BMO Round 2 · USAMO P1/P4 · IMO P1/P4 | 300 |
| 8 | Work for a long time without knowing whether you are close. | IMO Shortlist mid-range · USAMO P2/P5 | 180 |
| 9 | Stay with one problem for hours. | IMO P2/P5 · hard shortlist | 52 |
| 10 | Face problems you may not solve at all. | Hardest shortlist tier | 32 |
1,964 problems. One deliberate sequence.
Difficulty rises gradually
A good training problem should feel possible, eventually. So every problem here sits on one scale. We graded 275 by hand, fitted the rest against those, then checked the fit by having a model attempt the ones with known answers. The climb gets harder without getting random.
The mathematics keeps changing
Real Olympiads don't give you twenty number theory questions and then twenty on geometry. Neither does this. The four topics keep rotating, so you have to work out what kind of problem you are looking at before you can solve it.
Proofs arrive before they become terrifying
Getting an answer and writing a proof are different skills, and the gap between them is where people stall. Stage 6 opens with two dozen proof problems set no harder than the stage below, so the change is a ramp rather than a wall.
You can always learn from the problem
Every problem has a worked solution from whoever published it. Struggle first, try an idea, throw it away, try another. When you finally need the solution it is there, so a hard problem becomes something you learn from rather than the place your training stops.
We started with nearly 900,000 problems.
Most never made the track.
- Collected from official competition booklets in 43 countries, international shortlists and two large open datasets.
- Duplicates removed.
- Problems with no reliable solution removed.
- Problems we could not place confidently removed.
- Difficulty put on one scale, topics classified, the sequence built.
1,964 problems remained. Those are the track. Another 14,000 sit in the library for anyone who would rather explore than follow a plan.
You don't have to know how far you can go.
You only have to know what to work on next.