2,000 problems · stages 3 to 10
Problems are easy to find.
Knowing which one to do next isn't.
This is one list, in one order, from AMC 10 level to the IMO shortlist. Work down it. When you get stuck, the solution is on the page.
Problems per stage
What went into the ordering
Difficulty came out of the data
Every problem has a 1–10 rating fitted against 275 problems graded by hand, and checked by having a model attempt the ones with known answers. Where the rating was shaky the problem was left out of the list rather than guessed at.
Topics rotate
Algebra, combinatorics, geometry and number theory take turns. No run of eight problems has more than three of the same kind, and all four turn up in any twenty. You don't get four hundred geometry problems in a row.
Answers give way to proofs gradually
Stages 3 to 5 want a number. From stage 6 most want an argument. Writing proofs is a separate skill from finding answers, so stage 6 opens with two dozen proof problems that are no harder than the stage before it.
Nothing without a solution
All 2,000 have a worked solution from the source that published them. Numerical answers are checked as you type. Proofs you mark yourself once you've read the official argument.
The stages
| Stage | Roughly | Problems | Proof | |
|---|---|---|---|---|
| 3 | AMC 10/12, early questions | 260 | 9% | open |
| 4 | AMC 12 late, AIME early | 340 | 12% | open |
| 5 | AIME late | 400 | 34% | open |
| 6 | National olympiad, first round | 400 | 68% | open |
| 7 | National olympiad second round; IMO P1/P4 | 300 | 80% | open |
| 8 | IMO Shortlist mid-range; USAMO P2/P5 | 180 | 86% | open |
| 9 | IMO P2/P5; hard shortlist | 80 | 99% | open |
| 10 | Hardest shortlist tier | 40 | 100% | open |
Where they came from
National olympiad booklets from 47 countries, international shortlists, and two large open datasets of competition problems. Just under 900,000 problems went in; these 2,000 came out.
Collected
897k
Duplicates
8,668
Graded
560k
Kept
2,000