BMO Shortlist
34 problems here, rated 6.9 to 9.2 on our scale (National Olympiad to IMO level). 34 of them ask for a proof. Years covered: 2010–2022.
| # | Topic | Diff | Type | Year | |
|---|---|---|---|---|---|
| 1 | Number theory | 6.9 | proof | 2022 | open |
| 2 | Algebra | 7.5 | proof | 2022 | open |
| 3 | Geometry | 7.7 | proof | 2010 | open |
| 4 | Geometry | 7.7 | proof | 2019 | open |
| 5 | Geometry | 7.8 | proof | 2019 | open |
| 6 | Algebra | 7.9 | proof | 2019 | open |
| 7 | Algebra | 8.0 | proof | 2022 | open |
| 8 | Geometry | 8.0 | proof | 2022 | open |
| 9 | Algebra | 8.1 | proof | 2010 | open |
| 10 | Geometry | 8.1 | proof | 2019 | open |
| 11 | Combinatorics | 8.2 | proof | 2010 | open |
| 12 | Algebra | 8.2 | proof | 2022 | open |
| 13 | Geometry | 8.3 | proof | 2010 | open |
| 14 | Geometry | 8.3 | proof | 2019 | open |
| 15 | Geometry | 8.3 | proof | 2022 | open |
| 16 | Algebra | 8.3 | proof | 2019 | open |
| 17 | Geometry | 8.4 | proof | 2022 | open |
| 18 | Geometry | 8.4 | proof | 2019 | open |
| 19 | Geometry | 8.4 | proof | 2010 | open |
| 20 | Algebra | 8.5 | proof | 2019 | open |
| 21 | Geometry | 8.5 | proof | 2010 | open |
| 22 | Geometry | 8.6 | proof | 2019 | open |
| 23 | Geometry | 8.7 | proof | 2022 | open |
| 24 | Geometry | 8.7 | proof | 2019 | open |
| 25 | Geometry | 8.7 | proof | 2010 | open |
| 26 | Geometry | 8.8 | proof | 2010 | open |
| 27 | Combinatorics | 8.8 | proof | 2010 | open |
| 28 | Combinatorics | 8.8 | proof | 2022 | open |
| 29 | Geometry | 8.9 | proof | 2022 | open |
| 30 | Combinatorics | 9.0 | proof | 2022 | open |
| 31 | Combinatorics | 9.0 | proof | 2019 | open |
| 32 | Algebra | 9.0 | proof | 2010 | open |
| 33 | Combinatorics | 9.1 | proof | 2019 | open |
| 34 | Combinatorics | 9.2 | proof | 2019 | open |
These are sorted by difficulty within the competition, but they aren't a course.
The track is the route through, drawn from all the sources at once.