IMO Shortlisted Problems
55 problems here, rated 7.5 to 9.2 on our scale (National olympiad, round 2 to IMO level). 55 of them ask for a proof. Years covered: 2006–2019.
| # | Topic | Diff | Type | Year | |
|---|---|---|---|---|---|
| 1 | Algebra | 7.5 | proof | 2006 | open |
| 2 | Algebra | 7.7 | proof | 2006 | open |
| 3 | Number theory | 7.9 | proof | 2006 | open |
| 4 | Combinatorics | 7.9 | proof | 2019 | open |
| 5 | Number theory | 7.9 | proof | 2019 | open |
| 6 | Number theory | 7.9 | proof | 2006 | open |
| 7 | Algebra | 8.0 | proof | 2019 | open |
| 8 | Number theory | 8.0 | proof | 2019 | open |
| 9 | Number theory | 8.0 | proof | 2019 | open |
| 10 | Geometry | 8.3 | proof | 2006 | open |
| 11 | Geometry | 8.3 | proof | 2006 | open |
| 12 | Geometry | 8.4 | proof | 2019 | open |
| 13 | Algebra | 8.4 | proof | 2019 | open |
| 14 | Geometry | 8.5 | proof | 2016 | open |
| 15 | Algebra | 8.5 | proof | 2006 | open |
| 16 | Geometry | 8.5 | proof | 2019 | open |
| 17 | Algebra | 8.5 | proof | 2019 | open |
| 18 | Combinatorics | 8.5 | proof | 2019 | open |
| 19 | Geometry | 8.5 | proof | 2019 | open |
| 20 | Algebra | 8.6 | proof | 2019 | open |
| 21 | Geometry | 8.6 | proof | 2019 | open |
| 22 | Algebra | 8.6 | proof | 2016 | open |
| 23 | Algebra | 8.7 | proof | 2019 | open |
| 24 | Number theory | 8.7 | proof | 2016 | open |
| 25 | Number theory | 8.7 | proof | 2016 | open |
| 26 | Geometry | 8.7 | proof | 2006 | open |
| 27 | Algebra | 8.7 | proof | 2019 | open |
| 28 | Geometry | 8.7 | proof | 2006 | open |
| 29 | Algebra | 8.7 | proof | 2006 | open |
| 30 | Combinatorics | 8.7 | proof | 2006 | open |
| 31 | Algebra | 8.7 | proof | 2006 | open |
| 32 | Geometry | 8.8 | proof | 2006 | open |
| 33 | Geometry | 8.8 | proof | 2016 | open |
| 34 | Geometry | 8.8 | proof | 2006 | open |
| 35 | Number theory | 8.8 | proof | 2019 | open |
| 36 | Geometry | 8.8 | proof | 2016 | open |
| 37 | Number theory | 8.8 | proof | 2019 | open |
| 38 | Geometry | 8.8 | proof | 2006 | open |
| 39 | Combinatorics | 8.8 | proof | 2016 | open |
| 40 | Geometry | 8.9 | proof | 2016 | open |
| 41 | Geometry | 8.9 | proof | 2016 | open |
| 42 | Geometry | 8.9 | proof | 2016 | open |
| 43 | Geometry | 8.9 | proof | 2019 | open |
| 44 | Algebra | 8.9 | proof | 2019 | open |
| 45 | Number theory | 8.9 | proof | 2016 | open |
| 46 | Geometry | 8.9 | proof | 2006 | open |
| 47 | Geometry | 9.0 | proof | 2019 | open |
| 48 | Geometry | 9.0 | proof | 2006 | open |
| 49 | Combinatorics | 9.0 | proof | 2019 | open |
| 50 | Geometry | 9.0 | proof | 2019 | open |
| 51 | Algebra | 9.1 | proof | 2016 | open |
| 52 | Combinatorics | 9.1 | proof | 2006 | open |
| 53 | Combinatorics | 9.1 | proof | 2019 | open |
| 54 | Combinatorics | 9.2 | proof | 2019 | open |
| 55 | Combinatorics | 9.2 | proof | 2016 | 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.