HMMT
79 problems here, rated 4.1 to 6 on our scale (AIME to National Olympiad). 70 of them ask for a proof. Years covered: 1998–2014.
| # | Topic | Diff | Type | Year | |
|---|---|---|---|---|---|
| 1 | Geometry | 4.1 | answer | 2013 | open |
| 2 | Number theory | 4.2 | answer | 2013 | open |
| 3 | Algebra | 4.5 | answer | 2013 | open |
| 4 | Number theory | 4.5 | answer | 2013 | open |
| 5 | Geometry | 4.6 | proof | 2014 | open |
| 6 | Geometry | 4.7 | proof | 2014 | open |
| 7 | Geometry | 4.8 | proof | 2013 | open |
| 8 | Geometry | 4.8 | proof | 2013 | open |
| 9 | Geometry | 4.8 | proof | 2014 | open |
| 10 | Geometry | 4.9 | proof | 2014 | open |
| 11 | Geometry | 4.9 | proof | 2013 | open |
| 12 | Geometry | 4.9 | proof | 2014 | open |
| 13 | Algebra | 5.0 | proof | 2013 | open |
| 14 | Geometry | 5.0 | proof | 2014 | open |
| 15 | Algebra | 5.0 | answer | 1998 | open |
| 16 | Geometry | 5.0 | proof | 2013 | open |
| 17 | Algebra | 5.0 | proof | 2002 | open |
| 18 | Number theory | 5.0 | proof | 2002 | open |
| 19 | Algebra | 5.0 | proof | 2014 | open |
| 20 | Combinatorics | 5.0 | answer | 2014 | open |
| 21 | Geometry | 5.0 | proof | 2013 | open |
| 22 | Geometry | 5.0 | proof | 2013 | open |
| 23 | Number theory | 5.1 | proof | 2014 | open |
| 24 | Algebra | 5.1 | proof | — | open |
| 25 | Algebra | 5.1 | proof | 2014 | open |
| 26 | Algebra | 5.1 | proof | 2013 | open |
| 27 | Algebra | 5.1 | proof | 2014 | open |
| 28 | Combinatorics | 5.1 | proof | 2014 | open |
| 29 | Algebra | 5.2 | proof | 2002 | open |
| 30 | Algebra | 5.2 | proof | 2014 | open |
| 31 | Algebra | 5.2 | answer | 2013 | open |
| 32 | Geometry | 5.2 | proof | 2013 | open |
| 33 | Algebra | 5.2 | proof | 2014 | open |
| 34 | Combinatorics | 5.2 | proof | 2013 | open |
| 35 | Combinatorics | 5.2 | answer | 2014 | open |
| 36 | Algebra | 5.3 | proof | — | open |
| 37 | Geometry | 5.3 | proof | 2013 | open |
| 38 | Algebra | 5.3 | answer | 2014 | open |
| 39 | Geometry | 5.3 | proof | 2013 | open |
| 40 | Number theory | 5.3 | proof | 2014 | open |
| 41 | Geometry | 5.3 | proof | 2014 | open |
| 42 | Combinatorics | 5.3 | proof | 2014 | open |
| 43 | Number theory | 5.3 | proof | 2002 | open |
| 44 | Number theory | 5.3 | proof | 2014 | open |
| 45 | Algebra | 5.4 | proof | 2014 | open |
| 46 | Geometry | 5.4 | proof | 2014 | open |
| 47 | Algebra | 5.4 | proof | — | open |
| 48 | Geometry | 5.5 | proof | 2013 | open |
| 49 | Number theory | 5.5 | proof | — | open |
| 50 | Combinatorics | 5.5 | proof | 2014 | open |
| 51 | Algebra | 5.5 | proof | 2014 | open |
| 52 | Geometry | 5.6 | proof | 2013 | open |
| 53 | Geometry | 5.6 | proof | 2013 | open |
| 54 | Combinatorics | 5.6 | proof | 2014 | open |
| 55 | Geometry | 5.6 | proof | 2014 | open |
| 56 | Geometry | 5.6 | proof | 2014 | open |
| 57 | Combinatorics | 5.6 | proof | 2013 | open |
| 58 | Geometry | 5.7 | proof | 2013 | open |
| 59 | Combinatorics | 5.7 | proof | 2013 | open |
| 60 | Combinatorics | 5.7 | proof | 2014 | open |
| 61 | Geometry | 5.7 | proof | 2014 | open |
| 62 | Geometry | 5.7 | proof | 2014 | open |
| 63 | Combinatorics | 5.7 | proof | 2013 | open |
| 64 | Geometry | 5.8 | proof | 2013 | open |
| 65 | Geometry | 5.8 | proof | 2014 | open |
| 66 | Algebra | 5.8 | proof | 2014 | open |
| 67 | Algebra | 5.8 | proof | 2014 | open |
| 68 | Number theory | 5.8 | proof | 2013 | open |
| 69 | Combinatorics | 5.8 | proof | — | open |
| 70 | Number theory | 5.9 | proof | 2013 | open |
| 71 | Combinatorics | 5.9 | proof | 2014 | open |
| 72 | Combinatorics | 5.9 | proof | — | open |
| 73 | Algebra | 5.9 | proof | 2013 | open |
| 74 | Geometry | 5.9 | proof | 2013 | open |
| 75 | Combinatorics | 5.9 | proof | 2014 | open |
| 76 | Algebra | 5.9 | proof | 2013 | open |
| 77 | Geometry | 6.0 | proof | 1998 | open |
| 78 | Combinatorics | 6.0 | proof | — | open |
| 79 | Number theory | 6.0 | proof | 1998 | 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.