HMIC

24 problems here, rated 4.8 to 6 on our scale (AIME to National Olympiad). 24 of them ask for a proof. Years covered: 2018–2024.

Algebra 5Combinatorics 10Geometry 6Number theory 3

#	Topic	Diff	Type	Year
1	Combinatorics	4.8	proof	—	open
2	Geometry	4.9	proof	—	open
3	Combinatorics	5.0	proof	—	open
4	Geometry	5.0	proof	—	open
5	Algebra	5.1	proof	2024	open
6	Number theory	5.1	proof	—	open
7	Geometry	5.2	proof	—	open
8	Number theory	5.2	proof	2023	open
9	Algebra	5.3	proof	2018	open
10	Algebra	5.4	proof	2023	open
11	Algebra	5.4	proof	—	open
12	Geometry	5.5	proof	—	open
13	Combinatorics	5.5	proof	—	open
14	Geometry	5.5	proof	—	open
15	Combinatorics	5.6	proof	—	open
16	Combinatorics	5.6	proof	—	open
17	Combinatorics	5.6	proof	2018	open
18	Combinatorics	5.7	proof	—	open
19	Number theory	5.7	proof	2018	open
20	Combinatorics	5.8	proof	2023	open
21	Combinatorics	5.8	proof	2021	open
22	Geometry	5.8	proof	—	open
23	Combinatorics	5.9	proof	2021	open
24	Algebra	6.0	proof	—	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.