BAMO

15 problems here, rated 4.5 to 7.8 on our scale (AIME to National Olympiad, round 2). 14 of them ask for a proof.

Algebra 3Combinatorics 5Geometry 5Number theory 2

#	Topic	Diff	Type	Year
1	Number theory	4.5	proof	—	open
2	Combinatorics	4.6	answer	—	open
3	Geometry	4.7	proof	—	open
4	Number theory	5.4	proof	—	open
5	Geometry	5.5	proof	—	open
6	Algebra	5.5	proof	—	open
7	Algebra	5.6	proof	—	open
8	Combinatorics	5.8	proof	—	open
9	Geometry	6.3	proof	—	open
10	Geometry	6.4	proof	—	open
11	Algebra	6.7	proof	—	open
12	Combinatorics	6.7	proof	—	open
13	Combinatorics	6.8	proof	—	open
14	Geometry	7.0	proof	—	open
15	Combinatorics	7.8	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.