Library /South African Mathematical Olympiad, Third Round

South African Mathematical Olympiad, Third Round

41 problems here, rated 5.6 to 7.5 on our scale (AIME, harder to National Olympiad, round 2). 41 of them ask for a proof.

Algebra 10Combinatorics 9Geometry 10Number theory 12

#	Topic	Diff	Type	Year
1	Number theory	4.9	proof	—	open
2	Geometry	5.1	proof	—	open
3	Algebra	5.2	proof	—	open
4	Geometry	5.6	proof	—	open
5	Number theory	5.6	proof	—	open
6	Number theory	5.7	proof	—	open
7	Number theory	5.7	proof	—	open
8	Number theory	5.7	proof	—	open
9	Geometry	5.7	proof	—	open
10	Number theory	5.7	proof	—	open
11	Algebra	5.7	proof	—	open
12	Geometry	5.8	proof	—	open
13	Number theory	5.8	proof	—	open
14	Algebra	5.9	proof	—	open
15	Number theory	5.9	proof	—	open
16	Algebra	6.1	proof	—	open
17	Geometry	6.1	proof	—	open
18	Combinatorics	6.2	proof	—	open
19	Combinatorics	6.2	proof	—	open
20	Geometry	6.2	proof	—	open
21	Combinatorics	6.3	proof	—	open
22	Geometry	6.3	proof	—	open
23	Algebra	6.4	proof	—	open
24	Algebra	6.4	proof	—	open
25	Number theory	6.4	proof	—	open
26	Geometry	6.4	proof	—	open
27	Combinatorics	6.5	proof	—	open
28	Algebra	6.6	proof	—	open
29	Number theory	6.8	proof	—	open
30	Geometry	6.8	proof	—	open
31	Algebra	6.8	proof	—	open
32	Number theory	7.0	proof	—	open
33	Geometry	7.1	proof	—	open
34	Combinatorics	7.3	proof	—	open
35	Algebra	7.4	proof	—	open
36	Combinatorics	7.4	proof	—	open
37	Algebra	7.4	proof	—	open
38	Combinatorics	7.5	proof	—	open
39	Number theory	7.5	proof	—	open
40	Combinatorics	7.7	proof	—	open
41	Combinatorics	8.1	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.