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Library /The South African Mathematical Olympiad, Third Round

The 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 13Combinatorics 8Geometry 9Number theory 11
#TopicDiffTypeYear
1 Geometry 4.9 proof — open
2 Number theory 4.9 proof — open
3 Algebra 5.2 proof — open
4 Algebra 5.2 proof — open
5 Geometry 5.6 proof — open
6 Number theory 5.6 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 Number theory 5.8 proof — open
13 Algebra 5.9 proof — open
14 Number theory 5.9 proof — open
15 Algebra 6.0 proof — open
16 Algebra 6.1 proof — open
17 Geometry 6.1 proof — open
18 Combinatorics 6.2 proof — open
19 Geometry 6.2 proof — open
20 Combinatorics 6.3 proof — open
21 Geometry 6.3 proof — open
22 Algebra 6.4 proof — open
23 Number theory 6.4 proof — open
24 Geometry 6.4 proof — open
25 Combinatorics 6.5 proof — open
26 Algebra 6.6 proof — open
27 Algebra 6.6 proof — open
28 Number theory 6.8 proof — open
29 Geometry 6.8 proof — open
30 Algebra 6.8 proof — open
31 Number theory 7.0 proof — open
32 Geometry 7.1 proof — open
33 Algebra 7.2 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.