Maths Olympiad Prep

Library /United States competition problems

United States competition problems

37 problems here, rated 3.8 to 7.7 on our scale (AMC 10/12 to National Olympiad, round 2). 18 of them ask for a proof.

Algebra 9Combinatorics 12Geometry 9Number theory 7
#TopicDiffTypeYear
1 Geometry 3.8 answer — open
2 Number theory 3.8 answer — open
3 Algebra 4.0 answer — open
4 Combinatorics 4.0 answer — open
5 Algebra 4.0 answer — open
6 Algebra 4.1 answer — open
7 Combinatorics 4.1 answer — open
8 Number theory 4.1 answer — open
9 Algebra 4.1 answer — open
10 Algebra 4.1 answer — open
11 Combinatorics 4.2 answer — open
12 Number theory 4.2 answer — open
13 Number theory 4.2 answer — open
14 Combinatorics 4.2 answer — open
15 Combinatorics 4.2 answer — open
16 Combinatorics 4.5 answer — open
17 Algebra 4.5 answer — open
18 Geometry 4.5 answer — open
19 Algebra 4.8 proof — open
20 Number theory 4.8 proof — open
21 Geometry 4.8 proof — open
22 Geometry 4.8 proof — open
23 Geometry 4.8 proof — open
24 Combinatorics 4.9 proof — open
25 Combinatorics 5.0 answer — open
26 Algebra 5.0 proof — open
27 Geometry 5.0 proof — open
28 Algebra 5.0 proof — open
29 Number theory 5.0 proof — open
30 Combinatorics 5.1 proof — open
31 Combinatorics 5.2 proof — open
32 Number theory 5.3 proof — open
33 Geometry 5.5 proof — open
34 Geometry 5.5 proof — open
35 Combinatorics 5.6 proof — open
36 Combinatorics 6.3 proof — open
37 Geometry 7.7 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.