Library /United States competition problems

United States competition problems

48 problems here, rated 3.6 to 7.7 on our scale (AMC 10/12 to National Olympiad, round 2). 20 of them ask for a proof.

Algebra 10Combinatorics 18Geometry 11Number theory 9

#	Topic	Diff	Type	Year
1	Geometry	3.6	answer	—	open
2	Geometry	3.8	answer	—	open
3	Number theory	3.8	answer	—	open
4	Combinatorics	3.8	answer	—	open
5	Combinatorics	3.9	answer	—	open
6	Combinatorics	3.9	answer	—	open
7	Algebra	4.0	answer	—	open
8	Combinatorics	4.0	answer	—	open
9	Algebra	4.0	answer	—	open
10	Combinatorics	4.0	answer	—	open
11	Algebra	4.0	answer	—	open
12	Number theory	4.1	answer	—	open
13	Algebra	4.1	answer	—	open
14	Combinatorics	4.1	answer	—	open
15	Number theory	4.1	answer	—	open
16	Algebra	4.1	answer	—	open
17	Algebra	4.1	answer	—	open
18	Combinatorics	4.2	answer	—	open
19	Number theory	4.2	answer	—	open
20	Number theory	4.2	answer	—	open
21	Combinatorics	4.2	answer	—	open
22	Combinatorics	4.2	answer	—	open
23	Combinatorics	4.4	answer	—	open
24	Combinatorics	4.5	answer	—	open
25	Algebra	4.5	answer	—	open
26	Geometry	4.5	answer	—	open
27	Combinatorics	4.8	answer	—	open
28	Algebra	4.8	proof	—	open
29	Number theory	4.8	proof	—	open
30	Geometry	4.8	proof	—	open
31	Geometry	4.8	proof	—	open
32	Geometry	4.8	proof	—	open
33	Geometry	4.8	proof	—	open
34	Combinatorics	4.9	proof	—	open
35	Combinatorics	5.0	answer	—	open
36	Algebra	5.0	proof	—	open
37	Geometry	5.0	proof	—	open
38	Algebra	5.0	proof	—	open
39	Number theory	5.0	proof	—	open
40	Combinatorics	5.1	proof	—	open
41	Number theory	5.1	proof	—	open
42	Combinatorics	5.2	proof	—	open
43	Number theory	5.3	proof	—	open
44	Geometry	5.5	proof	—	open
45	Geometry	5.5	proof	—	open
46	Combinatorics	5.6	proof	—	open
47	Combinatorics	6.3	proof	—	open
48	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.