Library /NMO Selection Tests for BMO and IMO

NMO Selection Tests for BMO and IMO

47 problems here, rated 7.2 to 9.2 on our scale (National Olympiad, round 2 to IMO level). 47 of them ask for a proof.

Algebra 9Combinatorics 11Geometry 17Number theory 10

#	Topic	Diff	Type	Year
1	Geometry	7.2	proof	—	open
2	Number theory	7.3	proof	—	open
3	Geometry	7.5	proof	—	open
4	Algebra	7.5	proof	—	open
5	Number theory	7.5	proof	—	open
6	Geometry	7.6	proof	—	open
7	Algebra	7.6	proof	—	open
8	Combinatorics	7.6	proof	—	open
9	Geometry	7.6	proof	—	open
10	Geometry	7.6	proof	—	open
11	Combinatorics	7.6	proof	—	open
12	Number theory	7.7	proof	—	open
13	Combinatorics	7.7	proof	—	open
14	Combinatorics	7.8	proof	—	open
15	Number theory	7.9	proof	—	open
16	Combinatorics	7.9	proof	—	open
17	Algebra	7.9	proof	—	open
18	Number theory	8.0	proof	—	open
19	Number theory	8.0	proof	—	open
20	Number theory	8.0	proof	—	open
21	Geometry	8.1	proof	—	open
22	Algebra	8.1	proof	—	open
23	Algebra	8.1	proof	—	open
24	Geometry	8.2	proof	—	open
25	Geometry	8.2	proof	—	open
26	Number theory	8.2	proof	—	open
27	Geometry	8.2	proof	—	open
28	Geometry	8.3	proof	—	open
29	Number theory	8.3	proof	—	open
30	Geometry	8.3	proof	—	open
31	Combinatorics	8.4	proof	—	open
32	Geometry	8.4	proof	—	open
33	Algebra	8.4	proof	—	open
34	Geometry	8.4	proof	—	open
35	Geometry	8.4	proof	—	open
36	Algebra	8.4	proof	—	open
37	Geometry	8.5	proof	—	open
38	Combinatorics	8.6	proof	—	open
39	Combinatorics	8.6	proof	—	open
40	Geometry	8.6	proof	—	open
41	Algebra	8.6	proof	—	open
42	Algebra	8.7	proof	—	open
43	Number theory	8.8	proof	—	open
44	Geometry	8.8	proof	—	open
45	Combinatorics	9.0	proof	—	open
46	Combinatorics	9.0	proof	—	open
47	Combinatorics	9.2	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.