Library /NMO Selection Tests for BMO and IMO

NMO Selection Tests for BMO and IMO

52 problems here, rated 7.2 to 9.2 on our scale (National Olympiad, round 2 to IMO level). 52 of them ask for a proof.

Algebra 9Combinatorics 11Geometry 19Number theory 13

#	Topic	Diff	Type	Year
1	Geometry	7.2	proof	—	open
2	Number theory	7.3	proof	—	open
3	Geometry	7.5	proof	—	open
4	Number theory	7.5	proof	—	open
5	Algebra	7.5	proof	—	open
6	Number theory	7.5	proof	—	open
7	Number theory	7.5	proof	—	open
8	Geometry	7.6	proof	—	open
9	Algebra	7.6	proof	—	open
10	Combinatorics	7.6	proof	—	open
11	Geometry	7.6	proof	—	open
12	Geometry	7.6	proof	—	open
13	Combinatorics	7.6	proof	—	open
14	Number theory	7.7	proof	—	open
15	Combinatorics	7.7	proof	—	open
16	Combinatorics	7.8	proof	—	open
17	Number theory	7.9	proof	—	open
18	Combinatorics	7.9	proof	—	open
19	Algebra	7.9	proof	—	open
20	Geometry	8.0	proof	—	open
21	Number theory	8.0	proof	—	open
22	Number theory	8.0	proof	—	open
23	Number theory	8.0	proof	—	open
24	Geometry	8.1	proof	—	open
25	Geometry	8.1	proof	—	open
26	Algebra	8.1	proof	—	open
27	Algebra	8.1	proof	—	open
28	Geometry	8.2	proof	—	open
29	Geometry	8.2	proof	—	open
30	Number theory	8.2	proof	—	open
31	Geometry	8.2	proof	—	open
32	Geometry	8.3	proof	—	open
33	Number theory	8.3	proof	—	open
34	Geometry	8.3	proof	—	open
35	Combinatorics	8.4	proof	—	open
36	Geometry	8.4	proof	—	open
37	Algebra	8.4	proof	—	open
38	Geometry	8.4	proof	—	open
39	Geometry	8.4	proof	—	open
40	Algebra	8.4	proof	—	open
41	Geometry	8.5	proof	—	open
42	Combinatorics	8.6	proof	—	open
43	Combinatorics	8.6	proof	—	open
44	Number theory	8.6	proof	—	open
45	Geometry	8.6	proof	—	open
46	Algebra	8.6	proof	—	open
47	Algebra	8.7	proof	—	open
48	Number theory	8.8	proof	—	open
49	Geometry	8.8	proof	—	open
50	Combinatorics	9.0	proof	—	open
51	Combinatorics	9.0	proof	—	open
52	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.