Library /Ukrainian Mathematical Olympiad

Ukrainian Mathematical Olympiad

49 problems here, rated 4.6 to 7.5 on our scale (AIME to National Olympiad, round 2). 49 of them ask for a proof.

Algebra 19Combinatorics 9Geometry 14Number theory 7

#	Topic	Diff	Type	Year
1	Geometry	4.6	proof	—	open
2	Algebra	4.8	proof	—	open
3	Combinatorics	4.8	proof	—	open
4	Algebra	4.8	proof	—	open
5	Algebra	4.9	proof	—	open
6	Geometry	4.9	proof	—	open
7	Algebra	4.9	proof	—	open
8	Geometry	4.9	proof	—	open
9	Number theory	4.9	proof	—	open
10	Algebra	5.1	proof	—	open
11	Algebra	5.1	proof	—	open
12	Algebra	5.2	proof	—	open
13	Algebra	5.2	proof	—	open
14	Number theory	5.3	proof	—	open
15	Algebra	5.3	proof	—	open
16	Number theory	5.3	proof	—	open
17	Algebra	5.3	proof	—	open
18	Algebra	5.4	proof	—	open
19	Geometry	5.5	proof	—	open
20	Geometry	5.7	proof	—	open
21	Combinatorics	5.7	proof	—	open
22	Geometry	5.7	proof	—	open
23	Number theory	5.7	proof	—	open
24	Algebra	5.7	proof	—	open
25	Geometry	5.7	proof	—	open
26	Number theory	5.8	proof	—	open
27	Geometry	5.8	proof	—	open
28	Geometry	5.8	proof	—	open
29	Algebra	5.9	proof	—	open
30	Algebra	5.9	proof	—	open
31	Algebra	6.0	proof	—	open
32	Geometry	6.0	proof	—	open
33	Algebra	6.0	proof	—	open
34	Number theory	6.1	proof	—	open
35	Combinatorics	6.1	proof	—	open
36	Algebra	6.2	proof	—	open
37	Geometry	6.2	proof	—	open
38	Combinatorics	6.3	proof	—	open
39	Number theory	6.3	proof	—	open
40	Geometry	6.4	proof	—	open
41	Geometry	6.5	proof	—	open
42	Geometry	6.5	proof	—	open
43	Combinatorics	6.6	proof	—	open
44	Algebra	6.8	proof	—	open
45	Combinatorics	6.9	proof	—	open
46	Combinatorics	7.0	proof	—	open
47	Combinatorics	7.0	proof	—	open
48	Combinatorics	7.2	proof	—	open
49	Algebra	7.5	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.