Library /Russian Mathematical Olympiad

Russian Mathematical Olympiad

141 problems here, rated 4.7 to 7.8 on our scale (AIME to National Olympiad, round 2). 141 of them ask for a proof.

Algebra 31Combinatorics 41Geometry 45Number theory 24

#	Topic	Diff	Type	Year
1	Geometry	4.7	proof	—	open
2	Algebra	4.8	proof	—	open
3	Algebra	4.9	proof	—	open
4	Geometry	4.9	proof	—	open
5	Geometry	4.9	proof	—	open
6	Number theory	5.0	proof	—	open
7	Algebra	5.0	proof	—	open
8	Geometry	5.1	proof	—	open
9	Algebra	5.1	proof	—	open
10	Algebra	5.1	proof	—	open
11	Combinatorics	5.1	proof	—	open
12	Number theory	5.1	proof	—	open
13	Combinatorics	5.2	proof	—	open
14	Number theory	5.2	proof	—	open
15	Number theory	5.2	proof	—	open
16	Geometry	5.3	proof	—	open
17	Algebra	5.4	proof	—	open
18	Algebra	5.4	proof	—	open
19	Number theory	5.4	proof	—	open
20	Geometry	5.4	proof	—	open
21	Algebra	5.4	proof	—	open
22	Algebra	5.4	proof	—	open
23	Number theory	5.4	proof	—	open
24	Geometry	5.5	proof	—	open
25	Algebra	5.5	proof	—	open
26	Algebra	5.5	proof	—	open
27	Geometry	5.5	proof	—	open
28	Geometry	5.6	proof	—	open
29	Number theory	5.6	proof	—	open
30	Geometry	5.6	proof	—	open
31	Algebra	5.7	proof	—	open
32	Number theory	5.7	proof	—	open
33	Number theory	5.7	proof	—	open
34	Algebra	5.7	proof	—	open
35	Geometry	5.7	proof	—	open
36	Algebra	5.7	proof	—	open
37	Geometry	5.7	proof	—	open
38	Geometry	5.7	proof	—	open
39	Number theory	5.7	proof	—	open
40	Number theory	5.7	proof	—	open
41	Geometry	5.7	proof	—	open
42	Combinatorics	5.8	proof	—	open
43	Number theory	5.8	proof	—	open
44	Geometry	5.8	proof	—	open
45	Algebra	5.8	proof	—	open
46	Geometry	5.9	proof	—	open
47	Geometry	5.9	proof	—	open
48	Geometry	5.9	proof	—	open
49	Algebra	5.9	proof	—	open
50	Algebra	5.9	proof	—	open
51	Algebra	6.0	proof	—	open
52	Combinatorics	6.0	proof	—	open
53	Algebra	6.0	proof	—	open
54	Geometry	6.0	proof	—	open
55	Number theory	6.0	proof	—	open
56	Number theory	6.1	proof	—	open
57	Geometry	6.1	proof	—	open
58	Number theory	6.1	proof	—	open
59	Geometry	6.1	proof	—	open
60	Algebra	6.1	proof	—	open
61	Number theory	6.2	proof	—	open
62	Number theory	6.2	proof	—	open
63	Algebra	6.2	proof	—	open
64	Combinatorics	6.2	proof	—	open
65	Combinatorics	6.2	proof	—	open
66	Geometry	6.3	proof	—	open
67	Number theory	6.3	proof	—	open
68	Combinatorics	6.3	proof	—	open
69	Algebra	6.3	proof	—	open
70	Combinatorics	6.3	proof	—	open
71	Geometry	6.3	proof	—	open
72	Geometry	6.4	proof	—	open
73	Algebra	6.4	proof	—	open
74	Combinatorics	6.4	proof	—	open
75	Combinatorics	6.4	proof	—	open
76	Geometry	6.5	proof	—	open
77	Geometry	6.5	proof	—	open
78	Combinatorics	6.5	proof	—	open
79	Combinatorics	6.6	proof	—	open
80	Geometry	6.6	proof	—	open
81	Algebra	6.6	proof	—	open
82	Number theory	6.7	proof	—	open
83	Number theory	6.7	proof	—	open
84	Combinatorics	6.7	proof	—	open
85	Geometry	6.7	proof	—	open
86	Geometry	6.7	proof	—	open
87	Geometry	6.7	proof	—	open
88	Combinatorics	6.7	proof	—	open
89	Number theory	6.8	proof	—	open
90	Number theory	6.8	proof	—	open
91	Geometry	6.8	proof	—	open
92	Combinatorics	6.8	proof	—	open
93	Geometry	6.8	proof	—	open
94	Combinatorics	6.8	proof	—	open
95	Combinatorics	6.8	proof	—	open
96	Algebra	6.8	proof	—	open
97	Combinatorics	6.8	proof	—	open
98	Combinatorics	6.8	proof	—	open
99	Combinatorics	6.9	proof	—	open
100	Combinatorics	6.9	proof	—	open
101	Combinatorics	6.9	proof	—	open
102	Geometry	6.9	proof	—	open
103	Geometry	6.9	proof	—	open
104	Algebra	6.9	proof	—	open
105	Geometry	7.0	proof	—	open
106	Geometry	7.0	proof	—	open
107	Combinatorics	7.0	proof	—	open
108	Algebra	7.0	proof	—	open
109	Geometry	7.0	proof	—	open
110	Algebra	7.1	proof	—	open
111	Geometry	7.1	proof	—	open
112	Geometry	7.1	proof	—	open
113	Algebra	7.1	proof	—	open
114	Combinatorics	7.1	proof	—	open
115	Combinatorics	7.1	proof	—	open
116	Algebra	7.1	proof	—	open
117	Geometry	7.2	proof	—	open
118	Combinatorics	7.2	proof	—	open
119	Algebra	7.2	proof	—	open
120	Combinatorics	7.2	proof	—	open
121	Combinatorics	7.3	proof	—	open
122	Geometry	7.3	proof	—	open
123	Combinatorics	7.4	proof	—	open
124	Number theory	7.4	proof	—	open
125	Combinatorics	7.4	proof	—	open
126	Combinatorics	7.5	proof	—	open
127	Number theory	7.5	proof	—	open
128	Combinatorics	7.5	proof	—	open
129	Combinatorics	7.5	proof	—	open
130	Combinatorics	7.5	proof	—	open
131	Combinatorics	7.5	proof	—	open
132	Geometry	7.5	proof	—	open
133	Combinatorics	7.5	proof	—	open
134	Geometry	7.5	proof	—	open
135	Geometry	7.6	proof	—	open
136	Combinatorics	7.6	proof	—	open
137	Combinatorics	7.6	proof	—	open
138	Combinatorics	7.6	proof	—	open
139	Geometry	7.7	proof	—	open
140	Combinatorics	7.7	proof	—	open
141	Combinatorics	7.8	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.