Maths Olympiad Prep

Library /NMO Selection Tests for the Junior Balkan Mathematical Olympiad

NMO Selection Tests for the Junior Balkan Mathematical Olympiad

62 problems here, rated 4.3 to 7.2 on our scale (AIME to National Olympiad, round 2). 62 of them ask for a proof.

Algebra 13Combinatorics 15Geometry 20Number theory 14
#TopicDiffTypeYear
1 Number theory 4.3 proof — open
2 Geometry 4.4 proof — open
3 Geometry 4.5 proof — open
4 Geometry 4.6 proof — open
5 Algebra 4.6 proof — open
6 Algebra 4.6 proof — open
7 Number theory 4.7 proof — open
8 Algebra 4.7 proof — open
9 Algebra 4.7 proof — open
10 Algebra 4.8 proof — open
11 Geometry 4.8 proof — open
12 Algebra 4.9 proof — open
13 Algebra 4.9 proof — open
14 Geometry 5.0 proof — open
15 Number theory 5.1 proof — open
16 Geometry 5.2 proof — open
17 Geometry 5.2 proof — open
18 Number theory 5.4 proof — open
19 Number theory 5.4 proof — open
20 Number theory 5.4 proof — open
21 Number theory 5.5 proof — open
22 Algebra 5.5 proof — open
23 Combinatorics 5.5 proof — open
24 Number theory 5.6 proof — open
25 Geometry 5.6 proof — open
26 Algebra 5.6 proof — open
27 Algebra 5.6 proof — open
28 Combinatorics 5.7 proof — open
29 Combinatorics 5.7 proof — open
30 Geometry 5.7 proof — open
31 Number theory 5.7 proof — open
32 Combinatorics 5.8 proof — open
33 Algebra 5.8 proof — open
34 Number theory 5.9 proof — open
35 Algebra 5.9 proof — open
36 Geometry 6.0 proof — open
37 Number theory 6.0 proof — open
38 Number theory 6.1 proof — open
39 Geometry 6.1 proof — open
40 Combinatorics 6.1 proof — open
41 Geometry 6.2 proof — open
42 Combinatorics 6.2 proof — open
43 Geometry 6.2 proof — open
44 Number theory 6.2 proof — open
45 Geometry 6.3 proof — open
46 Geometry 6.4 proof — open
47 Combinatorics 6.4 proof — open
48 Number theory 6.5 proof — open
49 Combinatorics 6.5 proof — open
50 Geometry 6.5 proof — open
51 Geometry 6.6 proof — open
52 Combinatorics 6.6 proof — open
53 Combinatorics 6.8 proof — open
54 Geometry 6.8 proof — open
55 Combinatorics 6.9 proof — open
56 Geometry 7.0 proof — open
57 Combinatorics 7.0 proof — open
58 Combinatorics 7.0 proof — open
59 Combinatorics 7.0 proof — open
60 Combinatorics 7.0 proof — open
61 Algebra 7.1 proof — open
62 Geometry 7.2 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.