Maths Olympiad Prep

Library /NMO Selection Tests for the Junior Balkan Mathematical Olympiad

NMO Selection Tests for the Junior Balkan Mathematical Olympiad

52 problems here, rated 4.3 to 7 on our scale (AIME to National Olympiad, round 2). 52 of them ask for a proof.

Algebra 11Combinatorics 12Geometry 16Number theory 13
#TopicDiffTypeYear
1 Number theory 4.3 proof — open
2 Geometry 4.4 proof — open
3 Geometry 4.5 proof — open
4 Geometry 4.5 proof — open
5 Number theory 4.5 proof — open
6 Geometry 4.6 proof — open
7 Algebra 4.6 proof — open
8 Algebra 4.7 proof — open
9 Algebra 4.7 proof — open
10 Number theory 4.7 proof — open
11 Algebra 4.8 proof — open
12 Geometry 4.8 proof — open
13 Algebra 4.9 proof — open
14 Algebra 4.9 proof — open
15 Geometry 5.0 proof — open
16 Number theory 5.1 proof — open
17 Geometry 5.2 proof — open
18 Geometry 5.2 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 Algebra 5.6 proof — open
25 Algebra 5.6 proof — open
26 Combinatorics 5.7 proof — open
27 Combinatorics 5.7 proof — open
28 Number theory 5.7 proof — open
29 Geometry 5.7 proof — open
30 Number theory 5.7 proof — open
31 Combinatorics 5.8 proof — open
32 Algebra 5.8 proof — open
33 Algebra 5.9 proof — open
34 Geometry 6.0 proof — open
35 Number theory 6.0 proof — open
36 Number theory 6.1 proof — open
37 Combinatorics 6.1 proof — open
38 Geometry 6.2 proof — open
39 Combinatorics 6.2 proof — open
40 Geometry 6.2 proof — open
41 Number theory 6.2 proof — open
42 Geometry 6.4 proof — open
43 Combinatorics 6.4 proof — open
44 Combinatorics 6.5 proof — open
45 Geometry 6.6 proof — open
46 Number theory 6.7 proof — open
47 Combinatorics 6.8 proof — open
48 Geometry 6.8 proof — open
49 Combinatorics 6.9 proof — open
50 Geometry 7.0 proof — open
51 Combinatorics 7.0 proof — open
52 Combinatorics 7.0 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.