Maths Olympiad Prep

Library /European Mathematical Cup

European Mathematical Cup

28 problems here, rated 5 to 7.8 on our scale (AIME, harder to National Olympiad, round 2). 15 of them ask for a proof.

Algebra 13Combinatorics 3Geometry 5Number theory 7
#TopicDiffTypeYear
1 Number theory 5.0 proof — open
2 Algebra 5.2 proof — open
3 Algebra 6.0 proof — open
4 Number theory 6.2 answer — open
5 Algebra 6.3 proof — open
6 Geometry 6.4 proof — open
7 Number theory 6.4 answer — open
8 Algebra 6.5 answer — open
9 Number theory 6.5 proof — open
10 Number theory 6.5 answer — open
11 Algebra 6.5 proof — open
12 Geometry 6.6 proof — open
13 Algebra 6.6 answer — open
14 Algebra 6.6 answer — open
15 Algebra 6.7 answer — open
16 Algebra 6.8 answer — open
17 Algebra 6.8 answer — open
18 Algebra 6.8 answer — open
19 Geometry 7.1 answer — open
20 Number theory 7.1 proof — open
21 Geometry 7.2 answer — open
22 Algebra 7.2 answer — open
23 Geometry 7.3 proof — open
24 Algebra 7.3 proof — open
25 Combinatorics 7.3 proof — open
26 Combinatorics 7.4 proof — open
27 Number theory 7.5 proof — open
28 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.