Mathematical competitions are like sport: Practice makes the champion!
Junior training with Kangourou (English, French, German)
Kangourou is an international mathematical competition: what you can do is try the test from a past edition and see how well you do. Then read the solutions and learn what was not yet clear to you! If you do not understand a solution, just ask us (or your math teacher)!
You can find multiple choice exercises (in French) on the website of the Kangourou
More precisely, look at the following pages with the exercises and solutions from old competitions:
And here are the old exercises (in German) from
Känguru der Mathematik
Here the Kangaroo in English: exercises
Junior and Advanced training with OMB/BxMO problems (French, English)
The website of the OMB (Olympiade mathématique belge) contains junior exercises
and advanced exercises
in French. You can try to solve these problems and send us your solution to be corrected!
At an advanced level, you can find very advanced exercises
from the past editions of the Benelux Mathematical Olympiads, in English and French.
Junior and Advanced training with the British Olympiads (English)
On this website
you find past problems (and the solutions) for various competitions, in English, at various levels: Junior, Intermediate, Senior. Selecting each competition there is a link to past problems, with solutions (look at the section 'Preparing for the Challenge'). See also the website from the British Olympiads
Junior and Advanced training with the Swiss Olympiads (English, French, German)
On this page
you can find a list of exercises from past editions of the Swiss mathematical olympiads, with solutions. By the way, you can find some resources (in French) also on the website of the French Olympiads
Do not miss to participate in the Online World Math Contest, available in English, French, and German here
Advanced training with mathraining (French)
If you are training for mathematical competitions (and you understand French), then we expect you to work with the wonderful interactive website
(non-commercial, made by the mathematician Nicolas Radu for pupils)
You can make a login and then freely access the material. There you find:
- Concise explanations of the theory.
- Multiple choice and calculation exercises (meant to check that you understood the theory).
- Very difficult problems : These are meant as personal challenges for high-level training.
Notice that in mathraining there is also a Forum to ask for hints, so you should not give up!
Advanced training with the art of problem solving, e.g. AIME (English)
The most comprehensive compendium of exercises related to mathematical contests (of many countries!) is
We recommend you this site to train for the AIME test.
You find here
problems and solutions
of the AIME competition of the past years.
If you want to have a look at the very very very advanced problems from the famous IMO, see this page
(the solutions are contained in the 'shortlist' pdf): here you can try to understand the solutions and learn the mathematics behind it.
If you do not understand a solution, you can ask us!
Advanced training with EGMO (many languages)
On the EGMO website you find, for every past edition, the problems
in very many languages.
Moreover, going into the homepage of the individual years you should also find the solutions. And some solutions are also discussed in the blog
Solving Mathematical Problems: A Personal Perspective
by Terence Tao;
Problem Solving Strategies
by Arthur Engel;
Les olympiades de mathématiques
by Tarik Belhaj Soulami;
Mathematical Olympiad Challenges
and Mathematical Olympiad Treasures
by Titu Andreescu; IMO Compendium
by Djukić, Janković, Matić, and Petrović.
Notice that these books are available at the public library in Campus Belval, by the University of Luxembourg. More books are under way, and you can also suggest the books that you would like to have...