Version française

**Problems**

**And References**

**Mathematical competitions are like sport: Practice makes the champion!**

**Junior training with Kangourou**

You can find multiple choice exercises (in French) on the website of the

Kangourou.

More precisely, look at the following pages with the exercises from old competitions:

2019;

2018;

2017;

2016;

2015;

2014;

2013;

2012;

2011;

2010;

2009;

2008;

2007;

2006;

2005;

2004.
For every year you find sheets of various levels (the easiest sheets are on top). There are the solutions to the multiple choice exercises.

If you do not understand a solution, just ask us!

**Advanced training with mathraining**

If you are training for mathematical competitions (and you understand French), we expect you to work with the wonderful interactive website
(non-commercial, made by the mathematician Nicolas Radu for pupils)

www.mathraining.be.
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**

The most comprehensive compendium of exercises related to mathematical contests (of many countries!) is

artofproblemsolving.com/community/ .
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 do not understand a solution, just ask us!

**Advanced training with OMB problems**

The website of the OMB (Olympiade mathématique belge) contains

here
the collection of the final contest problems of the last years. You can try to solve these problems and send us your solution to be corrected.
You can also ask us for hints!

**Advanced training with our Problem Sets**

In these problem sets we explain you some mathematical facts and then propose you some exercises. You can send us written solutions for correction.
You do not have deadlines, and you do not have to complete the problem set before sending us solutions.
We correct your solutions to see if they are mathematically complete and well-written: this is only meant to help you learning, and we do not assign grades.
Sometimes it can be helpful for you to ask us for hints (if you are stuck please do not give up but ask for a hint!).

**Material from the Défis course **

At the University of Luxembourg, there is a course, Défis mathématiques par approches élémentaires,
which is open to high school students. Each semester different topics are covered. Here the material from this course about arithmetic:

Division,

gcd and lcm,

Linear Diophantine equations,

Prime Numbers,

Number Systems,

The Euler function,

Rational numbers,

Modular Arithmetic.
Here the material from this course about combinatorics:

Counting,

Exercises about Counting;

The pigeonhole principe,

Exercises about the pigeonhole principle;

Binomial coefficients;

Permutations,

Exercises about Permutations;

Arrangements,

Exercises about Arrangements;

Combinations,

Exercises about Combinations;

Drawing lots;

Invariants,

Exercises about Invariants;

The inclusion-exclusion principle.

**Books**

*Solving Mathematical Problems: A Personal Perspective* by Terence Tao;

*Problem Solving Strategies* by Arthur Engel;

*Les olympiades de mathÃ©matiques* 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.