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Problems
And References
- Every solved exercise is a BIG success!
- Do not be discouraged if you cannot immediately solve the problems.. you can take your time to think about them and ask for advice!
- The ordering of the problems in general does not represent how challenging they are! And you can of course pick any of them to start with...
- As soon as you have written down a definite solution to one or more problems, you can send it to us for checking!
- Feel free to write if you are unsure of something, we can explain things and you may learn more...
January 2018
Question of the month:
Can you dissect a square into 5 smaller squares?
- Problems around sets: Theme 1
- Problems around tilings and dissections: Theme 2
December 2017
Question of the month:
Allan is on the 5th floor and about to take the elevator number 1 to go the basement.
At the same time, John is in the basement and about to take the elevator number 2 to go the 5th floor.
One minute later, Allan is in the basement and John is on the 5th floor.
Justify that, during this minute, John and Allan must have been at the same height.
November 2017
Question of the month:
True or false? "A polynomial that takes integer values when evaluated at the integers must have integer coefficients."
- Problems around the induction principle: Theme 1
- Problems around polynomials: Theme 2
October 2017
Question of the month:
You have done two tests (each one has maximal 60 points) but they will be counted together.
Do you prefer to get half of the sum of the two scores,
or the square root of the product of the two scores?
- Problems around the pigeonhole principle: Theme 1
- Problems around inequalities: Theme 2
Problems from mathematical contests
References
- Have a look at the wonderful interactive website (in French)
www.mathraining.be.
You can make a login and then access to the material...
- Many nice preparation courses are online (in French) on the webpage:
www.animath.fr
- The most comprehensive compendium of exercises related to mathematical contests (of many countries!) is the world-wide-known
artofproblemsolving.com/community/