Contest Math Problems

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I've got a friend who participated in Waterloo Math Contest, etc. He has never encountered these types of problems which the Ontario Math Curriculum did not teach. Could you recommend any number theory books, etc. (math topics used in contests) that do not focus on proving theorems. Just enough to answer these questions.

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Well, to make a better comment, I needed to make it an answer:

As I said, you can look for the books of the AMT of math contests. By other side you can enter to artofproblemsolving.com (They have a lot of problems of many contries, so it's a nice place.) Also, four books that I like are:

  • 101 Problems in Algebra
  • 102 Problems Combinatorial problems from the training of the USA IMO team
  • 103 Trigonometry problems from the training of the USA IMO team
  • 104 Number theory problems

All from the famous Titu Andreescu.

In fact, you can see the sample problems of the page of the AMT:

http://www.amt.edu.au/information/for-students/practice-problems/

If your friend knows spanish, the MMO (Mexican Mathematics Olympiad) have very nice books about math contests problems:

http://www.ommenlinea.org/publicaciones/libros-de-olimpiada/#prettyPhoto

If your friend don't talk spanish, it won't be a problem. The mathematics are universal, so he/she will understand the problems.