I recently started reading Arthur Engel's "Problem Solving Strategies" and it's first three chapters blew my mind. Most of the time in standard maths olymiads like IMO have a majority of questions based on Invariance, Coloring proofs and Extremal Principle.(First 3 chapters of book) and Functional Equations.

Is it enough to score good marks just by making a excellent grip on these 4 chapters??


closed as primarily opinion-based by Ben West, YuiTo Cheng, Martin R, dantopa, Paul Frost May 24 at 17:30

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    $\begingroup$ I doubt that that will allow you to win gold single-handedly, but it is certainly a good start. You know, there is always that one problem that requires some other trick, and there is the overall exam situation $\endgroup$ – Hagen von Eitzen May 24 at 6:08
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As an IMO gold medalist, I can say that understanding all the theory in the world won't guarantee a good score in the IMO. IMO is not just centred around theory that you can learn in books; it involves ingenuity and intuition that often cannot be taught. Even then, it took hundreds of hours of comprehensive study over many, many topics, much more diverse than the three you've listed, which don't even touch on geometry or number theory, and barely go into algebra. This renders three quarters of the IMO inaccessible if that theory is all you know. However, personally, I found that doing a large number of problems, and learning the theory for them as I went, was much more useful than studying theory then trying to apply that theory to problems.

In the end, it’s important to enjoy the maths you do. IMO isn’t like a school exam where you study for hours being bored - it’s ultimately a journey of learning and improvement, and it’ll be worth it no matter how well you do in competitions.


If you are preparing yourself just to score good, then you are wasting your time. IMO preparation is meant for enhancing your thinking skills, problem solving skills and gaining knowledge.

Learn for yourself, not for marks.

Coming back to your answer, yes majority of question belong to the chapters that you listed. But as stated by @Hagen in his comment, there can be a question which test your thinking skills rather than knowledge and that single question can spoil your confidence and time.