In my school-going days I was very much involved in the math olympiad scene. Part of me relished the challenge of solving problems, part of me enjoyed the constant exposure to new ideas. Early on I devoured any math olympiad material I could get my hands on. After all, there was so much to learn and to master!
I would often pick up a compendium of past olympiads and read through the problems and solutions, marveling at how elegant the solutions were. I remember thinking to myself, “how smart these solvers must have been to dream of such solutions from thin air!”
However, in the years just before college I began to realise that, more often than not, elegant solutions do not come about by strokes of pure genius (although there are such moments from time to time). It just looks like that when it’s written. Very often the solutions written in these puzzle books do not reveal the thought process through which the solver discovers the solution.
This has implications for students who want to improve their problem solving abilities. Simply attempting problems and reading solutions is not enough to progress quickly in your problem solving abilities. That is like learning how to make a movie by watching many movies over and over. Rather, you should “go behind the scenes” and see what the director does. Dig deeper and ask yourself: “How did the author think of this solution? How could I have thought of it myself?”
The goal of this blog is to give you some tools to help you approach math problems in a systematic manner. We will do this by example. Each blog post will consist of one (or more) math olympiad problems, followed by my train of thought in working out the solution. The problems in this blog will range in difficulty but will generally come from competitions for grades 10-12.
We hope you learn something from this blog; do give us feedback on what else you’d like to see! 🙂