Physics solver’s mosaic

What is needed to be able to solve problems so well that you could get a gold medal at IPhO? Is it enough to be just very gifted? Of course not, there are other students, who have solved a lot of problems – while you are thinking hard trying to "invent a bicycle", they are already writing the solution, because they had solved a similar problem earlier. Is it enough to solve a lot of problems and read a lot of problem solutions? Most often, no. Just solving or reading solutions, of course, will increase your technical skills, but you also need to think over, what were the main ideas which made it possible to solve the problem, and take these ideas into your permanent arsenal; if you solve too many problems, you don't have time to think over. Is it possible to learn "the art of problem solving" and if yes then how? Well, 99% of the Olympiad problems are solved using a rather limited set of ideas (for mathematics, that set is somewhat larger). So, if you acquire those ideas well enough – so that you can recognize them even if they are carefully hidden – then the IPhO gold will be yours! Do not worry, no-one expects you to discover a solving technique which has been never seen before, because that would be an achievement worth of a Nobel Prize! 

Since we started the topic of Nobel Prize – is it enough to be the absolute winner of the IPhO to get, at a later stage, a Nobel Prize? (Each year, there is one Nobel Prize in physics – similarly to the absolute winner of IPhO.) Of course, it is not; however, you'll have better chances than anyone else. Becoming a great physicist requires several components, one of which is having brilliant problem solving skills (tested at IPhO). Another one is ability to make solvable models –  formulate problems which can be solved and which reflect important aspects of reality. Third component is ability to distinguish, which problems are important and which are not. You can be very skilful and smart, but if you study problems of marginal interest, no-one will pay attention to your research results. Finally, you need a considerable amount of luck. Indeed, that particular field of physics in which you start your studies, eg. start making your PhD thesis, depends on somewhat random decisions – it is almost impossible to foresee, where are the biggest scientific challenges after five or ten years. Also, in order to perfect yourself in regard of the above-mentioned three components, you need excellent supervisors and excellent lab; although you have some freedom in choosing your supervisor and lab, you still need to be very lucky to find outstanding ones!

I coined to name this section as "mosaic", because we shall describe here a set of solving techniques, fragments of the whole arsenal needed for a perfect problem solver. With a large number of pieces, the picture would become recognizable, but we need to start making it piece by piece … While some "tiles" will be  useful for solving a spectrum of problems, other tiles are aimed to give more insight into certain physical concepts.

Jaan Kalda, Academic Committee of IPhO-2012

Tile 1: minimum or maximum?
Tile 2: fast or slow?
Tile 3: force diagrams or generalized coordinates?
Tile 4: Tile 4: are trojans stable?
Tile 5: 5 images or roulette?

Additional resources (under development).