Yesterday I was giving my old-age sweet-heart HBCSE olympiads page a kind visit. What I found was really astonishing. I have done a bit of work on geometry and number theory but INMO calls for not only knowing the theorems but using multitude of them to make a problem visible. It’s fine if the problem is on e.g. similarity of triangles but its not enough. Geometrical setup makes the going tougher. Like have a look at this one I tried a hand on today –
Now You are adept at solving such problems for your high school exams but the thing with olympiads is to reach a certain point using them “substantially well”. Now the weirdest approach can be to write what you think at that instant but what you have to do is to ask yourself ” Are you watching closely” which is the punchline of Christopher Nolan classic – The Prestige. I like mathematical statements for the fun of them and that’s it. The most simple reason why great mathematical prodigies fail at such examinations is to make out quickly what does the problem want from them to arrive to which people neglect and go on and on. This is because I have seen myself and others who are “really good” at problem solving at the nadir of such examination results. On the other hand, Don’t ever think IMO can be explained on the same grounds. INMO requires analytical skills and no more than that. There are least mathematical tools you are going to need for this exam I say !!
Try and figure out the solution for it shall disabuse you of your modern notions of mathematical olympiads being the orthodox mind-trenching event but shall give you a perspective “the other-side” kind of a thing to explore with problems which motivate you even a little speck.
Solution to above problem is (Try before you because of your diplopia tend to have a look at this..Practice Askance)
Disclaimer – I appeared in INMO 2009 and got such pathetic marks that our regional RMO Coordinator called me up to give me a nice hell of a “diatribe” because that year none of the candidates from Jharkhand made it to the IMO Camp. So don’t treat me as an erudite or a savant of this field.