Math Olympiads
What are olympiads?
Essentially, there is an examination known as the International Mathematical Olympiad (IMO, and no - it's not run by SOF) where each country sends 6 high school contestants to represent the country.
Each country has its own selection procedures, and in India the selection is done by HBCSE. The stages of selection are as follows (You can check the HBCSE website for more details):
IOQM or PRMO - This is the first round of selection, and there are 30 questions with answers in range 00-99 to be solved over 3 hours. Typically around 200-300 students from grade 8 to 11 and 40 students from grade 12 in each state qualify.
Regional Mathematics Olympiad (RMO) - This has 6 subjective questions to be solved over 3 hours (yes, the questions are that hard) and around 30 students from each region clear it.
Indian National Mathematical Olympiad (INMO) - This too has 6 subjective questions to be solved over 4.5 hours (yes, the questions are even harder) and around 60 students from India clear it, and qualify for the IMO training camp
IMO Training Camp - This is a month long training camp with several selection tests, and a team of 6 students is selected who represent India at the IMO.
What's the difference between school math and olympiad math?
In short, everything.
The idea behind Olympiad Mathematics is to create a set of problems where the solutions require nothing but elementary math, but even graduates in the subject struggle to solve the questions. So these questions become a test of your thinking skills, and it's often not too useful if you know lots of fancy or obscure theorems.
The main difference between school math and olympiad math is that at school, we're often shown a certain type of questions, and then we're asked to replicate the same work in very slightly different scenarios. As an example, you're taught the formula of compound interest and how to apply it, and then there can be a couple of questions asking you to calculate the Amount, and another couple where you need to calculate the time, etc. Regardless, when you see the question - you're often almost certain about what needs to be done. All that is left, is to do the calculations.
In olympiads on the other hand, when you see a question, you're often going to be clueless. You have no idea where to start, or what is the right way to approach the problem. It is unlikely you've seen a similar problem before, and it is unlikely you'll see it ever again. You need to think, and create on-the-spot, and so olympiad math is a true test of your thinking.
Sounds fun! Where do I start my preparation?
Here!