The International Maths Olympiad (IMO) is one of the most prestigious examinations at the college level. Every year, six of the most talented students in mathematics represent their country among nearly 100 competing countries. They solve a series of extremely challenging problems to fetch the coveted Gold Medal. These students are usually selected through a National Level Olympiad held in respective countries. In India, we have the Indian National Maths Olympiad (INMO) at the national level. INMO is the gateway to the IMO. About 30 candidates are shortlisted from all over the country through this test. These candidates are then further trained at the Orientation Cum Selection Camp (OCSC), and six from amongst them are chosen to represent India at the IMO.
INMO is quite a difficult exam. It requires a special aptitude for mathematics as well as thorough knowledge of the subject.
The Selection Process of IMO
The first stage is the Regional Mathematical Olympiad(RMO), which is held at the regional level. The country is divided into various regions and each region conducts the RMO. Currently, only students of STD IX, X and XI are eligible for the exam. Some regions may hold a pre-RMO to shortlist students for the RMO as well. The pre-RMO consists of 20 questions, which are relatively easy. This exam then shortlists students for the RMO.
The RMO is a 3-hour examination typically consisting of 6-8 questions of moderate difficulty worth 100 marks. To ensure uniformity, the same set of questions are asked in every region. However, some regions may opt to hold their own RMOs. The cutoffs are typically low (usually between 40-50 marks) but may vary with the difficulty of the paper.
About 30 students from every region are then selected for INMO, which is the second stage. The problems asked in INMO are quite challenging. It’s no surprise that the students are expected to solve only about 6 problems over a period of 4 hours! Such is the difficulty that despite there being plenty of time, students have a hard time solving even 2-3 problems. Usually solving 4 problems is enough to qualify for the OCSC.
All the Olympiads have pre-calculus mathematics. However, that does not make them simple in any way. The INMO is different from most examinations wherein students are expected to solve many questions in a short span of time. Its questions involve deep and strategic thinking. The problems involve rigorous mathematics and not the tedious kind that we are accustomed to. The solution won’t strike you immediately after you see the problem.
You have to first comprehend the problem properly. Then try and get an idea of how you might proceed to solve the problem. Every solution consists of many ideas joined together. It’s obviously very difficult for anybody to visualize the entire solution all at once. It’s all about taking small steps and building the solution gradually. The complex-looking solution is built from a number of elementary steps. So, while the problems and their solutions may appear impossible at first, they are very much possible to solve. You just need to build it using small and basic steps.
There are a number of reference books for the Olympiads. For beginners, Mathematical Circles by Dimitri Fomin is recommended. This is a beautiful book to begin your Olympiad Journey with. Even if you have a fair bit of knowledge, it is recommended that you read this book as it gives a good insight into some concepts.
An Excursion in Mathematics is a comprehensive book for the Olympiads. This book has all the content that you will require. All INMO qualifiers receive this book as an award.
For the advanced reader, Problem-Solving Strategies by Arthur Engel is a great book. It aims at giving an insight into techniques used to solve the problem. Every chapter is dedicated to one specific technique and contains some problems directly from the International Maths Olympiad. This book too is awarded to the INMO qualifiers. Apart from these, there are numerous books for the different subsections viz. Number Theory, Geometry, Algebra and Combinatorics.
Students preparing for the Olympiads are usually pre-occupied with the entrance exam preparations. Hence, it is difficult for them to devote a significant amount of time to the Olympiad preparation. However, if you are a Math lover, then I would highly recommend appearing for these Olympiads as you will come across a lot of beautiful Mathematical ideas in these exams. It indeed offers a very enriching experience and also the knowledge it provides may come in handy later on in your education. Good Luck!