The Indian National Mathematical Olympiad (INMO) is a high school mathematics competition held annually in India since 1989. It is the second tier in the Indian team selection procedure for the international mathematical olympiad and is conducted by the Homi Bhabha centre for senior education (HBCSE) under the aegis of the National Board of Higher Mathematics (NBHM).
INMO

• Eligibility & participant selection process:
The INMO is conducted by the MO which is held on the third Sunday of January at 30 centres across the country. Prospective candidates first need to write the Regional Mathematical Olympiad(known as RMO) of their respective state or region, usually held on the first Sunday of October of the previous year. Around thirty students are selected from each region, to write the INMO. The bestperforming students from the RMO (approximately 900) qualify for the second stage INMO.
• Structure of the examination:
The Indian National Mathematical Olympiad (INMO) examination paper comprises six problems to be solved over a time of four hours. These problems are in the areas of algebra, geometry number theory and combinatorics. No calculus is required, though calculusbased approaches are allowed to solve the questions.
• Further stages:
》 The international mathematical Olympiad training camp (IMOTC):
The qualifying students are invited to the (IMOTC), a onemonth mathematics camp hosted by the Homi Bhabha centre of science education in Mumbai. For first time participants, it usually extends from late April till the end of May, while it begins about 1014 days later for senior participants. In this camp, the students are taught Olympiad mathematics and some other general mathematics. Four selection tests and two practice tests are held during this period and the top six students in the selection tests qualify to represent India in the International Mathematical Olympiad.
》 The Predeparture training camp for IMO:
The selected team of 6 students goes through another round of training and orientation for about 10 days before departure for IMO.
》 International Mathematical Olympiad (IMO):
The sixmember team selected at the end of IMOTC accompanied by a leader, a deputy leader and an observer represents the country at the IMO, held in July each year in a different member country of the IMO. Ministry of Human Resource Development (MHRD) finances international travel of the team, the leader and the deputy leader, while NBHM(DAE) finances the other expenditure connected with the international participation and the entire incountry programme.
》 Post IMOTC training of qualified candidates for subsequent seasons:
Students who qualify the INMO once and come to attend the IMO Training Camp are sent postal problems during the period July – December that they have to solve and send back (if they are still in school). Based on their responses, some of the students are invited to the IMO Training Camp the next year directly. Others have to rewrite the INMO again (they do not have to write the Regional Mathematics Olympiad).
• Perks upon qualification:
Students qualifying the INMO are automatically eligible for admission to the B.Sc. (Hons) Mathematics course in the Chennai Mathematical Institute.
Since 2008, INMO awardees applying for B. Stat or B. Math courses of the Indian statistical the institute is directly called for the interview without having to write the written test.
INMO awardees are also eligible for an NBHM scholarship that currently stands at about Rs. 2500 per month, if they continue their studies in mathematics. They are also offered a 4year programme of training in Mathematics through correspondence and periodic contact with a chosen faculty. The programme is also available to INMO awardees who do not pursue an undergraduate degree in Mathematics but have a special interest in the subject. They are offered an annual cash award of Rs. 9,000 subject to satisfactory performance in the programme.
Students who make it to the IMO are eligible for the Kishore Vaigyanik Protsahan Yojana (KVPY) fellowship provided they pursue their studies in the science subjects in India. The fellowship amount stands at Rs. 5000 per month.
Indian team members who receive a gold, silver or bronze at IMO are given cash awards by the NBHM of Rs. 5,000, Rs. 4,000 and Rs. 3,000 respectively.
All travel expenses for the IMO Training Camp and all expenses for the IMO are borne by the Ministry of HRD, Government of India.
• How to Prepare For The Indian National Mathematics Olympiad:
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 a thorough knowledge of the subject.
• Selection Process of IMO:
The RMO is a 3hour examination typically consisting of 68 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 4050 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 for 4 hours! Such is the difficulty that despite there being plenty of time, students have a hard time solving even 23 problems. Usually solving 4 problems are enough to qualify for the OCSC.
All the Olympiads have precalculus 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 period. 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 complexlooking solution is built from some 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.
• Reference Books:
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 preRMO to shortlist students for the RMO as well. The preRMO consists of 20 questions, which are relatively easy. This exam then shortlists students for the RMO.
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, ProblemSolving 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 preoccupied 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!
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