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The maths olympiad is one of the few competitions where a Class 8 student and a Class 12 student sit the same paper. It needs no special syllabus beyond school maths, yet the questions feel nothing like school maths. This post explains each stage, who is eligible, what the papers look like, and how to start preparing.
How does the maths olympiad work in India?
The 2026-27 Mathematical Olympiad brochure says the programme is organised by the Homi Bhabha Centre for Science Education (HBCSE) on behalf of the National Board for Higher Mathematics, Department of Atomic Energy. India has taken part in the International Mathematical Olympiad (IMO) since 1989. For 2026-27 the brochure lists these stages:
IOQM (Indian Olympiad Qualifier in Mathematics), held on 6 September 2026.
RMO (Regional Mathematical Olympiad), on 15 November 2026.
INMO training camp, then INMO (Indian National Mathematical Olympiad) on 17 January 2027.
IMO training camp, then a pre-departure camp.
The 68th IMO, in Budapest, Hungary, in July 2027.
Dates change every year, so check the HBCSE Mathematical Olympiad 2026-2027 page and the official IOQM site for the current cycle.
What is IOQM and who can take it?
The brochure describes IOQM as a three-hour exam with 30 questions, each with an integer answer from 00 to 99, marked on an OMR sheet. The IOQM portal says in its FAQ that the 2026 paper had no negative marking and that the enrolment fee was ₹300, or ₹180 for Kendriya Vidyalaya and Jawahar Navodaya Vidyalaya students.
The IOQM 2026 eligibility criteria required students to be born between 1 August 2007 and 31 July 2014 and studying in Class 8, 9, 10, 11 or 12, among other conditions. A student who has already passed the Class 12 board exam cannot take it.
How do students move from IOQM to RMO and INMO?
For 2026, HBCSE's criteria for moving from IOQM to RMO required at least 10% of the total IOQM marks. From each region, the top 200 students from Classes 8 to 11 and the top 40 from Class 12 qualify, plus 5 more girls from Classes 8 to 11.
RMO and INMO are different kinds of exam. The HBCSE page lists RMO as three hours with six questions, each needing a detailed proof, and INMO as four and a half hours with six proof questions. The brochure says the top 48 INMO students from Classes 8 to 11 and the top 12 from Class 12 become INMO awardees.
What maths does the olympiad cover?
The IOQM FAQ says familiarity with number theory, geometry, algebra and combinatorics helps, that calculus and statistics are excluded, and that success depends more on clarity of thought than on extensive knowledge.
Worked example (IOQM style). How many positive integers less than 100 are divisible by 3 or 5 but not by 15?
Multiples of 3 below 100: 3, 6, ..., 99, which is 33 numbers.
Multiples of 5 below 100: 5, ..., 95, which is 19 numbers.
Multiples of 15 below 100: 15, ..., 90, which is 6 numbers. These were counted twice.
Divisible by 3 or 5: 33 + 19 − 6 = 46.
Remove the multiples of 15: 46 − 6 = 40.
Answer: 40. The common mistakes are including 100 when the question says "less than 100", and subtracting the multiples of 15 only once when the question excludes them entirely.
Worked example (RMO style). Prove that n² + n is even for every integer n.
*Proof.* n² + n = n(n + 1). Of any two consecutive integers, one is even, so their product is even. ∎
A proof has to cover every case. "I tried n = 1, 2 and 3" is not a proof.
How should you start preparing?
Past papers first. HBCSE posts past olympiad papers, including RMO papers with solutions and INMO papers. Try one problem a day and give it at least 30 minutes before you look at the solution.
One topic a fortnight. Rotate through number theory, combinatorics, algebra and geometry.
Write full solutions. Even for IOQM problems, write out why the answer is right, not just the number.
Keep a problem diary. Note the idea that cracked each problem, such as "complementary counting" or "pair up terms".
Use Polya's steps when stuck. Our post on Polya's How to Solve It shows how to restate a problem and try a smaller case.
The IOQM 2026 date has passed. If you qualified, RMO is next. If not, watch for the IOQM 2027 announcement and use the year to build up. Counting problems are a good place to start, and our guide to permutations and combinations covers the basics.
When a solution uses an idea you have not met, such as modular arithmetic, learn the idea properly before moving on. The Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, each with its own lesson.
Open one past RMO paper this week and spend an hour on its first problem, writing a full proof.
