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Extension & competition maths

India’s maths olympiad pathway: IOQM, RMO, INMO and the IMO

India’s Mathematical Olympiad is a ladder of stages. Each stage selects students for the next, and the top of the ladder is the team that represents India at the International Mathematical Olympiad (IMO). HBCSE runs the programme; this page is our plain-English guide to the stages, with links to the official pages for every rule and date.

We print a date or rule only after checking it on the official page, with the date we checked. Where we have not, you will see a link to the official page instead. Rules and dates change every year.

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The five stages

1. IOQM Indian Olympiad Qualifier in Mathematics

The first stage and the only one you register for directly. It is a written qualifying paper sat at exam centres; the best scorers in each region move on to the RMO. Registration is announced by HBCSE and MTA(I).

  • Who can take it: Students in Classes 8 to 12, born between 1 August 2007 and 31 July 2014, who are eligible to hold an Indian passport (OCI cardholders only provisionally) and have been living and studying in India since 30 October 2024 or earlier. (IOQM eligibility (PDF), last checked 5 October 2026)
  • Paper: 30 questions, each with a whole-number answer from 00 to 99; 100 marks (ten questions of 2 marks, ten of 3 and ten of 5); 3 hours; no negative marking. (HBCSE brochure 2026-27, last checked 5 October 2026)
  • Syllabus: Algebra, combinatorics, geometry and number theory. Calculus and statistics are not included. (IOQM site (MTA(I)), last checked 5 October 2026)
  • IOQM 2026 date: Sunday 6 September 2026, 10:00 to 13:00 (already held). (IOQM site (MTA(I)), last checked 5 October 2026)
  • Registration (2026): Exam centres registered 1 to 26 June 2026; individual registration opened on 29 June 2026 and closed in late July (the official pages give 25 July and 27 July). (MTA(I): IOQM 2026, last checked 5 October 2026)

2. RMO Regional Mathematical Olympiad

A written olympiad for students selected from the IOQM, region by region. Here you write full solutions: the answer alone earns little, the argument earns the marks.

3. INMO Indian National Mathematical Olympiad

The national olympiad for students selected at the RMO stage. The strongest are invited to the training camp.

4. IMOTC International Mathematical Olympiad Training Camp

A training and selection camp run by HBCSE for the top INMO students. The team for the International Mathematical Olympiad is chosen here.

  • Camp: A month-long camp in April to May; about 65 students are invited. Exact dates are not on the official page yet. (HBCSE: stages, last checked 5 October 2026)

5. IMO International Mathematical Olympiad

The world olympiad for school students. India’s team is selected through the stages above.

  • Team selection: The best six students from the selection tests at the IMOTC form India's team. (HBCSE: stages, last checked 5 October 2026)
  • IMO 2027 dates: see HBCSE

Practise at IOQM level

Four original sets, one per olympiad area. The first three problems in each set are free with full solutions; hints and solutions for the rest are included with every A Level, IB, IGCSE and CBSE plan. No calculus, no calculator. These are our own problems, not past IOQM or RMO questions.

Number theory

Divisibility, remainders, divisor counting and equations in whole numbers.

3 free with solutions, 5 with a plan

8 problems →

Geometry

Triangles and circles: inradius, circumradius, chords, bisectors, lattice points.

3 free with solutions, 5 with a plan

8 problems →

Algebra

Roots and Vieta, identities, AM–GM, functional equations and telescoping sums.

3 free with solutions, 5 with a plan

8 problems →

Combinatorics

Counting with choices, gaps, stars and bars, inclusion–exclusion and pigeonhole.

3 free with solutions, 5 with a plan

8 problems →

Then: Olympiad-style problems (proof practice for the RMO) · Problem-solving strategies · Olympiad calendar 2026-27

Official pages

Eligibility, registration, dates, syllabus and past papers come only from these organisers. We link to their pages and never host their papers.

Questions

What is the IOQM?

The Indian Olympiad Qualifier in Mathematics is the first stage of India’s Mathematical Olympiad programme, run by HBCSE. It is a written qualifying paper; the best scorers in each region go on to the Regional Mathematical Olympiad (RMO). Eligibility, dates and the paper format are published each year on the HBCSE and MTA(I) websites.

What comes after the IOQM?

The RMO, then the Indian National Mathematical Olympiad (INMO), then a training camp at HBCSE where India’s team for the International Mathematical Olympiad (IMO) is chosen. Each stage selects students for the next.

How do I register?

Registration for the IOQM is announced each year on the HBCSE Olympiad site and the MTA(I) website, usually through an exam centre or your school. You do not register for the later stages: you are selected for them.

Where can I find past IOQM and RMO papers?

HBCSE publishes past papers on its Olympiad site; we link to them and never host or copy them. For extra practice, our four IOQM-level sets are original problems, not past questions.

Do the practice sets use calculus or a calculator?

No. Every problem in our IOQM-level sets is solved by hand with school algebra, geometry, number theory and counting. Check the official syllabus on the HBCSE site.

Where next: the Indian and UK routes · National Mathematics Day puzzles · Class 10 · Class 12 · Extension & competition maths