What Do You Need for RMO?
RMO at a Glance
The Regional Mathematical Olympiad is the second stage of India’s Mathematical Olympiad programme. It tests problem-solving and the ability to write rigorous proofs.
Based on recent RMO papers. Always confirm the current rules on olympiads.hbcse.tifr.res.in.
Where RMO Fits
The Mathematical Olympiad pathway, from IOQM to the IMO.
IOQM
Qualifier exam — 30 integer-answer problems. Top scorers move on to RMO. IOQM page →
RMO
Regional Mathematical Olympiad — 6 proof-based problems in 3 hours.
INMO
Indian National Mathematical Olympiad — for top RMO performers.
IMOTC
Training camp at HBCSE for top INMO performers.
IMO
India’s team of six is selected for the International Mathematical Olympiad.
RMO Pattern
Six problems in three hours — about 30 minutes per problem. Every solution must be written out in full.
| Item | Detail |
|---|---|
| Problems | 6 |
| Marks per problem | 17 |
| Duration | 180 min |
| Answer type | Written proofs |
| Total marks | 102 |
6 × 17 = 102 marks; 180 ÷ 6 = 30 minutes per problem on average.
How to Write an RMO Solution
Graders reward clear, complete and correct reasoning.
State the claim
Begin with what you will prove. For long solutions, state key lemmas separately and prove each one.
Justify every step
Name theorems you use, check every case, and never write “clearly” for something that needs proof.
Write partial progress
If you can’t finish, write down proven cases, useful lemmas and reductions — they can earn partial marks.
Draw clean diagrams
For geometry, draw a large, labelled figure — but the proof must not depend on how the figure looks.
Check special cases
Test small values and edge cases before and after writing your argument.
Keep it readable
Use short paragraphs and clear notation; a grader must be able to follow your logic.
RMO Topics and Proof Techniques
Pre-college mathematics, no calculus — at a deeper level than IOQM. Tap a topic to see its areas.
AlgebraRMO level
- Polynomials — roots, Vieta’s relations, factorisation
- Inequalities — AM-GM, Cauchy-Schwarz, rearrangement
- Functional equations
- Sequences, recurrences and sums
Number TheoryRMO level
- Divisibility and primes
- Congruences; Fermat’s and Euler’s theorems
- Diophantine equations
- Orders, residues and digit problems
GeometryRMO level
- Angle chasing and cyclic quadrilaterals
- Similar triangles and ratio lemmas
- Power of a point, radical axis
- Ceva’s and Menelaus’ theorems
- Trigonometric and coordinate approaches
CombinatoricsRMO level
- Counting and bijections
- Pigeonhole principle
- Invariants and monovariants
- Colouring and tiling arguments
- Games and graph ideas
Proof TechniquesUsed across all topics
- Direct proof
- Proof by contradiction
- Mathematical induction (weak and strong)
- Extremal principle
- Pigeonhole principle
- Invariants
- Constructing examples and counter-examples
Free RMO Study Material
Theory, solved examples and problem sets at RMO level.
These resources are being added topic by topic. Pages marked “Coming soon” are not published yet.
Proof Techniques Guide
Each technique with worked examples.
Coming soon →Olympiad Geometry
Key lemmas and configurations.
Coming soon →Olympiad Number Theory
Congruences, orders and equations.
Coming soon →Olympiad Combinatorics
Pigeonhole, invariants and counting.
Coming soon →IOQM Page
Pattern, syllabus and preparation for the qualifier.
Explore →RMO Practice
Write full solutions under exam conditions, then compare with model solutions.
Under development. The practice sets below are planned and will open here when ready.
RMO Full Mock
Topic Proof Sets
INMO-Level Problems
Problem of the Week
RMO Previous-Year Papers
Problems with complete model solutions, arranged by year.
Coming soon. Official question papers are published by HBCSE on olympiads.hbcse.tifr.res.in.
How to Prepare for RMO
Solving and writing are separate skills — practise both.
Learn the techniques
Study each proof technique with solved examples before attempting hard problems.
Write every solution
After solving a problem, write a full proof as if for a grader.
Solve past RMO papers
Attempt real RMO problems under a 3-hour limit.
Get feedback
Have a teacher or friend check your proofs for gaps.
Balance the four topics
Questions usually cover algebra, number theory, geometry and combinatorics.
Manage time in the exam
Read all six problems first, start with the one you understand best, and write partial progress.
RMO and INMO Dates
RMO 2026 is scheduled for 15 November 2026 and INMO 2027 for 17 January 2027. Always check the official website. We will post verified updates here.
RMO FAQs
Who conducts RMO?
RMO is part of India’s Mathematical Olympiad programme run by the Homi Bhabha Centre for Science Education (HBCSE), held through regional centres. Official information is on olympiads.hbcse.tifr.res.in.
How do I qualify for RMO?
Through IOQM. Students who meet the IOQM cut-off and selection rules announced each year are invited to write RMO.
How is RMO different from IOQM?
IOQM asks for integer answers only. RMO asks for complete written proofs — you must show and justify every step, and the reasoning earns the marks.
Are partial marks given?
Yes. Graders give credit for correct, meaningful progress, such as proving a key lemma or solving an important case, even if the full solution is not complete.
What can I take into the exam?
Usually pens, pencils, a ruler and a compass. Calculators, protractors and electronic devices are not allowed. Follow the instructions on your admit card.
What comes after RMO?
Top RMO performers are selected for INMO, as per the cut-offs announced each year. INMO performers can be invited to the IMO Training Camp at HBCSE.