What Do You Need for INMO?
INMO at a Glance
The Indian National Mathematical Olympiad is the third stage of India’s Mathematical Olympiad programme and the gateway to the IMO Training Camp.
Based on recent INMO papers. Always confirm the current rules on olympiads.hbcse.tifr.res.in.
Where INMO Fits
The Mathematical Olympiad pathway, from IOQM to the IMO.
IOQM
Qualifier exam — 30 integer-answer problems. IOQM page →
RMO
Regional Mathematical Olympiad — 6 proof-based problems in 3 hours. RMO page →
INMO
Indian National Mathematical Olympiad — 6 proof-based problems in 4.5 hours.
IMOTC
Training camp at HBCSE for top INMO performers.
IMO
India’s team of six is selected for the International Mathematical Olympiad.
Selection from RMO
INMO seats are given region by region, based on RMO scores. Numbers below are from the latest announced rules.
| Group (per region) | Selected |
|---|---|
| Category A — Class 8 to 11 | Top 30 |
| Category B — Class 12 | Top 6 |
| Girls, Category A | 5 more |
A non-zero RMO score is needed; ties are broken using IOQM scores. Rules can change each year — check olympiads.hbcse.tifr.res.in.
INMO Pattern
Six problems in four and a half hours — about 45 minutes per problem. Every solution must be written out in full.
| Item | Detail |
|---|---|
| Problems | 6 |
| Marks per problem | 17 |
| Duration | 270 min |
| Answer type | Written proofs |
| Total marks | 102 |
6 × 17 = 102 marks; 270 ÷ 6 = 45 minutes per problem on average.
INMO Topics and Techniques
Pre-college mathematics, no calculus — at national-olympiad depth. Tap a topic to see its areas.
AlgebraNational level
- Polynomials — roots, irreducibility, interpolation
- Inequalities — AM-GM, Cauchy-Schwarz, Schur, Jensen
- Functional equations over integers and reals
- Sequences, recurrences and complex numbers
Number TheoryNational level
- Congruences, orders and primitive roots
- Quadratic residues
- Diophantine equations and p-adic valuation
- Lifting the exponent; Zsigmondy-type ideas
GeometryNational level
- Cyclic configurations and angle chasing
- Power of a point, radical axes and centres
- Homothety, spiral similarity and inversion
- Trigonometric, complex and barycentric methods
CombinatoricsNational level
- Advanced counting, bijections and generating ideas
- Invariants, monovariants and extremal principle
- Graph theory
- Combinatorial geometry and games
Proof TechniquesUsed across all topics
- Induction (including strong and structural)
- Contradiction and infinite descent
- Pigeonhole and double counting
- Extremal principle and smoothing
- Constructions and counter-examples
Free INMO Study Material
Advanced theory, solved examples and problem sets at INMO level.
These resources are being added topic by topic. Pages marked “Coming soon” are not published yet.
Olympiad Algebra
Inequalities, polynomials and functional equations.
Coming soon →Advanced Geometry
Inversion, homothety and key configurations.
Coming soon →Advanced Number Theory
Orders, residues and valuations.
Coming soon →Advanced Combinatorics
Graphs, extremal and double counting.
Coming soon →RMO Page
Proof writing and preparation for the previous stage.
Explore →INMO 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.
INMO Full Mock
Topic Proof Sets
IMO-Level Problems
Problem of the Week
INMO 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 INMO
Between RMO (November) and INMO (January) there are only about nine weeks — use them well.
Fill topic gaps
Review your RMO paper and strengthen the weakest of the four topics first.
Learn advanced tools
Add inversion, orders, LTE, Schur and graph ideas to your toolkit with solved examples.
Solve past INMO papers
Attempt full papers under a 4.5-hour limit.
Stay with hard problems
Spend an hour or more on a single problem before reading its solution.
Write and get feedback
Write complete proofs and have a teacher or friend check them for gaps.
Manage time in the exam
Read all six problems first, start with the most approachable, and write partial progress.
INMO 2027 Date
INMO 2027 is scheduled for 17 January 2027, 12:00 noon to 4:30 PM. Always check the official website. We will post verified updates here.
INMO FAQs
Who conducts INMO?
INMO is conducted by the Homi Bhabha Centre for Science Education (HBCSE) as part of India’s Mathematical Olympiad programme. Official information is on olympiads.hbcse.tifr.res.in.
How do I qualify for INMO?
Through RMO. In recent years about the top 30 Class 8–11 students and the top 6 Class 12 students from each region were selected, plus additional seats for girls. Check the current year’s rules on the official website.
How is INMO different from RMO?
Both are proof-based with six problems, but INMO allows 4.5 hours instead of 3, and the problems are harder and need deeper ideas.
Are partial marks given?
Yes. Graders give credit for correct, meaningful progress, such as a proven lemma or a solved important case.
What happens after INMO?
Top INMO performers are invited to the International Mathematical Olympiad Training Camp (IMOTC) at HBCSE. India’s IMO team of six — and the team for the European Girls’ Mathematical Olympiad (EGMO) — is selected from the camp.
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.