What Do You Need for the IMO?
IMO at a Glance
The International Mathematical Olympiad is the final stage of India’s Mathematical Olympiad programme and the most prestigious maths competition for school students.
Official rules, problems and results: imo-official.org.
India’s Road to the IMO
Every Indian IMO contestant comes through HBCSE’s Mathematical Olympiad programme.
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. INMO page →
IMOTC
Training camp at HBCSE with selection tests for the IMO team. IMOTC page →
IMO
India’s team of six competes with students from over 100 countries.
IMO Format
Two papers on consecutive days. Each paper has three problems, usually in rising difficulty.
| Item | Detail |
|---|---|
| Papers | 2 (two days) |
| Problems per paper | 3 |
| Time per paper | 4.5 hours |
| Marks per problem | 7 |
| Maximum score | 42 |
6 × 7 = 42 marks; 270 ÷ 3 = 90 minutes per problem on average.
Scoring and Medals
Individual medals, decided by score.
Marking
Each problem is marked out of 7 by the team leaders and coordinators, using an agreed marking scheme.
Medal share
Fewer than half of all contestants get medals.
Medal ratio
Gold, silver and bronze roughly in the ratio 1 : 2 : 3.
Cut-offs
Medal cut-offs are set each year from the score distribution.
Honourable mention
For a contestant without a medal who solves at least one problem fully (7 marks).
Team ranking
Unofficial, by adding the scores of a country’s contestants.
India at IMO 2026
The 67th IMO was held in Shanghai, China in July 2026.
As reported in the press, citing HBCSE. Full official results: imo-official.org.
IMO Topics
There is no official syllabus. Problems come from pre-college mathematics, without calculus. Tap a topic to see its areas.
AlgebraIMO level
- Functional equations — injectivity, substitutions, Cauchy-type
- Inequalities — SOS, tangent line trick, majorization
- Polynomials over integers and reals
- Sequences and recurrences
Number TheoryIMO level
- Orders, primitive roots and quadratic reciprocity
- p-adic valuations and LTE
- Diophantine equations and bounding
- Additive and combinatorial number theory
GeometryIMO level
- Projective ideas — cross-ratio, poles and polars
- Inversion and spiral similarity
- Complex and barycentric coordinates
- Classic configurations — mixtilinear circles, isogonal conjugates
CombinatoricsIMO level
- Extremal and probabilistic arguments
- Graph theory and colourings
- Algorithms, processes and games
- Combinatorial geometry
Free IMO Study Material
Advanced notes and problem sets for IMO preparation.
These resources are being added topic by topic. Pages marked “Coming soon” are not published yet.
IMO Algebra
Functional equations, inequalities and polynomials.
Coming soon →IMO Geometry
Projective, inversive and coordinate methods.
Coming soon →IMO Number Theory
Valuations, orders and bounding.
Coming soon →IMO Combinatorics
Extremal, algorithmic and graph problems.
Coming soon →IMOTC Page
The training camp that selects India’s team.
Explore →IMO Practice
Sit IMO-style papers under exam conditions, then compare with model solutions.
Under development. The practice sets below are planned and will open here when ready.
IMO-Style Paper
Two-Day Mock
Shortlist Problem Sets
Problem of the Week
Past IMO Problems
IMO problems with complete model solutions, arranged by year.
Coming soon. Official IMO problems in many languages are on imo-official.org.
How to Aim for the IMO
The IMO is a multi-year goal. Start early and build steadily.
Start in middle school
Students from Class 8 can enter IOQM — early starters gain years of experience.
Build all four topics
IMO papers usually cover algebra, number theory, geometry and combinatorics.
Solve shortlist problems
IMO shortlists from past years are the best practice material.
Sit full papers
Practise three problems in 4.5 hours to build stamina.
Write rigorous proofs
Marks depend on complete, clearly written arguments.
Learn from others
Discuss problems with peers and mentors, and read multiple solutions.
IMO 2027 Dates
The 68th IMO is scheduled for 16–26 July 2027 in Budapest, Hungary. India’s team is selected at IMOTC 2027. Always check the official websites.
IMO FAQs
What is the IMO?
The International Mathematical Olympiad is the world championship mathematics competition for school students, held every year since 1959. Official information is on imo-official.org.
How do I get into India’s IMO team?
Through India’s Mathematical Olympiad programme run by HBCSE: IOQM, then RMO, then INMO, then the IMO Training Camp (IMOTC), where the team of six is selected.
Who is eligible?
Under IMO rules, contestants must be under 20 on the day of the second paper and must not be enrolled at a university or equivalent. Each country sends up to six students.
How are medals given?
Fewer than half of all contestants receive medals, given roughly in the ratio 1:2:3 for gold, silver and bronze. Contestants without a medal who score full marks on at least one problem get an honourable mention.
How did India do at IMO 2026?
At the 67th IMO in Shanghai, all six Indian students won medals — 2 gold and 4 silver. HBCSE reported an unofficial team rank of 7th, among 117 countries.
Is there a team for girls?
Yes. India also sends a team of four girls to the European Girls’ Mathematical Olympiad (EGMO), selected through the same programme.