International Mathematics Olympiad
Mathematics Olympiad conducted by SOF for class 1 to 12
IMO Study Material
The International Mathematical Olympiad (IMO) is the world championship of mathematics for school students. It is held every year in a different host country and is the oldest of the international science olympiads. The first edition took place in Romania in 1959 with seven countries. Today, more than 100 countries send teams. The exam is also written as the International Mathematics Olympiad.
Table of Contents
This guide explains how the IMO works, who can take part, what the papers look like, and how Indian students reach the national team. The dates for IMO 2027 and India's 2026-27 selection cycle have been checked against official sources, and the page is updated when new dates are announced.
IMO at a Glance
Particular | Details |
|---|---|
Exam | International Mathematical Olympiad (IMO) |
Level | Pre-university (school) students |
First held | 1959, Romania (7 countries) |
Frequency | Every year, in a different host country (not held in 1980) |
Next edition | 68th IMO, Budapest, Hungary, 16 to 26 July 2027 |
Team size | Up to six contestants per country, plus a team leader and deputy leader |
Papers | Two days, three problems each day, 4.5 hours per day |
Maximum score | 42 marks (7 marks per problem) |
Age limit | Under 20 years on the day of the second paper |
India's organiser | Homi Bhabha Centre for Science Education (HBCSE), for the National Board for Higher Mathematics |
Official website | imo-official.org |
What Is the International Mathematical Olympiad?
The IMO tests how well a student can reason, not how much formula-based mathematics they have memorised. Problems look simple to state but need creative, rigorous proofs. Calculus is never required, and calculators are banned.
History and Growth
The IMO began as a competition among a handful of Central and Eastern European countries. It has since grown into a global event with more than 100 participating countries across five continents. It has been held every year since 1959 except 1980. In 2020 and 2021 the contest was held online because of the pandemic.
Who Runs It
Each year the host country organises the contest, while the IMO Board makes sure the regulations and traditions are followed. Every country selects its own team through a national process. Contestants compete as individuals, and awards go to individuals. Team rankings are unofficial, although they attract the most attention.
IMO 2027 Dates and Important Dates for India
The 68th IMO will be hosted in Budapest by Hungary, with the HUN-REN Alfred Renyi Institute of Mathematics as main organiser. Indian students who want to compete in 2027 or later need to follow the national stages below.
Event | Date |
|---|---|
IOQM 2026 (first stage, already held) | 6 September 2026 |
RMO 2026 (second stage) | 15 November 2026, 1:00 PM to 4:00 PM |
INMO (third stage) | 17 January 2027, 12:00 PM to 4:30 PM |
IMO Training Camp (IMOTC) | April to May 2027 (as per HBCSE's stage description) |
IMO 2027, Budapest | 16 to 26 July 2027 |
Dates for the next IOQM cycle have not been announced yet. Follow the official HBCSE and IOQM portals for the notification, and note that tentative dates can change.
IMO Eligibility
The international rules are short. A contestant must be under 20 years of age on the day of the second paper, which is normally in July, and must not be registered at a university or similar institution. Contestants normally need to be citizens or long-term residents of the country they represent. A student may compete in more than one IMO as long as these conditions hold.
Eligibility for India's Selection Process
India adds its own conditions at the first stage. The IOQM 2026 rules, which show the pattern for the cycle, were as follows.
Condition | IOQM 2026 rule |
|---|---|
Date of birth | Between 1 August 2007 and 31 July 2014 |
Class | Studying in Class 8, 9, 10, 11 or 12 |
Citizenship | Must be eligible to hold an Indian passport; OCI cardholders can take part in earlier stages but cannot represent India at the IMO |
Residence | Residing and studying in India, or studying in an Indian school system, since 30 October 2024 or earlier |
Class 12 | Must not have already passed the Class 12 board examination |
University | Must not start university or equivalent studies by 1 June 2027 |
The IOQM fee in 2026 was Rs. 300, or Rs. 180 for Kendriya Vidyalaya and Jawahar Navodaya Vidyalaya students. According to the organisers, there is no payment for later stages, and the expenses of the Indian team at the IMO are borne by the Government of India. Always read the latest eligibility notice, because details change every cycle.
IMO Exam Pattern and Marking
Feature | Details |
|---|---|
Number of papers | 2 (on consecutive days) |
Problems per paper | 3 |
Time per paper | 4 hours 30 minutes |
Marks per problem | 7 |
Total marks | 42 |
Answer type | Full written solutions and proofs |
Calculators | Not allowed |
How the Problems Are Chosen
Countries suggest problems to a committee set up by the host. The committee prepares a shortlist, and the team leaders, who form the jury, select the final six. The problems are arranged so that difficulty rises from Problem 1 to Problem 3 on the first day and from Problem 4 to Problem 6 on the second day. In terms of overall difficulty, the usual order is Problems 1, 4, 2, 5, 3 and 6.
What This Means for You
Marks reward partial progress: A problem is worth 7 marks, and a half-correct argument can still earn marks. Always write down what you have proved.
Time is generous but tight: You get 4.5 hours for three problems, so the real skill is deciding which problem to attack first.
Proof writing counts: A correct idea written loosely may lose marks. Practise writing complete, readable solutions.
Medals and Awards
Slightly fewer than half of the contestants receive a medal. The gold, silver and bronze cut-offs are chosen so that the numbers of medals are roughly in the ratio 1 : 2 : 3. A contestant without a medal who scores full marks on at least one problem receives an honourable mention.
Award (IMO 2026) | Minimum score (out of 42) | Number awarded |
|---|---|---|
Gold | 29 | 55 |
Silver | 23 | 105 |
Bronze | 16 | 189 |
Honourable mention | 7 on at least one problem | 141 |
Medal boundaries change every year with the difficulty of the paper, so treat these figures as a benchmark only. Special prizes for particularly elegant solutions are rare.
Difficulty Level and Problem Areas
The IMO is widely regarded as the most prestigious school-level mathematics competition in the world, and the problems are deliberately hard. Problems 3 and 6 are the hardest on each day, and even medal-winning contestants often score little on them.
Area | Typical flavour of problems |
|---|---|
Algebra | Inequalities, functional equations, polynomials, sequences |
Combinatorics | Counting, games, constructions, pigeonhole-style arguments |
Geometry | Triangles and circles, concurrency, collinearity, constructions |
Number theory | Divisibility, congruences, Diophantine equations, prime numbers |
Several former contestants have gone on to win the Fields Medal, the highest honour in mathematics. For most students, though, the real reward is the problem-solving habit, which also helps in later exams such as JEE and university entrance rounds.
How India Selects Its IMO Team
India's programme is run by HBCSE on behalf of the National Board for Higher Mathematics (NBHM), Department of Atomic Energy. Its purpose is to spot mathematical talent among pre-university students.
Stage | What it is | Format |
|---|---|---|
IOQM | Indian Olympiad Qualifier in Mathematics, conducted by the Mathematics Teachers' Association (India) | 3 hours, 30 questions, answers are one-digit or two-digit numbers on an OMR sheet; no negative marking in 2026 |
RMO | Regional Mathematical Olympiad | 3 hours, 6 problems, each needing a detailed proof |
INMOTC | Regional training camps for INMO | Training |
INMO | Indian National Mathematical Olympiad | 4.5 hours, 6 problems, proof-based |
IMOTC | International Mathematical Olympiad Training Camp | About 65 top INMO students; several selection tests |
PDC and IMO | Pre-departure camp, then the IMO itself | Six students represent India |
Students cannot skip IOQM and RMO, except that INMO awardees may write the next INMO directly if they meet the age and other rules. India first took part in 1989. Its best team rank is 4th, achieved in 2024, and Indian students have collected gold, silver and bronze medals regularly since.
IMO 2026 Snapshot
The 67th IMO was held in Shanghai, China, in July 2026, with papers on 15 and 16 July and 117 countries taking part. China finished first as a team, followed by the United States, Russia and Singapore. India's six students all won medals, two gold and four silver, and the team scored 166 points to rank 7th. The next stop is Budapest in 2027.
IMO Syllabus: What You Need to Know
The IMO has no official syllabus. Problems come from four areas of school-level mathematics: algebra, combinatorics, geometry and number theory. They do not need university mathematics, yet they are designed to be hard. HBCSE advises Olympiad aspirants to be comfortable with the NCERT mathematics books of Classes 8, 9 and 10, and then to build depth in the four areas. The detailed topic list is on the International Mathematical Olympiad syllabus page.
How to Prepare for the IMO
Olympiad preparation is a multi-year habit rather than a short course. A practical plan for a Class 8 to 12 student looks like this.
Build the base (first months): Be fluent with school mathematics through Class 10, including algebraic manipulation, triangles, circles and basic number properties.
Learn the four areas: Study one area at a time from standard Olympiad books, and solve problems rather than only reading theory.
Practise past papers: Solve IOQM, RMO and INMO papers from earlier years. Attempt each one under time limits, then study the official solutions.
Learn to write proofs: From RMO onwards, marks depend on rigorous writing. Ask a teacher or senior to review your solutions.
Review mistakes: Keep a notebook of problems you could not solve and the idea that unlocked each one.
Timed practice makes a real difference at the IOQM stage, where you must handle 30 questions in 3 hours. You can practise IMO-style problems with online mock tests on Testkart, and use the section-wise analysis to see which of algebra, geometry, number theory or combinatorics needs more work. Keep a study notes collection for the IMO alongside it for formulas, theorems and solved examples.
For Teachers and Coaching Institutes
Teachers who train students for olympiads can use Testkart to create timed tests from their own problem sets, group them into a test series, and share them with students. Educators can also publish notes and courses, and manage everything from one account. Visit the teacher resources on Testkart to see how test creation works.
IMO vs the School-Level Mathematics Olympiad
Two different exams are often called "IMO" in India. The International Mathematical Olympiad described on this page is the global contest for the world's top school mathematicians, reached through IOQM, RMO and INMO. The other is a school-level International Mathematics Olympiad run by the Science Olympiad Foundation (SOF) for students in Classes 1 to 12, based on the school curriculum. The two have different organisers, patterns and syllabuses, so check which exam you are preparing for.
Where to Start
If you are in Class 8 to 12 and curious about the International Mathematical Olympiad, start by solving previous IOQM papers and see how many you can finish in three hours. For official updates, dates and past papers, use the official IMO website and the HBCSE Olympiads website.