What it is
The International Mathematical Olympiad (IMO) is the world championship of school mathematics. It is held every year in July, in a different host country each time, and each participating country may send a team of up to six students. India has taken part since 1989.
Students compete as individuals even though they travel as a team. The contest is two papers on two consecutive days. Each paper has three problems and lasts four and a half hours, so a student has around ninety minutes per problem, and many problems take all of that and more. Only writing and drawing instruments such as a ruler and compasses are allowed; calculators are not. Every answer is a full written proof.
This is not the same as a school olympiad with a similar name. Several school-level exams use “mathematics olympiad” in their titles. HBCSE, which runs India’s selection, warns that many privately run olympiads do not lead to the international olympiads. The only way to the IMO for a student in India runs through IOQM.
Who can take it
At the international level, the IMO’s regulations require contestants to be under 20 around the time of the contest and still in school, not yet at university. Each country chooses its own team through its national olympiad.
In India, the team is chosen through the Mathematical Olympiad Programme, which the Homi Bhabha Centre for Science Education (HBCSE) runs on behalf of the National Board for Higher Mathematics. Entry starts with IOQM, open to students in Classes 8 to 12 within a birth-date window, who are eligible to hold an Indian passport and meet residence and schooling rules. Students with OCI cards may take part in every stage up to the training camp and its selection tests, but under current court orders they cannot represent India at the IMO. Check the official eligibility rules for this year, because they are strict and they change.
The stages
| Stage | Who | What happens |
|---|---|---|
| IOQM | Classes 8–12 | Three hours, 30 questions with whole-number answers |
| RMO | Selected from IOQM, region by region | Six proof problems in three hours |
| INMO | Selected from RMO, plus last year’s awardees | Six proof problems in four and a half hours |
| IMOTC | INMO awardees | A camp of about a month with selection tests |
| Pre-departure camp | The team of six | Final training and orientation |
| IMO | India’s team | Two papers, three problems each, on two days |
The IMO Training Camp (IMOTC) has a junior and a senior batch. Students who were INMO awardees the year before form the senior batch; first-time awardees form the junior batch. The team of six is chosen from both batches together, on the basis of selection tests held at the camp. Our page on RMO and INMO explains how students move from one round to the next.
The same route also feeds two other contests. Girls who are eligible can be selected, through a separate camp, for the European Girls’ Mathematical Olympiad (EGMO), with a team of up to four. Awardees and senior camp students who are eligible write the Asian Pacific Mathematics Olympiad (APMO) in their regions.
When it happens
The route to one July’s IMO takes most of the year before it. Registration for IOQM usually runs in June and July, and IOQM is usually in September. RMO usually follows in November and INMO in January. The training camp is usually in April and May, and the IMO itself is in July. For this year’s dates, follow HBCSE’s maths olympiad page.
How to prepare
Nobody prepares for the IMO in one season. The structure itself is built for several years of effort: a student can sit IOQM from Class 8, so there can be several attempts across school, and INMO awardees from Classes 8 to 11 go straight to the next year’s INMO.
Useful habits at every stage:
- Work through past papers. HBCSE publishes earlier RMO and INMO papers with solutions; IMO problems from past years are public too.
- Read widely in the four main areas: algebra, combinatorics, geometry and number theory. HBCSE’s brochure lists recommended books for each, and a standard olympiad problem book goes a long way.
- Write proofs, and have them checked. The IMO marks arguments, not answers.
- Be patient with hard problems. Staying with one problem for an hour or more, without looking up the answer, is the core skill.
Most students who try will not reach the team, which has only six places. HBCSE’s own brochure is reassuring here: the olympiads are meant to build a love of mathematics, they do not replace the school curriculum, and they do not count against students who are not selected.
Where daily practice fits
At this level, a short quiz has a modest role and it is worth saying so. Ado is a free daily quiz of 8 questions, including a 60-second sprint, in maths, science, English, GK and reasoning, ranked only against students the same age. It can keep a daily habit and some speed going between long problem sessions, and its Ado Rank, built from a student’s top three subjects, never resets. It is not IMO preparation; that happens over hours with hard problems and a notebook.