RMO preparation

What RMO asks

IOQM asks for a number. RMO asks you to show why. A typical problem says “prove that”, “show that” or “find all”, and the answer is a page of reasoning that a reader can check line by line. The topics are the same four as IOQM (algebra, geometry, number theory, combinatorics); the difference is the depth, and the writing. (source: HBCSE)

From IOQM answers to written solutions

Most strong IOQM students lose RMO marks not because they cannot solve the problem, but because the write-up leaves gaps. A solution that reads well does five things:

1. Says what it will prove, in one sentence, before starting.
2. Names things once (“let n be the smallest such number”) and uses the names consistently.
3. Gives a reason for every step, even the obvious ones: “since p is odd”, “by the angle bisector theorem”.
4. Handles every case, and says why the cases cover everything.
5. Ends by saying what has been shown, and for a “find all” problem, checks that each answer really works.

Practise by taking IOQM problems you have already solved and writing them up as if for a stranger. Then ask a teacher, a senior student or a parent to find the first line they would question.

A study plan

If your child qualified for RMO 2026: seven weeks

• Weeks 1 and 2One area a week. Three problems, each written up in full, each read by someone else.
• Weeks 3 to 5One past RMO problem a day: 45 minutes to solve, then a clean write-up. Keep the mistakes notebook.
• Week 6Two full past papers, three hours each, at 1 pm on a Sunday, the real time of day.
• Week 7Nothing new. Re-read the notebook and your best write-ups. Sleep well.

For next year: a steady year

Two or three hard problems a week from the start of Class 9 or 10, one full write-up a week, and HBCSE’s past papers from about four months before the date. Keep IOQM practice going too: without IOQM there is no RMO.

RMO preparation books

These are from HBCSE’s own list of olympiad books. (source: HBCSE)

• Problem Primer for the Olympiads

  C R Pranesachar, B J Venkatachala and C S Yogananda

  Short chapters by area, with problems at RMO level. A good first book.

• Challenge and Thrill of Pre-College Mathematics

  V Krishnamurthy, C R Pranesachar, K N Ranganathan and B J Venkatachala

  Covers the whole syllabus, area by area, with worked examples.

• An Excursion in Mathematics

  edited by M R Modak, S A Katre, V V Acharya and V M Sholapurkar

  Wide and friendly, with a long reading list at the back.

• Problem-Solving Strategies

  Arthur Engel

  Organised by method (invariants, extremes, pigeonhole). Harder; best once the basics are secure.

• Mathematical Circles

  Fomin and others

  Russian maths-circle problems. Excellent for younger students moving towards proofs.

Past RMO papers with solutions are free on HBCSE’s past papers page, and they are worth more than any book in the last month.

How Kiwimath’s proof study cards work

Level 6 is Kiwimath’s RMO level, with topics in algebra, combinatorics, combinatorial geometry, geometry and number theory. Proof problems there are study cards, not quizzes. The card shows the problem and asks your child to try it on paper first. When they are ready, the full solution opens one step at a time, so they can stop at the step they missed and try again from there.

There is no score on a proof card. A machine cannot mark a written proof fairly, so we do not pretend to; the check is your child’s own write-up against the steps.

From RMO to INMO

To be considered, a student must score above zero. Then, in each region, the top 30 from Class 8 to 11, 5 more girls from that group, and the top 6 from Class 12 go through to INMO, on Sunday 17 January 2027. Ties are broken by IOQM scores. (source: HBCSE) INMO preparation.