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Moving from IOQM to RMO and INMO changes what you hand in. IOQM wants a two-digit number. RMO and INMO want a written argument that a stranger can check line by line. Many strong problem solvers lose marks here, not because they cannot solve the problem, but because their write-up leaves gaps. This post explains what the official rules say about marking and how to write a solution that holds up.
How are INMO answers marked?
The HBCSE Mathematical Olympiad 2026-2027 page lists RMO as 3 hours with six questions and INMO as 4.5 hours with six questions, and says each question "requires writing detailed proof". The INMO 2026 paper gives the key instructions: all questions carry equal marks, the maximum is 102, each answer starts on a new page, and "No marks will be awarded for stating an answer without justification." Six equal questions out of 102 means 17 marks per question. HBCSE does not publish its detailed marking scheme on these pages, so do not assume a fixed partial-credit rule.
At the International Mathematical Olympiad, the IMO General Regulations say each contestant receives an integer score out of 7 for each problem, and that solutions are assessed by team leaders and, independently, by coordinators "in accordance with the marking schemes approved by the Jury". Leaders and coordinators then try to agree each score, and disagreements go to the problem captain, then the Chief Coordinator and, if still unresolved, the Jury. The lesson for India's olympiad stages is the same: a grader must be able to follow and verify your argument.
Why is a correct answer not enough?
A proof is a text that someone else reads. Selden and Selden (2003) studied mathematics undergraduates reading arguments that claimed to prove a theorem, and found that they tended to focus on surface features and were very limited at judging whether an argument was a proof. Moore (1994) observed 16 undergraduates learning to write proofs and found three main sources of difficulty: understanding the concepts, mathematical language and notation, and getting started. Weber (2001) found that undergraduates often knew the facts needed for a proof but still failed, because they lacked strategic knowledge about which facts to apply, which doctoral students had.
The practical point: your own reading of your proof is not a reliable check. Build habits that make gaps visible.
Worked example: a weak write-up and a complete one
Problem: prove that n³ − n is divisible by 6 for every integer n.
Weak write-up: "n = 2 gives 6, n = 3 gives 24, n = 4 gives 60. All divisible by 6, so it is true." This checks three cases out of infinitely many. It would score little or nothing.
Complete write-up:
Factorise: n³ − n = (n − 1)n(n + 1), a product of three consecutive integers.
Of any two consecutive integers, one is even, so the product is divisible by 2.
Of any three consecutive integers, exactly one is divisible by 3, so the product is divisible by 3.
Since 2 and 3 have no common factor, the product is divisible by 6. This holds for every integer n, including zero and negatives. ∎
Each line states one fact and why it is true. A reader never has to guess.
What does a complete olympiad solution include?
The official INMO 2024 solutions show the structure well. Problem 2 asks for a maximum: the solution first proves an upper bound, then says "To prove this is achievable" and gives a construction. Problem 1 includes a remark that the figure has two possible configurations and that the angles must be handled so that the argument works in both.
A checklist drawn from these:
State the answer or claim first, in one line.
Cover every case. Odd and even, acute and obtuse, positive and negative.
Prove both directions for "find all" problems, such as INMO 2026 Problem 1, which asks for all positive integers with a property.
Bound and construct for maximum and minimum problems.
Say why each step holds, with the theorem's name where one is used.
Never write "clearly" for a step you have not checked.
A short example of case coverage
Find all integers n for which n² + 1 is divisible by 3. Every integer leaves remainder 0, 1 or 2 when divided by 3. If the remainder is 0, n² + 1 leaves remainder 1. If it is 1 or 2, n² leaves remainder 1, so n² + 1 leaves remainder 2. No case gives 0, so there are no such integers. Three cases, all covered: that is a proof.
A weekly proof-writing routine
Pick one RMO or INMO problem from the HBCSE past papers page and give it at least 45 minutes.
Write a full solution as if for a grader, on a fresh page.
Put it away for a day, then read it as a stranger would. Mark every line where you had to fill in a reason.
Compare with the official solution. Note any case or direction you missed.
Swap write-ups with a friend and mark each other's work, out of 7, before discussing.
For the stages before INMO, our guide to the maths olympiad in India covers IOQM and RMO, and our post on Polya's How to Solve It helps with getting started.
When you are stuck on the first move rather than the write-up, Fermi's AI tutor can work out what you already know and build a plan for the session, and checks understanding as it goes.
Next step: write a complete proof that the product of any four consecutive integers is divisible by 24, then check it against the checklist above.
