I got a perfect score (102/102) in the Karnataka RMO as a 11th grader, and qualified for INMO in 10th grade the year before that, so I might be of some help.
What I've learnt along the way is this:
1. Don't ever be intimidated by the problems. You get scared, you lose. I learnt this the hard way in INMO - I couldn't solve problems in the test that I would have easily solved at home. Dealing with pressure and expectations is difficult, but don't let it get to you during the test.
2. Read the Art of Problem Solving Part 1. Many of the strategies there are extremely useful; there's a reason it's so popular. Wishful thinking and 'keeping your eye on the ball' are two of my favorites.
3. Every RMO problem is killed by one key observation/ fact. Get this, and you're pretty much done. Examples are, a certain quadrilateral is cyclic, this expression is a perfect square, and so on. Not very difficult to see, but not obvious either.
4. You only need to solve 3-4 problems out of 6 to qualify. Make significant progress in one problem and you'll get more marks than had you spent trying all of the 6 problems. From what I've seen, you get either 0,1,2 or 6,7,8 or 15,16,17 marks based on your progress. This makes it crucial to focus on the problems you know you can solve.
5. Geometry is important, there are generally 2 questions every year. It's pretty fun too. Don't be afraid to bash (try big computations) if you have the time. Some questions require patience. A lot of it.
6. Inequalities are dead at the IMO level (almost) because of calculus based techniques like the tangent line method, uvw, pqr, Langrange multipliers, and so on. But, you will never need to know any of these for RMO. Stick to your basics, such as the Power Mean, Cauchy Schwartz and Chebyshev inequalities. I guarantee you that these will be enough for now. Recently however, there are fewer inequalities being asked in the RMO.
7. Number theory is useful. Always look out for an application of Fermat's little theorem or some other congruence if asked to solve an equation in natural numbers.
That's all I have, feel free to ask any questions.
–
Ameya Daigavane
·
1 year, 3 months ago

Log in to reply

@Ameya Daigavane
–
hello, i am abhishek .i want to ask u that is the brilliant rmo wiki is enough to get qualified for krmo
i am in 10 th standard
–
Abhishek Alva
·
9 months, 4 weeks ago

@Ameya Daigavane
–
is "Art of Problem Solving" that you mentioned about in point 2, a book?
i didnt understant point 3.
Thanks! I am in 10th class now, i appeared for Delhi RMO last year after clearing PreRMO, and got severly dumped.
–
Yash Mehan
·
1 month ago

@Ameya Daigavane Can you share something about 'Wishful Thinking' and 'Keep your eye on the ball' here? We would love to learn those techniques from you. \[\huge\ddot\smile\]
–
Swapnil Das
·
1 year, 3 months ago

Log in to reply

@Swapnil Das
–
Sorry for the late reply, I've been off Brilliant lately.
'Wishful Thinking' comes down to, "If this situation was simpler, how could I solve the problem?" and then looking at characteristics that could simplify the problem greatly.
An example would be - if \( ABCD \) were a cyclic quadrilateral, then I can then invoke Ptolemy's...and I'm done!
And then we try to prove the statement we want to be true.
Note that a lot of times we could go wrong with our wishes, so you should carefully analyze and check a few cases, or draw a few diagrams before diving in.

"Keeping your eye on the ball" is just another way of saying "Don't lose focus of what you're trying to prove".
During a proof, you might find something interesting that may or may not be related to the problem itself. At this point, you need to ask yourself, "Does this property simplify my proof, or shed new light on the problem?"
Otherwise, you risk going off on a tangent, wasting time and effort.
This advice is best for competitions, as you should always try to discover stuff on your own, when you have the time to.
Mathematics is all about the joy of discovery.
–
Ameya Daigavane
·
9 months, 4 weeks ago

Which books do you refer to for preparation and which books should I refer to (as I am much below your intelligence )seeing my present level. Does learning a no. Of theorems useful?Please enlighten me 😆
–
Ambuj Shrivastava
·
1 year, 3 months ago

Log in to reply

@Ambuj Shrivastava
–
Nah bro, don't underestimate yourself. You have a great potential. You can refer books I recommended in the RMO board. And coming to theorems, I have some tips that you may follow:

Yes, learning of theorems is useful, really useful.

On the other side, don't try to just cram up the theorems without knowing what they mean or deriving them yourself once.

Don't try to learn everything, particularly algebra. Many algebraic theorems are easily derivable. Learn some geometrical ones so that the solution to a given question seems somewhat 'obvious' to you.

These are some points I could gather from my own experience. I hope you find this useful :)
–
Swapnil Das
·
1 year, 3 months ago

Log in to reply

@Swapnil Das
–
Thank you for your invaluable tips and by R.M.O. board you mean the one which you created earlier right and can you please suggest the important topics as this would be my last chance(I would be in class 11 after completion of my ICSE boards next week)so I have minimal time.
–
Ambuj Shrivastava
·
1 year, 3 months ago

Important topics to study for RMO, you need that, right? Let me gather some for you in the comment.

Do study Algebra and Geometry carefully. After you finish up, study combinatorics with some stress on proof based problems.

For Algebra, study Theory of Equations and Inequalities. Don't give much stress on the latter, as it is becoming non-existent nowadays.

Study about Circles and Triangles in Geometry, and learn lot of theorems about the same. Work more on construction problems.

I would not encourage you to learn Number Theory now, as it is your last shot for RMO. It is an entirely new topic, and studying the same would be highly time consuming.

Make questions of your own, and try posting them here as a note or to any of us privately. This would help you get you work verified.

Take time, 2 months for each topic. Have patience while solving problems, though they may look tedious at the first sight. I had spent 6 hours for a single geometry problem, and at last got that right!

@Swapnil Das
–
Hey I am slightly weak at geometry which books would u suggest and would u have any tips for me @Swapnil Das
–
Sahil Rane
·
2 weeks, 2 days ago

I remember one guy telling me that he wanted to be like Albert Einstein. He wanted to learn calculus before the age of 15 (just like Einstein). I don't know what has happened to that guy.
–
Aditya Kumar
·
1 year, 4 months ago

Log in to reply

@Aditya Kumar
–
See, knowledge has no value if it is not executed properly.
–
Swapnil Das
·
1 year, 4 months ago

I am in class 9. I want to participate in RMO this year.as I don't know anything about combinatorics,functional equations and higher algebra please suggest me some books and ways to prepare.please suggest those books that can help me.understand the topic as I am a beginner.
–
Suvansh Sharma
·
4 months ago

@Swapnil Das
–
sorry for another question, but how much time (days/months) should i give to each topic? i also have david m burton elementary number theory
–
Shubhang Dadhich
·
5 months, 1 week ago

@Swapnil Das
–
thank you , i basically study on my own . are you sure only these 2 books will help? are there OTHERS?
–
Shubhang Dadhich
·
5 months, 1 week ago

@Ameya Daigavane- I am Alapan. I am giving RMO this year (class 10) and I am pretty confused about geometry. I feel I am not good at it. Please help.
–
Alapan Chaudhuri
·
9 months, 2 weeks ago

Log in to reply

Shall we create a RMO board similar to the one last year? I found it very helpful.
–
Svatejas Shivakumar
·
9 months, 3 weeks ago

RMO is coming near!9th sept!put full effort as much as you can guys!best of luck!There is a sample paper available at rmomath.mah have a look at it!
–
Yash Joshi
·
9 months, 3 weeks ago

@Ambuj Shrivastava
–
Well!I have many questions on induction presently!please convey of which topic u want!one such simple question is prove that 3^(n+2) does not divide 2^3^n+1 for any positive integer n!(hint use a lemma for 3^(n+1))☺
–
Yash Joshi
·
10 months, 2 weeks ago

Log in to reply

@Yash Joshi
–
If p is a prime and p^k/a^n,then p /a.
3^(n+2) does not divide 2^3^n+1 , since 3 does not divide 2.
–
Aditya Das
·
1 month ago

## Comments

Sort by:

TopNewestI got a perfect score (102/102) in the Karnataka RMO as a 11th grader, and qualified for INMO in 10th grade the year before that, so I might be of some help.

What I've learnt along the way is this:

1. Don't ever be intimidated by the problems. You get scared, you lose. I learnt this the hard way in INMO - I couldn't solve problems in the test that I would have easily solved at home. Dealing with pressure and expectations is difficult, but don't let it get to you during the test.

2. Read the Art of Problem Solving Part 1. Many of the strategies there are extremely useful; there's a reason it's so popular. Wishful thinking and 'keeping your eye on the ball' are two of my favorites.

3. Every RMO problem is killed by one key observation/ fact. Get this, and you're pretty much done. Examples are, a certain quadrilateral is cyclic, this expression is a perfect square, and so on. Not very difficult to see, but not obvious either.

4. You only need to solve 3-4 problems out of 6 to qualify. Make significant progress in one problem and you'll get more marks than had you spent trying all of the 6 problems. From what I've seen, you get either 0,1,2 or 6,7,8 or 15,16,17 marks based on your progress. This makes it crucial to focus on the problems you know you can solve.

5. Geometry is important, there are generally 2 questions every year. It's pretty fun too. Don't be afraid to bash (try big computations) if you have the time. Some questions require patience. A lot of it.

6. Inequalities are dead at the IMO level (almost) because of calculus based techniques like the tangent line method, uvw, pqr, Langrange multipliers, and so on. But, you will never need to know any of these for RMO. Stick to your basics, such as the Power Mean, Cauchy Schwartz and Chebyshev inequalities. I guarantee you that these will be enough for now. Recently however, there are fewer inequalities being asked in the RMO.

7. Number theory is useful. Always look out for an application of Fermat's little theorem or some other congruence if asked to solve an equation in natural numbers.

That's all I have, feel free to ask any questions. – Ameya Daigavane · 1 year, 3 months ago

Log in to reply

– Abhishek Alva · 9 months, 4 weeks ago

hello, i am abhishek .i want to ask u that is the brilliant rmo wiki is enough to get qualified for krmo i am in 10 th standardLog in to reply

– Ameya Daigavane · 9 months, 4 weeks ago

It's all about how much you practice, not the topics you learn.Log in to reply

– Swapnil Das · 9 months, 4 weeks ago

No, as per my opinion.Log in to reply

@Swapnil Das @Ameya Daigavane – Sahil Rane · 2 weeks, 2 days ago

Hey would u have any tips for pre-rmo?Log in to reply

– Yash Mehan · 1 month ago

is "Art of Problem Solving" that you mentioned about in point 2, a book? i didnt understant point 3. Thanks! I am in 10th class now, i appeared for Delhi RMO last year after clearing PreRMO, and got severly dumped.Log in to reply

– Upamanyu Mukharji · 3 weeks, 4 days ago

Art of Problem Solving Volume 1 It's a good book!Log in to reply

– Swapnil Das · 1 year, 3 months ago

Excellent tips! Thank you!Log in to reply

– Ambuj Shrivastava · 1 year, 3 months ago

Great Tips!Log in to reply

@Ameya Daigavane Can you share something about 'Wishful Thinking' and 'Keep your eye on the ball' here? We would love to learn those techniques from you. \[\huge\ddot\smile\] – Swapnil Das · 1 year, 3 months ago

Log in to reply

'Wishful Thinking' comes down to, "If this situation was simpler, how could I solve the problem?" and then looking at characteristics that could simplify the problem greatly. An example would be - if \( ABCD \) were a cyclic quadrilateral, then I can then invoke Ptolemy's...and I'm done!

And then we try to prove the statement we want to be true.

Note that a lot of times we could go wrong with our wishes, so you should carefully analyze and check a few cases, or draw a few diagrams before diving in.

"Keeping your eye on the ball" is just another way of saying "Don't lose focus of what you're trying to prove".

During a proof, you might find something interesting that may or may not be related to the problem itself. At this point, you need to ask yourself, "Does this property simplify my proof, or shed new light on the problem?"

Otherwise, you risk going off on a tangent, wasting time and effort.

This advice is best for competitions, as you should always try to discover stuff on your own, when you have the time to.

Mathematics is all about the joy of discovery. – Ameya Daigavane · 9 months, 4 weeks ago

Log in to reply

Nicely written! Thanks! – Harsh Shrivastava · 1 year, 4 months ago

Log in to reply

– Swapnil Das · 1 year, 4 months ago

You are most welcome!Log in to reply

Nicely written and an inspirational note ! Nice job... – Chinmay Sangawadekar · 1 year, 3 months ago

Log in to reply

– Swapnil Das · 1 year, 3 months ago

Thank you very much :)Log in to reply

Which books do you refer to for preparation and which books should I refer to (as I am much below your intelligence )seeing my present level. Does learning a no. Of theorems useful?Please enlighten me 😆 – Ambuj Shrivastava · 1 year, 3 months ago

Log in to reply

Yes, learning of theorems is useful, really useful.

On the other side, don't try to just cram up the theorems without knowing what they mean or deriving them yourself once.

Don't try to learn everything, particularly algebra. Many algebraic theorems are easily derivable. Learn some geometrical ones so that the solution to a given question seems somewhat 'obvious' to you.

These are some points I could gather from my own experience. I hope you find this useful :) – Swapnil Das · 1 year, 3 months ago

Log in to reply

– Ambuj Shrivastava · 1 year, 3 months ago

Thank you for your invaluable tips and by R.M.O. board you mean the one which you created earlier right and can you please suggest the important topics as this would be my last chance(I would be in class 11 after completion of my ICSE boards next week)so I have minimal time.Log in to reply

Important topics to study for RMO, you need that, right? Let me gather some for you in the comment.

Do study Algebra and Geometry carefully. After you finish up, study combinatorics with some stress on proof based problems.

For Algebra, study

Theory of EquationsandInequalities. Don't give much stress on the latter, as it is becoming non-existent nowadays.Study about

CirclesandTrianglesin Geometry, and learn lot of theorems about the same. Work more on construction problems.I would not encourage you to learn Number Theory now, as it is your last shot for RMO. It is an entirely new topic, and studying the same would be highly time consuming.

Make questions of your own, and try posting them here as a note or to any of us privately. This would help you get you work verified.

Take time, 2 months for each topic. Have patience while solving problems, though they may look tedious at the first sight. I had spent 6 hours for a single geometry problem, and at last got that right!

Log in to reply

@Swapnil Das – Sahil Rane · 2 weeks, 2 days ago

Hey I am slightly weak at geometry which books would u suggest and would u have any tips for meLog in to reply

– Ambuj Shrivastava · 1 year, 3 months ago

Thank you for your help!you're truly great 😊Log in to reply

– Swapnil Das · 1 year, 3 months ago

Oh no, I am no great. It was a pleasure helping you :)Log in to reply

– Shivam Mishra · 1 year, 3 months ago

amazing tips!!!Log in to reply

– Swapnil Das · 1 year, 3 months ago

Oh Thanks :)Log in to reply

I remember one guy telling me that he wanted to be like Albert Einstein. He wanted to learn calculus before the age of 15 (just like Einstein). I don't know what has happened to that guy. – Aditya Kumar · 1 year, 4 months ago

Log in to reply

– Swapnil Das · 1 year, 4 months ago

See, knowledge has no value if it is not executed properly.Log in to reply

– Swapnil Das · 1 year, 4 months ago

I even don't know what has happened to me :PLog in to reply

I am in class 9. I want to participate in RMO this year.as I don't know anything about combinatorics,functional equations and higher algebra please suggest me some books and ways to prepare.please suggest those books that can help me.understand the topic as I am a beginner. – Suvansh Sharma · 4 months ago

Log in to reply

– Swapnil Das · 4 months ago

See RMO Board created by me.Log in to reply

i have 8 months left for rmo . i have started with number theory . is it correct ? – Shubhang Dadhich · 5 months, 1 week ago

Log in to reply

– Swapnil Das · 5 months, 1 week ago

Sure. Starting way ahead of time helps.Log in to reply

– Shubhang Dadhich · 5 months, 1 week ago

what should be the sequence . and what resources should i use ?Log in to reply

– Swapnil Das · 5 months, 1 week ago

Use Titu Andreescu Books and also Evan Chen notes.Log in to reply

– Shubhang Dadhich · 5 months, 1 week ago

sorry for another question, but how much time (days/months) should i give to each topic? i also have david m burton elementary number theoryLog in to reply

– Swapnil Das · 5 months, 1 week ago

2-3 hours everyday. Any topic you like.Log in to reply

– Shubhang Dadhich · 5 months, 1 week ago

thank you , i basically study on my own . are you sure only these 2 books will help? are there OTHERS?Log in to reply

– Swapnil Das · 5 months, 1 week ago

search rmo board created by me. i and others have cited some.Log in to reply

@Ameya Daigavane- I am Alapan. I am giving RMO this year (class 10) and I am pretty confused about geometry. I feel I am not good at it. Please help. – Alapan Chaudhuri · 9 months, 2 weeks ago

Log in to reply

Shall we create a RMO board similar to the one last year? I found it very helpful. – Svatejas Shivakumar · 9 months, 3 weeks ago

Log in to reply

here – Svatejas Shivakumar · 9 months, 3 weeks ago

Done :) ClickLog in to reply

– Harsh Shrivastava · 9 months, 3 weeks ago

Sure! Create a board!Log in to reply

RMO is coming near!9th sept!put full effort as much as you can guys!best of luck!There is a sample paper available at rmomath.mah have a look at it! – Yash Joshi · 9 months, 3 weeks ago

Log in to reply

– Svatejas Shivakumar · 9 months, 3 weeks ago

Thanks for mentioning.Log in to reply

Thanks you very much for creating this very helpful note. – Svatejas Shivakumar · 1 year, 3 months ago

Log in to reply

– Swapnil Das · 1 year, 3 months ago

Oh, my pleasure :)Log in to reply

You have done a Very courageous work! Hats off to you ..

SWAPNIL BROTHER– Atanu Ghosh · 1 year, 3 months agoLog in to reply

– Swapnil Das · 1 year, 3 months ago

Thank you brother!Log in to reply

Thnks – Gaurav Anand · 1 year, 4 months ago

Log in to reply

– Swapnil Das · 1 year, 4 months ago

You are welcome :)Log in to reply

@Swapnil Das How can one improve their Geometry problem solving skills....it takes A LOT of creative thinking! – Upamanyu Mukharji · 1 year, 3 months ago

Log in to reply

– Swapnil Das · 1 year, 3 months ago

True, you have to practice a lot.Log in to reply

– Upamanyu Mukharji · 1 year, 3 months ago

Is there any good book which one may use... Thanks in advance!Log in to reply

Log in to reply

– Ambuj Shrivastava · 1 year, 3 months ago

can you please suggest me some good questions on inductionLog in to reply

– Yash Joshi · 10 months, 2 weeks ago

Well!I have many questions on induction presently!please convey of which topic u want!one such simple question is prove that 3^(n+2) does not divide 2^3^n+1 for any positive integer n!(hint use a lemma for 3^(n+1))☺Log in to reply

– Aditya Das · 1 month ago

If p is a prime and p^k/a^n,then p /a. 3^(n+2) does not divide 2^3^n+1 , since 3 does not divide 2.Log in to reply