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Tips to qualify RMO

Hi guys!

It has been a long time since I posted the RMO board. Some of us qualified RMO, but many of us disqualified. Oh yeah, it's a bitter truth. Even I lost first of the only three chances I will get in my life. And why did we disqualify? Just because of our preparation. Maybe you are shocked, but I'm not.

We do math, all day long, spend even sometimes five to six hours on Brilliant.So where do cracks lie? As per my experiences, the answer is preparation. Yup, I said that once again, just so put emphasis on the fact that we just studying whatever looks good, rather than what is good for us, currently.

We people read Calculus, and I find many junior geniuses on Brilliant posting problems on it. We have a very common misconception, that learning Calculus early is a symbol of genius. No, that's not true. Even one of the Calculus masters of Brilliant, Ishan Dasgupta said,"It is important how well you learn it, rather than how early you learn it." True fact.

So, what's next? If you have chances left, then do try to follow the following list of habits which I have gathered from others experience in order to excel in RMO:

  • First, what to read? Decide that. I am personally weak at Number Theory, so I have thought to leave it for RMO. That is nothing bad, since the Jack of all trades is the master of none . Prepare other sections well, you can qualify RMO easily. If you feel that you can cover all subjects, that's great!

  • Do study basic olympiad mathematics first. Don't get allured by Calculus and Linear Algebra. Why? Mathematical Olympiads like RMO focus on conceptual understanding, rather than the number of concepts you know.

  • Enjoy mathematics, and do it on a regular basis. All of us do, so nothing to worry about this.

  • Don't get discouraged for your speed. Speed has almost nothing to do in mathematics. I don't say it, but the one who said was none other than Terry Tao. I just read an interview of his in the New York Times.

  • Prove it! Don't apply useless logic, like it is a multiple of three of seven, and seems to be correct. Neither plug good values for it. Prove it, because that's what makes you a good mathematician.

Ooh, Lots of points. Think about it, and comment down. Feel free to post critical comments, even I commit mistakes. I wish you qualify RMO this year, and make all of us proud.

                         Best of luck!

Swapnil Das

Note by Swapnil Das
6 months, 1 week ago

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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 · 6 months, 1 week ago

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@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 · 3 days, 8 hours ago

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@Abhishek Alva It's all about how much you practice, not the topics you learn. Ameya Daigavane · 2 days, 17 hours ago

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@Abhishek Alva No, as per my opinion. Swapnil Das · 2 days, 20 hours ago

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@Ameya Daigavane Excellent tips! Thank you! Swapnil Das · 6 months, 1 week ago

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@Ameya Daigavane Great Tips! Ambuj Shrivastava · 6 months, 1 week ago

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@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 · 6 months ago

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@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 · 2 days, 16 hours ago

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Nicely written! Thanks! Harsh Shrivastava · 6 months, 1 week ago

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@Harsh Shrivastava You are most welcome! Swapnil Das · 6 months, 1 week ago

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Nicely written and an inspirational note ! Nice job... Chinmay Sangawadekar · 6 months, 1 week ago

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@Chinmay Sangawadekar Thank you very much :) Swapnil Das · 6 months, 1 week ago

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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 · 6 months, 1 week ago

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@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 · 6 months, 1 week ago

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@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 · 6 months, 1 week ago

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@Ambuj Shrivastava Yes, I meant the one I created long 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 · 6 months, 1 week ago

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@Swapnil Das Thank you for your help!you're truly great 😊 Ambuj Shrivastava · 6 months, 1 week ago

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@Ambuj Shrivastava Oh no, I am no great. It was a pleasure helping you :) Swapnil Das · 6 months, 1 week ago

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@Swapnil Das amazing tips!!! Shivam Mishra · 6 months, 1 week ago

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@Shivam Mishra Oh Thanks :) Swapnil Das · 6 months, 1 week ago

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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 · 6 months, 1 week ago

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@Aditya Kumar See, knowledge has no value if it is not executed properly. Swapnil Das · 6 months, 1 week ago

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@Aditya Kumar I even don't know what has happened to me :P Swapnil Das · 6 months, 1 week ago

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Thanks you very much for creating this very helpful note. Svatejas Shivakumar · 6 months, 1 week ago

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@Svatejas Shivakumar Oh, my pleasure :) Swapnil Das · 6 months ago

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You have done a Very courageous work! Hats off to you .. SWAPNIL BROTHER Atanu Ghosh · 6 months, 1 week ago

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@Atanu Ghosh Thank you brother! Swapnil Das · 6 months, 1 week ago

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Thnks Gaurav Anand · 6 months, 1 week ago

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@Gaurav Anand You are welcome :) Swapnil Das · 6 months, 1 week ago

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@Swapnil Das @Swapnil Das How can one improve their Geometry problem solving skills....it takes A LOT of creative thinking! Upamanyu Mukharji · 5 months, 2 weeks ago

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@Upamanyu Mukharji True, you have to practice a lot. Swapnil Das · 5 months, 2 weeks ago

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@Swapnil Das Is there any good book which one may use... Thanks in advance! Upamanyu Mukharji · 5 months, 2 weeks ago

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@Upamanyu Mukharji

  • Geometry revisited
  • Olympiad notes by Evan Chen
  • Arihant RMO and INMO by Rajeev Manocha
Swapnil Das · 5 months, 2 weeks ago

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@Swapnil Das can you please suggest me some good questions on induction Ambuj Shrivastava · 5 months, 2 weeks ago

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@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 · 2 weeks, 4 days ago

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