r/MathOlympiad • u/Every_Drag8012 • 2d ago

IMO Help on improving

Im currently trying to get better at math specifically Olympiad math and i struggles so muchh esp on proving and the first step to start solving. I just started so any advice or help would be very much appreciated.

6 Upvotes

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u/Old_Answer8047 2d ago

Hire a tutor bruh or else it's not s piece of cake

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u/Every_Drag8012 2d ago

I wish.i dont think my country has one ,olympiad math is pretty much a new concept here i think

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u/Old_Answer8047 2d ago

ig Online thingy exists in your nation

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u/Diligent__4339 2d ago edited 2d ago

Well, you need to try very hard, even when it's very very hard also you need to put in the hours, also there are sites like The art of problem solving and grate professors online, it will help a lot, also if you make it on your own to a certain level let's say nationals, hopefully the state will help with free amazing theachers, don't give up, the best of faith to you

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u/Every_Drag8012 2d ago

Thank you 🙏 i actually got up to nationals by myself this year but i didnt make it into the top 4

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u/Diligent__4339 2d ago

Wow, in what county? And sorry for asking but if you are so good why you are you asking these questions?

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u/Every_Drag8012 2d ago

Cambodia! And no im not so good as i remember the national test was mostly answer based problems and i dont think anyone could get a full score so they choose student that get the highest score. and i asked because i tried to solve imo problem and i couldnt even form a sentence of proofs like i dont know how to prove that only this condition work

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u/Diligent__4339 2d ago

A, intrising, well best of luck!

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u/Sea_Platform_7049 2d ago

u definitely don’t need a tutor bro. i’m coming from a similar situation as u but i just self studied. i think the hardest part is learning how to like sit there n actually work on a problem for a super long time; its rly different from school maths. but honestly, what worked best for me is just to try a real example as the first step for every question, like for a combo game id do a dry run or a nt problem id try it on a real number. personally it just helps like understand the mechanics n find patterns easier.

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u/matham_combageom 1d ago

Proving problems is a separate skill from computing, and it trains separately. The single most useful habit: before trying anything, write down (a) exactly what is given, (b) exactly what must be shown, and (c) one line for each object in the problem. Most stuck moments are a missing definition, not a missing idea.

Then build a small toolkit and drill it on purpose: pigeonhole, parity and modular arithmetic, induction (ordinary and strong), AM-GM and Cauchy-Schwarz, telescoping, double counting, and the extremal principle (pick the largest or smallest object and see what the definition forces). When you read a solution, write down which tool it used and file the problem under that tool, not under its topic. After a few dozen problems you start recognising the situation instead of the subject.

For the first step specifically: try small cases by hand, look for an invariant or a quantity that always decreases, and check what happens in the extreme case. If nothing comes, prove the contrapositive, or assume the conclusion fails and derive a contradiction.

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u/Every_Drag8012 23h ago

Thank youuu