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Hey fellow problem-solvers.... Good evening here... I would like you to give an advice especially in problem-solving... I am somehow troubled solving problems here in Brilliant... How much should I study the subject matter to solve (if not all) but most of the problems here? Cite also good references... Thank you!

Note by John Ashley Capellan
3 years, 3 months ago

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Hey John! I'm here to give you some tips about problem solving. While my levels are decent, I make lots of mistakes which makes them lower than they should be. Anyways, that's a topic for a different discussion. Nonetheless, I do have a couple of aces up my sleeve that I can share with you. For Brilliant problems, you will need to know most of the standard curriculum, and a couple of tricks (mostly in Geometry and Number Theory). To learn these, I would suggest Art of Problem Solving. The name says it all. I wouldn't worry too much about getting really into topics, though (after all, I'm in Algebra 1, but I still solve Olympiad-level problems). Of course, it's always good to know as much as possible. As for individual problems, you will need to follow these steps:

  • Read the problem multiple times It's better to spend 30 extra seconds figuring out what you're solving than to spend 30 minutes solving the wrong problem and missing it.

  • Choose a battle plan and stick to it Whenever you first approach a problem, think through exactly how you're going to solve it. Then, use that method AND DON'T SWITCH METHODS. This is a huge waste of time, unless the method you've chosen is really horrible. That's why you have to think it through.

  • Do whatever you have to do to solve it If it's an equation, solve it. If it's anything, just solve, count, measure, or do what you have to do to figure it out. This step should take the least amount of time.

  • Check your work It shouldn't take long, just see if there's any fault in your calculations, or if you've overcounted, or done anything wrong.

If you stick to these steps, you should be golden. Don't be like me and skip the last step! Note that these rules do not apply to speed problems and tests (most of the time). Finn Hulse · 3 years, 3 months ago

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@Finn Hulse Some awesome tips. Sharky Kesa · 3 years, 3 months ago

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@Sharky Kesa Thanks! Hey, I mean, you're the Level 5 Algebra guy, so I shouldn't really be talking. Do you have any of your own tips? Finn Hulse · 3 years, 3 months ago

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@Finn Hulse Yeah, a couple.

  1. Work from the roots of math. Basically, before trying any hard problems, get your basics stronger. This helps you a lot when solving problems.

  2. When learning a new technique, dedicate a couple of hours to it so you can solve it with as less error as possible.

  3. Always revise on all your techniques so you never forget them.

  4. Look at Finn's tips.

Sharky Kesa · 3 years, 3 months ago

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@Sharky Kesa Hahaha yeah. Finn Hulse · 3 years, 3 months ago

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@Sharky Kesa In my opinion when you learn a new technique/ formula try to learn how that formula was derived so that even if you can't recall the formula during the tests you can use the previous step of deriving the formula Ashtik Mahapatra · 3 years, 3 months ago

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@Ashtik Mahapatra I agree. Finn Hulse · 3 years, 3 months ago

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@Finn Hulse Nice easy tips! :) One tip I have for geometry- 1. Try to remember any useful result or beautiful result you discover or prove while solving a problem as a theorem. This is sometimes very helpful, very. Sagnik Saha · 3 years, 3 months ago

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@Finn Hulse Really awesome. Finn, do u plan to be a teacher in the future? Ashtik Mahapatra · 3 years, 3 months ago

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@Ashtik Mahapatra It's funny that you ask that. Yes, I plan on being an applied mathematics teacher. But also, I'm starting a pre-MATHCOUNTS training program for bright 5th-graders! It's awesome. :D Finn Hulse · 3 years, 3 months ago

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@Finn Hulse Wow 5th graders will get an awesome teacher. Won't they? Ashtik Mahapatra · 3 years, 3 months ago

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@Ashtik Mahapatra Yeah I guess! :D Finn Hulse · 3 years, 3 months ago

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@Finn Hulse Have u seen my levels? Plz see. None of you should really be talking Ashtik Mahapatra · 3 years, 3 months ago

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@Ashtik Mahapatra Wait are you saying Sharky and I are stupid? Finn Hulse · 3 years, 3 months ago

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@Finn Hulse No you are not stupid at all. I think you both are awesome. Since u we're talking about levels I told you to see mine. Ashtik Mahapatra · 3 years, 3 months ago

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@Ashtik Mahapatra Oh. Well they are rather awesome! :D Finn Hulse · 3 years, 3 months ago

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@Finn Hulse Thanks Ashtik Mahapatra · 3 years, 3 months ago

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I think the best approach to participating is to solve the problems to the best of your ability. If you can research online about a topic before you answer, do. You can read about similar problems elsewhere and figure out solutions. However, there is a fine border-line between cheating and learning. It is best to find your true abilities and if you get something wrong, discuss with others to see what you did wrong. It is a good way to learn. Hatim Zaghloul · 3 years, 3 months ago

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Thank you people! John Ashley Capellan · 3 years, 3 months ago

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A favorite book of mine and an old classic on strategies and tips on solving math problem is this Venture Hi · 3 years, 3 months ago

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In addition to the responses here, I have seen that noticing patterns by literally writing long tables down has helped me learn (and solve problems using) many new techniques/approaches that I would have otherwise just mindlessly memorized after reading about it somewhere. Milly Choochoo · 3 years, 3 months ago

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