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What makes others different?

I was shocked by the solutions posted by others.They have a very different approach and they do problems in just few lines.My question is what makes them different.I had noticed that almost every student has a different solution..So I would ask all to share the process by which they solve a question....Like what do they try to find in the question, and and how they think if they r given a problem to solve.Yes I know that in maths practice matters but I believe that besides practice, approach matters and the thinking process.....I lack behind in thinking.I am not able to think that others on Brilliant like Zi Song, Lei Wang, and many others can.So please help me to overcome my weak point.Hope I receive useful answers.Thank You.......

Note by Kiran Patel
4 years ago

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The thinking process can definitely be improved by practice. I asked a similar question on AoPS and they told me the same: practice is key. Of course, there are certain techniques that help you solve problems (telescoping, pigeonhole, induction, etc.) but it is the process of solving many questions that will make you capable of tackling the harder ones. There is not really some particular way to look at a problem, because all problems are different. I suggest you read the other solutions carefully, as those techniques might be helpful for you in future problems. Tim Vermeulen · 4 years ago

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@Tim Vermeulen Hey Tim, recently you added a discussion named as "Stats", now it's nowhere to be found,have you deleted it? Bhargav Das · 4 years ago

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@Bhargav Das It's in the feature requests category. You can also find it by clicking on the side tab on the main page. Peter Taylor Staff · 4 years ago

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I'd say just practice, as others have said, and think through problems one step at a time. Sometimes, problems seem daunting because they look complicated at first glance but really aren't. Try outlining a way of solving the problem which you think might work before trying to work outthe details. The more you do that, the better you'll get at seeing the major steps in a solution quickly.

Also, strive to really understand what a problem is asking. If you think about the question for a while, you might realize that it's similar to a problem you've seen before or can be greatly simplified through small assumptions which you can then deal with in cases.

Again, as others have said, practice makes perfect (or at least makes you better)! So keep on solving. Sotiri Komissopoulos · 4 years ago

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I began solving problems around 6 months ago. My experience is that a lot of practice is what allows oneself to improve. The more problems you do, the better your intuition becomes. Along the way you learn new techniques and tricks, either through your own discovery or through reviewing someone else's solution.

I find that one of the best ways to learn new ways to think about problems is to look at the solutions of others to problems that I was either unable to solve or where I used an awkward approach. I'll skim a solution, just enough to give me an idea of a better approach, or some necessary insight, and then I'll create a similar solution of my own to test my own understanding. Martin McFly · 4 years ago

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practice,practice,that will surely help,be passionate about it,have wider perspective.but don't forget that people have different intelligence,u might disagreebut,i am being realistic,intelligence can be a limiting factor Beakal Tiliksew · 4 years ago

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