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My thoughts about solution writing..

In mathematics proofs, we always want to look for the most "elegant" answer. That is, the one that requires the least explanation, as its simplicity leaves the reader awestruck. However, I wonder if this same thing applies to solutions to problems, especially in a community such as this.

Many solutions currently are very concise, and since the majority of people looking at the solutions are those who got the problem right, those are the ones which are voted to the top. However, isn't it true that the solution section should be more for the person who did not get the problem rather than for the person who did?

Personally, I think a little more explanation thought process / approach is completely necessary to have in such solutions. Our current solutions, while very good, do not really help somebody who didn't get the problem in that it doesn't tell them how to approach a similar problem in the future. Most of the time, the reader has a reaction of "oh, so that's how you did it" but has no idea about the motivation behind the thought process. So, while they understand why the answer is what it is, they wouldn't know how to solve a similar problem if they were given one. I think that this is one of the biggest and only problems of our solutions currently and can be remedied by just adding in a few notes about motivation.

Note by Michael Tong
3 years, 11 months ago

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Judging by the number of upvotes, I'd say a lot of people agree.

You're absolutely right. I also believe solutions should be more conversational; they should include 'why I did that there', 'how I got stuck at this point', 'how my first approach was a dead end' and things like that.

I also believe being conversational doesn't make the elegance of a solution go away. Coming up with a wonderful way to solve a problem and telling people how you came up with it makes it even better according to me.

To sum it all up, I don't think solutions on Brilliant should be like solutions you write in exams. "All problems on Brilliant strive to be interesting and better than your common math problem". Why shouldn't the solutions be the same?

Mursalin Habib - 3 years, 11 months ago

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I echo this sentiment, by asking Legendary solution writers to "Include motivation" and "Generalize the problem". There are a lot of gains to be achieved from having the solution discussions be an actual discussion, as opposed to a monologue.
You can shape the conversations that happen. Awarding up votes to similar solutions that you admire, and encouraging such solutions by stating your appreciation, are very encouraging to these solution writers. Feel free to ask "Can you explain ...?", to understand how someone else thinks. I look forward to seeing the community grow forward from here.

Shout outs to Anqi for numerous solutions this week that seek to explain the motivations and ideas behind the problems. It takes time to perfect this skill, and I congratulate you for taking the first step.

Calvin Lin Staff - 3 years, 11 months ago

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Dare I put a alternate view forward here? Putting lots of motivation and background thinking in is all very well, but there is a danger that too much effort is spent on the explanation why something was done, and not enough on the actual details of the doing.

Mathematics is a precision subject, and proofs need to be precise. I think that solutions would be improved, and would certainly read better, if they came in two parts. The first should be the neatly expressed proof, which should aim for clarity of expression. Then there could be an opportunity for a paragraph explaining why various stages were done, if that were felt necessary. The best of both worlds - writing accurate and clear solutions, and explaining thought processes - could be encouraged, without mixing the two together.

Mark Hennings - 3 years, 11 months ago

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@Mark Hennings Agreed. This is why motivation and generalization is listed as a legendary guideline, since there are other more important aspects to focus on. It is much better to explain clearly and precisely, than to explain a general case badly.

Solution writing is an art. There is no hard and fast rule as to how to combine these different parts, and it comes with experience. For example, if there is a bunch of algebra to slog through, I often want the motivation/ideas first.

Calvin Lin Staff - 3 years, 11 months ago

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i think that the brilliant masters should provide solutions atleast to those questions to which no elegant solutions have been provided

Space Sizzlers - 3 years, 11 months ago

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The double negative in your last paragraph confuses me. Do you think solutions on Brilliant should or should not be like solutions you write in exams?

Tim Vermeulen - 3 years, 11 months ago

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Certainly they can't be like them since paper checkers in our country require a solution to be as they want, just as per how they taught without seeing the thought process involved. My experience with Brilliant clearly distinguishes a person scoring 98/99/100 in exam from the ones scoring around 80-90 and still understanding the funda & principles involved......

Nishant Sharma - 3 years, 11 months ago

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About that...that was a typo. Oops!

Mursalin Habib - 3 years, 11 months ago

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