## How to write a solution

For honorable Teachers and Parents
nayel
Posts:268
Joined:Tue Dec 07, 2010 7:38 pm
Location:Dhaka, Bangladesh or Cambridge, UK
How to write a solution
Writing good solutions requires skills. Your solution is meaningless if you are the only one who understands it. The point of writing a solution is to let other people read it and understand why your solution works. If you want to improve your proof-writing skills, there is no better way than to practice. One way to do it is to write your solutions neatly and post them as you solve problems in this forum.

Some things to bear in mind while writing up your solution:
1. There can be no logical gaps: every step has to be justified.
2. There is no such thing as obvious/trivial. Try to avoid these words as much as possible.
3. Try to arrange the different steps of your solution in a sequential manner so that it is clear which step comes after which.
4. Label Lemmas/Theorems/Propositions/Claims. This is a good way of making a solution look less messy.
5. Discuss different cases separately and clearly.
6. Do write some words. A solution isn't just a combination of numbers and symbols.
7. Don't write useless/unnecessary things. This can confuse the reader and she might get angry at you!

I will keep adding new ideas if something pops up in my mind.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein

divyas
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Joined:Fri Aug 19, 2011 10:20 am

### Re: How to write a solution

yes ofcourse, you have said the things which needed, thank for this post

nafistiham
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### Re: How to write a solution

in a solution, which theorems one can mention without a proof ?
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

tanvirab
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Joined:Tue Dec 07, 2010 2:08 am

### Re: How to write a solution

There is now answer to it except that it depends on the context.

Masum
Posts:592
Joined:Tue Dec 07, 2010 1:12 pm

### Re: How to write a solution

Actually there is no rule for determining whether a theorem is trivial or well known. However, there is a line which said "avoid these words as much as possible". Better if you can write the solution. And also we can sometimes easily conclude which theorem needs not be proven. For example, you won't prove Pythagoras's theorem. But the lemmas you describe yourself must be proven, even common lemmas like LTE too I am afraid. So there is no definite answer to your question. That is up to your common sense.
One one thing is neutral in the universe, that is $0$.

sourav das
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### Re: How to write a solution

http://www.artofproblemsolving.com/Reso ... howtowrite

Honestly speaking, this link helps a lot....
You spin my head right round right round,
When you go down, when you go down down......
(-$from$ "$THE$ $UGLY$ $TRUTH$" )

emeryhen121
Posts:17
Joined:Fri Jul 16, 2021 6:04 pm

### Re: How to write a solution

I agree with your point. It is vital that people clearly and rightly understand your solutions/ workings. If you are posting it for the people, it needs to have those components that people are looking for when they need to understand the solutions they couldn't do on their own.
An ideal solution working for a student would include all the points and steps mentioned in the process. Students also greatly help from the written footnotes, which explain the reasoning behind the solution process. It allows them to identify the reason for the specific step taken in the solution. It would also be helpful if alternative logic and answers are provided so that it helps the audience decide which solution they prefer over the options provided and the one they see as easier to understand.

Asif Hossain
Posts:194
Joined:Sat Jan 02, 2021 9:28 pm

### Re: How to write a solution

actually writing solution is a completely different muscle to build aside from problem solving. For this I think the best way is to read other's(experienced) solutions.For example sometimes you have vague idea that solves the problem (especially in combii) but to write it in the language of math it needs effort and skill aside from solving the problem.
Hmm..Hammer...Treat everything as nail