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Framing good problems !!

I have tried so hard to frame some good problems,but I just can't seem to overcome this juggernaut in creating them. All,I seem to make are some problems with poor application of concepts and are just some previous ones twisted in sense.While I am absolutely good with solving good problems, I just don't get enough inspiration to frame them.My question to all those good problem framers is simply that 'How do you do it,people ? What do you people refer to? Where do you get inspired from to frame them? What are the prerequisites to frame such problems ?'.It'd be very generous of you to help.

Note by Priyatam Roy
2 years, 6 months ago

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I am not an inspiration around here, my opinions may sound rude and crude, but I'll give my two cents anyway.

I'm with Calvin when he says that you should inspire yourself in problems you like. Don't bother sounding plastic or repetitive, because "imitation is the sincerest form of flattery", and by assimilating the good skills from your idols, you can forge yourself a unique creative personality, a product of all this good mixtures you've selected so far.

The road to making good problems is making as many as you can. Focus on posting a problem a day, and creating three, at least, every single day. Don't be afraid of making a lot of shitty questions. If you think "thoughts arrive like butterflies", you'll plateau on your production; you must force yourself to be creative and be great every single day of your life. That's discipline.

To "exercise the proper technique", rather than focus on "poor application of concepts", you also should study whenever you can. Focus on learning new things, but never forget to review the ones you've seen already, especially the ones that you don't remember quite well, and even more especially the one that you don't like! This may sound counter-intuitive, but not to "go with the flow" is a good way to go your own way.

Steven Johnson says that good ideas flourish better in places where they are shared, combined and discussed, rather than kept in secrecy or overprotected. This is why Brilliant should be a major workplace; you can get mad if people "steal" your ideas sometimes, but you'll grow much more if you absorb our criticism, judge our solutions and appreciate our feedback.

Please write me back.

PS: Sorry for the word "shitty" and for the sexual content on the "Go With The Flow" video. That really might have offended someone. Guilherme Dela Corte · 2 years, 6 months ago

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@Guilherme Dela Corte Sounds good....................but that's not what I meant when I said 'poor application of concepts'.I meant that I always build direct application problems.But,I'll keep in my all your suggestions.Thanks! Priyatam Roy · 2 years, 6 months ago

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Being a good problem solver does not imply that you will be a good problem creator (and vice versa). It takes a lot more understanding to identify what makes a problem good, and in what context to frame the problem.

When first starting out to write a problem, I encourage you to look at problems that you yourself enjoyed, and think about what made those problems great. It could be the way in which you need to interpret the problem, or the method which you ultimately used to solve the problem, or the thought processes that you had while struggling with the problem. Next, modify the problems slightly to keep that aspect that you find interesting, while removing parts of it that you find boring (often, less is more). Over time, as you create your own problems, you will find it easier to frame it so that the problem is immediately interesting.

Note: Of course, not all problems are interesting, or can be made interesting. We still need "plain" problems when first learning how to apply a concept. In those cases, make the question as direct and clear as you can. Calvin Lin Staff · 2 years, 6 months ago

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@Calvin Lin Given that: I have little query that might be slightly impertinent here (but I have no idea where it might be pertinent! I'm virtually new here!) and that is: After posting your problem, when does it get a level to it? Only if it gets popular? Just asking. Aditya Kumar · 2 years, 6 months ago

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@Aditya Kumar The simplest approach would be for you to state the topic and level when you first post it.

I do my best to add levels to (relevant) problems that become really popular. Calvin Lin Staff · 2 years, 6 months ago

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@Calvin Lin But then,what I wanted to know from you is 'How are original problems like those in contests framed ?' Where does the inspiration come from ? Priyatam Roy · 2 years, 6 months ago

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@Priyatam Roy There are many sources of inspiration for creating problems (not just contest problems). Let me list a few:

1) Start from a given technique that you want to test, and create a problem with that as the base idea
This is my favorite kind of problem to set, especially for Level 3/4.

2) Take an existing problem and modify it slightly. Change values, move points, generalize, etc
I like doing this, especially if the original problem is not immediately deducible. See this problem.

3) When working through a solution to a problem, you realize "hm, this fact is interesting ..."
For example, see all of my "Inspired by XXX" problems, which often arise from discussions (and mistakes) in the solutions.

4) Arise out of fields of research.
For contest problems, this often results in extremely technical results which do not have a clear line of approach. Technically, 3 is a subset of this, where your field of research is in working through solutions.

5) Looking at the world around you and asking question.
Especially for physics and computer science. Sometimes combinatorics.

6) Playing around with stuff (much rarer) This is hard to do without some kind of motivation Calvin Lin Staff · 2 years, 6 months ago

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@Calvin Lin Sounds really helpful.I'll keep in mind,all of your worthy suggestions.Thank you,Sir! Priyatam Roy · 2 years, 6 months ago

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Read as much Math as you can & while doing that, always crave for the 'connections' . Always ask the 'what if..' question. Keep note of the good problems that you come across and see if you can generalize anything. Generalizations always give way to abundance of good problems. A good problem framer does not just solve a problem he digs its various parts & plays with them to create a symphony out of them.

These are the points that are crucial. But above all i believe that there's a single line to master anything on the face of Earth:

Keep trying in spite of your failures. Sanjeet Raria · 2 years, 6 months ago

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well , i also started framing problems. i am greatly engrossed in incentre - excentre configuration and i have made two problems on them . check them out problem 1 and problem 2 . my advice to you is that choose one topic in which u are totally engrossed . examine it minutely everything , derive some results , and systematically you would be able to make good quality problems! Nihar Mahajan · 2 years, 6 months ago

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When I post a problem or note I think about how much I can teach to how enjoyable the problem is when it is solved. Whether or not a problem is "good" is rather subjective. Different people appreciate different forms of maths, and no two individuals appreciate maths identically.

In my opinion, a routine problem (or old problem) is a terribly posed problem because it will most likely bore your audience. But hard routine problems might still be important. Classics are still good! To circumvent the posing of a boring problem, I look into the mathematical properties. By incorporating mathematical properties, problem solvers will gain more knowledge and deepen their level of thinking.

For my last words, I enjoy proofs and derivations, so I look into good problems that require derivations to solve. Of course, there are many ways to search for direct solutions on the internet. I hope people still read the derivations though! Steven Zheng · 2 years, 6 months ago

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Do the problems I've recently posted seem challenging to all of you? Priyatam Roy · 2 years, 6 months ago

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Sir @Calvin Lin, @Deepanshu Gupta, @Sreejato Bhattacharya ,Sir @David Mattingly ,Sir @Sanjeet Raria ,@megh choksi , @Sandeep Bhardwaj ,@Sharky Kesa, @Finn Hulse,@Sandeep Mehra,@Aditya Raut,@Krishna Sharma and all others out there.I'm a great fan of your problems.Please help me with my problem. :( Priyatam Roy · 2 years, 6 months ago

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