How do you cope with not being able to solve a problem?

[Ryker]

I was wondering what everyone here does when they can't solve a specific problem, be it one from homework or just one tackled on their own. How do you cope with that? Me, I get totally frustrated and angry, and I really want to change that. Today, for example, I really wanted to do some Physics reading, but when I got home I thought I'll look up some problems the professor posted first and try to solve the one that looked most interesting. Surely enough, I got stuck on it for 3 - 4 hours, banging my head against the wall (metaphorically), and in the end wasn't able to solve it. That completely messed up my day even though I tried telling myself to just move on and deal with other stuff. Still, I just get totally frustrated when I can't do stuff I was supposed to be able to do and it seems that no amount of rational thoughts can overcome my irrationality.

 

[Fizex]

Find someone who can guide you through the problem like a professor or TA, or another student. Then do similar problems and understand it thoroughly on your own. You can't just skip a problem, that is admitting defeat and leaving a big hole in your knowledge about physics. Would you want your doctor to have that kind of philosophy?

 

[Ryker]

Yeah, I think the professor is going to post the solutions in a week or so, after we're done with the chapter (said problem wasn't homework). And I do want to understand the problem, but I guess my question was on a more general level, because a week from now is a long time and I just want to prevent this stuff from completely throwing me off track. Because what pisses me off most is not actually having the problem unsolved, but the fact that I can't do it on my own, without someone showing me how to.

 

[General_Sax]

Welcome to the real world -- you need to learn to seek help when you need it.

 

[twofish-quant]

Surely enough, I got stuck on it for 3 - 4 hours, banging my head against the wall (metaphorically), and in the end wasn't able to solve it.

1) Time allocation. Finish all of the other problems that you can solve first.
2) Do something else and have your subconscious work on it.
3) Find someone else and then if they know the answer have them give you a hint.
4) Find a study group.
5) Finally, get used to not being able to find the answer. In the professional world, it's common to have problems that people spend years if not decades trying to solve.

 

[stevenb]

Welcome to the real world -- you need to learn to seek help when you need it.

In the real world, sometimes your problem is so unique or new, there is no one else to help you.

I'm with the OP on this one. It's very rare for me to give up on a problem that I've been assigned, whether it be back in school or now working in industry. I don't get angry, and I don't feel frustrated, but I do get obsessed with solving the problem. Eventually the answer comes, and the most troublesome problems are solved when I'm sleeping.

 

[G01]

Getting confused on a problem can mess up my whole day if I'm not careful, since I tend to get tunnel vision on these kind of things. Seriously, If I'm confused on a problem, I have trouble keeping up a conversation because my mind just keeps wandering back to it.

It's a pain, but it's something we all deal with. It's ok to get frustrated, but you have to remember not to let that problem take over your life. You really just got to train yourself to have the right kind of outlook on these situations.

In the real world, sometimes your problem is so unique or new, there is no one else to help you..

This is a good point. One of the best reasons to get used to dealing with these situations and handling them correctly is that once you start independent research, you are going to be confused, VERY confused! We all are! There most likely won't be anyone else out there with the answer, either. It's just the nature of the job.

 

[Ryker]

One of the best reasons to get used to dealing with these situations and handling them correctly is that once you start independent research, you are going to be confused, VERY confused! We all are! There most likely won't be anyone else out there with the answer, either. It's just the nature of the job.

That's true, but at least for me these two situations differ a bit in that in the situation I described above you are supposed to be able to solve an exercise, whereas altough you're kind of expected to solve the problem in your example, as well, the expectations aren't really on the same level.

But I'm glad to hear I'm not only whose day gets "ruined" or at least altered by these kind of things. And if I do solve at the end that makes it all better and I don't really care that much about "wasting" so much time, but it's those situations when I'm NOT able to come up with an answer that bother me.

 

[Mark44]

1) Time allocation. Finish all of the other problems that you can solve first.
2) Do something else and have your subconscious work on it.
3) Find someone else and then if they know the answer have them give you a hint.
4) Find a study group.
5) Finally, get used to not being able to find the answer. In the professional world, it's common to have problems that people spend years if not decades trying to solve.

These are all good points, but #2 is an especially good one. It's often better to put in several separate blocks of time on a problem, with a rests in between, rather than trying to solve it all in one go.

 

[Saladsamurai]

1) Time allocation. Finish all of the other problems that you can solve first.
2) Do something else and have your subconscious work on it.
3) Find someone else and then if they know the answer have them give you a hint.
4) Find a study group.
5) Finally, get used to not being able to find the answer. In the professional world, it's common to have problems that people spend years if not decades trying to solve.

These are all good points, but #2 is an especially good one. It's often better to put in several separate blocks of time on a problem, with a rests in between, rather than trying to solve it all in one go.

+1 about the 2nd point. When you start getting into spending 3 hours on a problem, you NEED to stop. This much time on one problem usually means that you have "taken a wrong turn" in your thinking somewhere and you need to "refresh" the thinking process. You are continuously building on some improper assumption or approach somewhere, yet since you are so invested (time wise) that you get tunnel vision and refuse to see your misconceptions.

It's kind of like driving: when I get lost because I took a wrong turn, I should go back and figure out where I made that wrong turn. But often I think that I ca figure out how to get to my destination without going back and instead by following my intuition or sense of direction. Unfortunately, the latter method usually takes 5 or 6 times longer than if I had just gone back and started over!

 

[General_Sax]

In the real world, sometimes your problem is so unique or new, there is no one else to help you.

So, researchers don't collaborate? I mean even in the BP blowout -- a unique problem as far as I know -- I'm sure they had a team working together and helping one another.

 

[Fizex]

... what pisses me off most is not actually having the problem unsolved, but the fact that I can't do it on my own, without someone showing me how to.

That's why I said get help and then solve similar problems. Surely there is another similar problem. You can even get help here if you need it, we usually give hints and not answers.

In the professional world, if the problem can't be solved by others, its you're specialty, but in general professionals have contacts who help them and they help in return.

 

[stevenb]

So, researchers don't collaborate? I mean even in the BP blowout -- a unique problem as far as I know -- I'm sure they had a team working together and helping one another.

Why would you take my statement to imply that researchers don't collaborate?

I simply meant that SOMETIMES collaboration doesn't help. If your problem is unique, new and difficult, then nobody knows the answer. What do you do when everyone you have access to is stumped? Sometimes, you are either the one responsible for getting the answer, or are the one in direct need of the answer? In those cases you either give up, or you persevere and succeed.

 

[General_Sax]

Why would you take my statement to imply that researchers don't collaborate?

I thought said implication was pretty strong in this sentence:

In the real world, sometimes your problem is so unique or new, there is no one else to help you.

==================================================================

In those cases you either give up, or you persevere and succeed.

Or you work with a team (in an official or unofficial capacity) of people to arrive at a solution. Of course the individual who developed (or is tasked) with the original and difficult problem may have to expend great energies, but there is no need to become a "lone warrior".

 

[Fragment]

I:

• 
  Solve as many as I can.
  Go back to the unsolved ones, see where I'm stuck.
  Go running/biking.
  I usually have the solution when I come back from my run/bike.
  This also refreshes my mind and I can then tackle more problems.

 

[stevenb]

Or you work with a team (in an official or unofficial capacity) of people to arrive at a solution. Of course the individual who developed (or is tasked) with the original and difficult problem may have to expend great energies, but there is no need to become a "lone warrior".

There is no need to seek becoming a lone warrior in the real world, but sometimes the need will be thrust upon you. When given a new project, I always talk to everyone who I believe can give advice and background. However, once into the details, it's rare for me to find anyone who can really solve the deep issues. It's not that I'm smarter than anyone else, but no one else is going to invest sufficient time to solve my problem. For that matter, they are not even going to have the time to truly understand the full depth of the questions. That's just how it is when you have a truly difficult problem. Sure, you can ask your boss to assign two people to your task, but what if he says "no"? What if he says, "OK I'll just give the problem to this other guy who always gets to the answer by himself"? I'd find that a little embarrassing myself.

Who will be more able to handle that situation in the real world: the person who trained himself to be a lone-warrior in school, or the one who avoided those challenges? Granted, sometimes you have to cut your losses and balance other things in your life, but to improve your skills it's best to avoid that as much as possible.

That said, teamwork is also very important in the real world. The thing is, often teams are setup so that individuals can tackle areas they are experts in. If the expert is stumped, the others on the team may be able to help, or they may be even more stumped. By all means, ask some questions and seek some advice, but don't be surprised when you don't hear what you want to hear.

Above, my use of the word SOMETIMES is intended to make my statement less strong than you took it. There are two valid sides to this. You presented one side, and I just wanted to mention the other side. A person needs to be able to handle both situations, since both are commonly seen in the real world.

 

[General_Sax]

There is no need to seek becoming a lone warrior in the real world, but sometimes the need will be thrust upon you. When given a new project, I always talk to everyone who I believe can give advice and background.

I think we are basically in agreement and seem to be "arguing" only because of misunderstandings or something of the like.

 

[Fizex]

Also, you need to develop an intuition of finding more ways to solve a problem. Tackling a problem from a different direction usually gives an answer.

 

[kaos86]

I:

• 
  Solve as many as I can.
  Go back to the unsolved ones, see where I'm stuck.
  Go running/biking.
  I usually have the solution when I come back from my run/bike.
  This also refreshes my mind and I can then tackle more problems.

That's what I do! It really helps, too.

 

[kaos86]

@Ryker: I know how you feel. What I usually do is re-read the chapter and see what I'm not understanding. If that doesn't work, then continue solving the other HW problems. Don't feel ashamed for getting help.

 

[twofish-quant]

Three other things things that help me a lot

1) work on hard but interesting problems which the teacher hasn't assigned, and which you *KNOW* that you are unlikely to solve on your own. Personally, I find it strangely relaxing to do math puzzles that I KNOW that I am unlikely to solve on my own, because I don't have the pressures of expecting myself to solve them,

2) peek at the answer. Sometimes when I'm stuck, I just look at the answer for a fraction of a second, and that helps me because I see part of the solution, but I'm still working on the problem. Something else that works surprisingly well for physics problem is for someone to give you the answer to the problem, and you still have to work through the steps to get to the answer.

3) read similar solved problems. Something that also helps a lot is to read lots of solved problems. That way you learn about new strategies for solving problems that you didn't think of before.

 

[Vanadium 50]

I disagree with peeking at the answer. Too often a peek becomes a glance, a glance becomes a gander, a gander becomes a look, and a look becomes a read. Before you know it, you're relying on the solution, and this is about as useful as watching someone else lift weights.

One piece of advice I received from John Wheeler was "never start a calculation until you know the answer". What he meant was to think about how the answer must look before starting - how does one variable depend on another? Are there symmetries one can exploit, or at least use to check the answer.

Polya suggests when getting stuck asking "can you solve a simpler problem?" This often provides insight into the real one. He also suggests "can you solve a more general problem?" This may seem like a step backwards, but sometimes it works! I've had problems that looked lie complete nightmares, but it turned out the way to the answer was to solve the general case and then plug in.

 

[Ryker]

1) work on hard but interesting problems which the teacher hasn't assigned, and which you *KNOW* that you are unlikely to solve on your own. Personally, I find it strangely relaxing to do math puzzles that I KNOW that I am unlikely to solve on my own, because I don't have the pressures of expecting myself to solve them,

2) peek at the answer. Sometimes when I'm stuck, I just look at the answer for a fraction of a second, and that helps me because I see part of the solution, but I'm still working on the problem. Something else that works surprisingly well for physics problem is for someone to give you the answer to the problem, and you still have to work through the steps to get to the answer.

These two are actually good tactics and I've used them in the past, as well. For example, during summer I was revising my high school maths knowledge and, since a lot of time has passed since then, I wasn't sure exactly what we did and what we proved (I didn't use notes, just a really concise book that was meant to supplement lectures and stuff while preparing us for the final exams, so it only contained the most important things and didn't go deep). Doing that, I wanted to prove some of the formulas on my own and got frustrated really quick when I just couldn't figure some out. Only when I looked it up online and saw that they used methods and stuff I haven't covered yet or was beyond high school level was I able to reconcile not being able to prove them.

And the second thing you mentioned is a good thing to do, as well. There's been countless times that I've looked up a solution and then move backwards from it, trying to understand how you actually get to it. And as for the third ...

3) read similar solved problems. Something that also helps a lot is to read lots of solved problems. That way you learn about new strategies for solving problems that you didn't think of before.

This one is good, as well, but I think the thing for me is that I rationally know of all of the tactics and strategies people in this thread mentioned. What I'm having problems with isn't really not being able to solve problems, but that I feel incompetent when I can't do it on my own or without looking at similar solved problems. I feel like I should be able to do it on my own and that if I go ask someone for help or look it up, it'll just be "cheating" and although I will get the answer I'm not really going to be satisfied because it wasn't really me who came up with it.

 

[Ryker]

I disagree with peeking at the answer. Too often a peek becomes a glance, a glance becomes a gander, a gander becomes a look, and a look becomes a read. Before you know it, you're relying on the solution, and this is about as useful as watching someone else lift weights.

I don't know if twofish meant it that way, but I took it as meaning that you peek at the answer when you're stuck anyway. And I guess it also depends on how elaborate the solution is. In my high school textbooks, the solutions were most of the time given as a single quantative answer, so you really didn't have a clue on how they arrived to the solution and still had to do work to understand the process.

 

[Klockan3]

Before you know it, you're relying on the solution, and this is about as useful as watching someone else lift weights.

Not at all, watching solutions is a big part of learning. Personally I don't even solve problems on my own except when it is required for something.

 

[DrummingAtom]

I disagree with peeking at the answer. Too often a peek becomes a glance, a glance becomes a gander, a gander becomes a look, and a look becomes a read. Before you know it, you're relying on the solution, and this is about as useful as watching someone else lift weights.

I agree, I can't let myself look at the solution. If I look then I feel guilty, almost like I cheated the system and got something for nothing.

Not at all, watching solutions is a big part of learning. Personally I don't even solve problems on my own except when it is required for something.

I'm surprised by this. I have to learn how to problem solve on my own before I am required to do so. Otherwise, I would crash and burn.


To the OP, I agree with the others that have said to take a break from the problem if you're really stuck. Sometimes the solution even comes to me after I stopped thinking about it! Good luck.

 

[╔(σ_σ)╝]

You must be an incredible brilliant fellow if you get upset when you can not solve a problem. For an average Joe like myself I got used to accepting defeat sometimes. If I got upset every time I could not answer a question I would probably be an unhappy fellow for the rest of my life; afterall I haven't figured out why people die.

If everyone got angry when they couldn't solve a problem just imagine how many agry professors you would have :-).

Follow the steps that were outlined in this thread and learn to accept defeat sometimes.

 

[╔(σ_σ)╝]

Not at all, watching solutions is a big part of learning. Personally I don't even solve problems on my own except when it is required for something.

This is the way a lot of student sucessfully pass engineering. It is a proven technique. I know students who studied solutions to problems figuring out why the solution is the right solution and under what conditions certain assumptions were valid. A lot of them passed with flying colours.

 

[fluxions]

"How do you cope with not being able to solve a problem"

I exist in a perpetual state of confusion punctuated with brief moments of clarity and understanding. Said moments make the discomfort of confusion worthwhile.

If you are doing everything well and everything is easy, then you are not doing enough or pushing yourself hard enough.

 

[mathwonk]

make the problem easier. i.e. give your self more hypotheses, or make the conditions more special, or choose simpler numbers, and then try to gradually work your way back to the original problem. solving an easier version of the problem gives you both confidence and experience.

 

[Saladsamurai]

make the problem easier. i.e. give your self more hypotheses, or make the conditions more special, or choose simpler numbers, and then try to gradually work your way back to the original problem. solving an easier version of the problem gives you both confidence and experience.

Where did mathwonk even come from!? Not that I knew you well, but I have not seen you in a while. Hope things are good!

 

[Theorem.]

Where did mathwonk even come from!? Not that I knew you well, but I have not seen you in a while. Hope things are good!

I am pretty sure he descended from the heavens holding only a vector calculus textbook and a hunting knife.

 

[twofish-quant]

Before you know it, you're relying on the solution, and this is about as useful as watching someone else lift weights.

Different people have different learning strategies, but I find looking at solved problems to be extremely useful for me. The thing that works for me is to read a *lot* of solved problems, and that's no more "cheating" then having a chess master look at games that have been played or an artist going into an art museum looking at old masters. Once you look at a lot of solved problems, then you start getting a sense of the strategies that are involved in mathematical problem solving.

Also, it's pretty easy to come up with problems that you don't have the immediate answer to. Once you figure out how to solve one problem, it's usually not that difficult to make the problem somewhat more complicated.

 

[bogarts21]

^ Agree.

To the OP, please don't feel very bad about not solving a problem. Just don't stop thinking and you'll get it, if not, somebody else would. And that's not a bad thing, scientists and engineers work together to build a better world.

 

[ronaldoshaky]

You know it's funny, that happens me a lot. I wouldn't say I was the most bright student of Physics, but I just keep at it. Eventually the penny drops. Hey, if Physics was easy then everybody would be doing it!

Oh yea, the secret to doing problems in Phys....read read read and read the textbook and read the other textbooks and the other ones too. There are so many resources out there.

Good luck!

 

[Theorem.]

I think that above all you have to remember that at the end of the day you are still only human.
Do your best, put in your full effort, use whatever resources are available (and there are always available resources) and keep yourself motivated.

 

[clope023]

Different people have different learning strategies, but I find looking at solved problems to be extremely useful for me. The thing that works for me is to read a *lot* of solved problems, and that's no more "cheating" then having a chess master look at games that have been played or an artist going into an art museum looking at old masters. Once you look at a lot of solved problems, then you start getting a sense of the strategies that are involved in mathematical problem solving.

 

[Ryker]

Just wanted to thank everyone for their input again. And I guess I wasn't (am not) really looking for a way to hack the problems themselves, but just a general philosophy, strategy or a mindset that I could apply to the fact that I am just not capable of solving a specific problem that I think I should. So this topic is more about accepting defeats than it is about avoiding them. From some of the posts it seems I didn't make my point clear enough, but what I wanted to say is that it seems I have imposed myself that, say, getting help for a problem isn't avoiding defeat, because defeat to me isn't not being able to solve the problem per se, but not being able to solve it by myself when I expect to be able to do so.

So, more generally, I was and am not looking for tactics on how to tackle Maths/Physics problems and, similary, not for ways of actually solving the problem, but for ways of dealing with not being able to solve it, when this not being able to solve is taken as an irrefutable fact.

Does it make sense?

 

[Klockan3]

Stop thinking "I should be able to solve this" and just think about the problem instead. If you can't solve it, then it doesn't mean anything other than that you can't solve it. There is a lot of problems I can't solve but there is also a lot of problems I can solve, I just figure that if I need to solve it at some time then I will learn how to solve it sooner or later so it is ok if I can't solve it right now.