How do you solve problem you cannot solve?

[heartless]

Sometimes I meet mathematical problems I'm not able to solve, and after about 30 minutes of trying, digging, and looking for some number hints, I give up and lose all the desire I had, to solve it. Then, When I often sit with clear mind, at the end I become frustrated and lie on bed hours not doing anything. I assume, you all have different methods of solving unsolvable problems. How do you do it? and what do you do when you aren't able to find anything helping you?

 

[Ivan Seeking]

When this has happened in the past, what was the problem? Had you missed a key concept, or was it a matter of applying what you had learned? Once you knew the answer, did you understand why you were unable to solve the problem?

 

[franznietzsche]

Well, 1) I can't give up on a problem. I'm kinda obsessive compulsive about it, I can't sleep if there's one I can't solve. Which is probably why I can't sleep much.

Personally, I prefer the Feynman Problem Solving Algorithm:

1) Write down the problem.
2) Think really hard.
3) Write down the answer

 

[Moonbear]

That's when you should head over to the homework help forums, post your question, explain everything you tried and considered and where you're stuck, and see if someone can help you figure out the next step. That's what they're there for. It's important to remember that the problem IS solvable, you just need a little help learning how to solve it. There's nothing wrong with asking as long as you're willing to keep putting in the effort.

 

[matt grime]

Sometimes I meet mathematical problems I'm not able to solve, and after about 30 minutes of trying, digging, and looking for some number hints, I give up and lose all the desire I had, to solve it.

At what level do you meet these problems? What kind of problems? 30 minutes would consititute a tiny amount of the time needed to solve some problems.

Sleep on it. Go for a walk. watch a film. Come back the next day. Let your subconscious have a go at it.

 

[SpaceTiger]

Sometimes I meet mathematical problems I'm not able to solve, and after about 30 minutes of trying, digging, and looking for some number hints, I give up and lose all the desire I had, to solve it. Then, When I often sit with clear mind, at the end I become frustrated and lie on bed hours not doing anything. I assume, you all have different methods of solving unsolvable problems. How do you do it? and what do you do when you aren't able to find anything helping you?

Mulling over a problem for a while can be good for you, but keep a check on it. If the problem is intended to be short and you don't get it after an hour or two, it's best to move on. As you progress, you gain experience that makes problems easier to solve in a shorter amount of time. Sometimes, having difficulty solving a problem simply boils down to missing a key piece of experience that you will gain eventually. Also, beware of the misinterpretation. Many hours of my undergraduate career were wasted on poorly-worded or misinterpreted questions.

 

[shmoe]

That's when you should head over to the homework help forums, post your question, explain everything you tried and considered and where you're stuck, and see if someone can help you figure out the next step.

Bolding a very key part here. Just trying to organize your work to explain what you've tried can lead to insight. I naively believe that there are many homework problems that don't get posted because they were solved midway through the student typing up their work (as all good people who follow the guidelines do).

 

[GregA]

Bolding a very key part here. Just trying to organize your work to explain what you've tried can lead to insight. I naively believe that there are many homework problems that don't get posted because they were solved midway through the student typing up their work (as all good people who follow the guidelines do).

hehe...I've done that a couple of times

It also helps trying to explain the problem to someone who someone who isn't very knowledgeable about a subject (but wants to help). Though the chances that they can throw something useful at you may be slim, the act of trying to communicate the problem in terms they can understand and dealing with statements such as: "eh?...I don't get ya! " forces you to find out what the problem *really* is!
From my experience, once I can actually *hear* myself trying to even explain the problem to someone I am also in the process of solving it.

 

[dsky]

one of my methods is to solve a similar proplem, if there is none on the solved problems manuals.

I suggest that you get your hands to every "solved problems" texts or books or compilations of instructors, students that you can lay your hands on that's related or not before even trying to solve the problem.

This cuts the crap out of it.
Remember you are studying to "be able to produce solutions" for real life work.
When you go blank just tell yourself that nothing is new under the sun.
and go back to method one, somebody had always done it before, just find that person, they could dead like aristotle, einstein ..etc

second method is how to deal with it when its really dry
first put the problem on your "list of unsolvable problems" then ask your self what would you gain if you solve this problem, as against other problems
in short forget about it and move on to the other problems.
solve something else that you know how to solve- the eazy ones

third method : be creative
make your own problem, recreate the conditions and restate to be simmilar to the original, add conditions or parts that are solvable.
this is what study means : disassemble the frog and stitch it back all together.

fourth method: solve the most important problem all:
how to use time for your personal objectives effetively and efficiently
if its home work problem its just tricks,
if its work or job problem then somebodys done it before,just ask.
if you can always solve the fourth method you will do fine,

dsky
finally let us share love with one another

 

[mathwonk]

basic rule: make them problem easier. i.e. relax some of the hypotheses, or add easier hypotheses. work backwards until you find a special case you can solve;. then try to work forwards and solve more difficult cases.

once you have solved one case, there is an idea there that surely can be used more generally. try reading polya's "how to solve it?"

he talks about problems as grapes, i.e. they come in bunches. once you find a solution to one you will have a solution to others nearby. i once worked 5 years on a single problem.

 

[Pyrrhus]

Problems?, heh what would i do without them?. Anyway, my way to tackle them is to read the problem and make sure i understand what it is exactly asking, then i look for relations between variables and/or conditions given. At the end, if i cannot see a relation, then i go read the textbook, again. Maybe i am missing something. Usually, i always end up solving them, except sometimes when i didn't see some clever math trick (got to be creative i guess)

 

[kudos213]

Personally my tennis game helps me solve some of my math and physics problems that I can't get anywhere with. When I'm on the court and I'm getting blown off by a good opponent I can't start thinking about the score or how the match is going (the solution to the problem in question). What I have to focus on is my feet, moving them and getting into position, watching the ball and making sure I'm doing all the little things right (fundamentals).

So, when I get stuck on a problem I agree with a lot of the advice given already. But i'd also suggest going back to the beginning of the chapter and rereading with the intent to teach the material pertaining to the problem. You understand that since you cannot solve the problem the answer lies beyond your currently limited scope of view, so try and broaden those horizons as you relearn the material. Hopefully it helps.

 

[kdinser]

Nine times out of ten, it's because you didn't memorize something that the professor expected you to have memorized.

 

[Mk]

there are many homework problems that don't get posted because they were solved midway through the student typing up their work (as all good people who follow the guidelines do).

Definitely, that may be of help: prepare your question to an imaginary teacher, and tell them what you have done so far.

Also, you sure end up learning a lot as you are teaching something (hopefully you already knew it well before you started teaching it).

 

[QuantumPlan]

If you can't solve a problem, try to solve that it is unsolvable :)

 

[vishal007win]

i do it by breaking up it into simpler chunks, if problem is nonlinear i try to break it up into simple linear parts. then finding solution for the parts, reassembling them , i find it really successful so far. although Google and physics forum are always there to help
Solved problems from modeling liquid sloshing to designing micro gripper, successfully with this approach.

 

[jeffasinger]

Talk to someone else about it (preferably someone who has the pre-requisites for the problem, but hasn't actually seen it yet), work on proving a sub-case, or if I can't even see why it might be true, try to find a counterexample. Sometimes the act of searching for a counterexample is enough to give some insight into why it might be true.

Sometimes, I need to take a break, and work on something else, or get outside, or grab some food, or get some exercise. Sometimes your subconscious will considerably help solving a problem, which is a very important reason to not start at the last minute.