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Joined: Aug 2005
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There are many problem solving techniques, from changing your perspective, to writing everything down, to the more fun ways like "Random Presentation."

My favorite way to solve problems is to challenge assumptions. As soon as I challenged the assumption that I needed a better job, I started making money in other ways. This method can really get you to the heart of the matter.

What works for the rest of you? I may use your ideas in an upcoming article, so thank you in advance.

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If you used my ideas, will I get the credit? Or are you using this forum as a research pool? Do we get honorable mention, even? A share of the profits would be really peachy too.

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Ok, here's my contribution. But if you use it in your article I want $6.00. My lawn mower needs gas.

I solve a difficult problem by directing it to my subconscious. I do this by repeatedly vocalizing the problem and then thinking about it for a short while. Then I let it go. I try not to think about it anymore.
The answer comes to me later.
Sometimes I do the above in the form of talking to God. I'm not a religious man by a long shot but I do believe that within all of us there is a reservoir of infinite knowledge. I find it easier to concentrate with the optimum sincerity and passion that is necessary to tackle the most difficult problems by just saying, "God, I need to know the answer to this or I need a solution to this problem." Then I leave it to my subconscious to point me in the right direction. This system works for me.
In other words it's easier for me to employ God as a focal point rather than asking my "subconscious" or the "pool of infinite knowledge" to help me out.

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When ever I solve a problem I try to analise what sequence of thoughts led to its solution. It hasn't served me well. My problems are still solved by repeated approaches but of course first time solutions don't manifest as problems. So I'll never know my own success.

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Get to the bottom line. If the premise to your solution is correct then the resulting logic following should be correct. Keep open your mind to as many possible solutions as you can. There is always an answer otherwise there would be no problem. Problems and solutions dance with each other always seeking each other out. Drawn together. You can find ten answers for the same problem. Choose what works best for you cool


"My God, it's full of stars!" -2010
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I work to define the problem as precisely as I can. I agree that solutions often become clear unexpectedly during quiet moments. Sometimes I purposely try to create moments where my mind is as clear as possible; I suppose it's functionally very similar to more formal types of meditation. I often begin pacing when I'm trying to think clearly. I don't do it on purpose; in fact, I didn't even know I did it until a friend pointed it out. I have since learned that many styles of formal meditation include pacing or rhythmic walking.

j6p - What the hell is a reservoir of infinite knowledge? Sounds to me like you're talking about the ability to think creatively.

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Yeah I guess I am. smile
I forget the exact term that a fellow named Napoleon Hill called it but after reading his book "Think and Grow Rich", about thirty years ago, I picked up on an idea that in each of us lies all the knowledge in the universe. All we have to do is learn how to tap it.
He set an experiment. What he did is suggest that when trying to solve a difficult problem ask a friend to join you in trying to reach a solution. Most times answers will materialize seemingly from nowhere. That nowhere is the reservoir.
I think they call it brainstorming today. It happens a lot in think tanks, lol.

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Quote:
Originally posted by j6p:
Yeah I guess I am. smile
I forget the exact term that a fellow named Napoleon Hill called it but after reading his book "Think and Grow Rich", about thirty years ago, I picked up on an idea that in each of us lies all the knowledge in the universe. All we have to do is learn how to tap it.
He set an experiment. What he did is suggest that when trying to solve a difficult problem ask a friend to join you in trying to reach a solution. Most times answers will materialize seemingly from nowhere. That nowhere is the reservoir.
I think they call it brainstorming today. It happens a lot in think tanks, lol.
PS I'm editing this post because I just remembered what ol Napoleon called his system. He referred to it as "forming a mastermind group". As I said, been many years but I think that was it.

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I solve complicated problems the same way i solve the simple ones. like opening a bag for example. If it is a bag i recognize, i draw on memory from previous attempts and repeat the most successful technique. If i do not recognize the bag, i observe it to find a seem. if there is no seem i use a pair of scissors and cut the stupid bag.

Step 1: Observe
Step 2: Draw on Memory
Step 3: Write down your thoughts(fr logic problems)
step 4: Break down the problem into segments and solve each segment individually. The answer to each segment will always be the simplest answer possible, because nature always finds the simplest way.
Step 5: Trial and error
step 6: Organize your thoughts and observations into the best - and usually simplest - possible solutions.


"The power of accurate observation is commonly called cynicism by those who have not got it."
George Bernard Shaw (1856 - 1950)
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One of the best systems of problem solving has been described by Richard Feynmann, How To Solve A Problem In Three Steps:

1. Write down the problem
2. Think very hard
3. Write down the solution

Although this is mainly meant as a joke, still I believe the described 3-step process lies at the heart of each solution. What makes a problem-solving process successful is to chop the problem up in manageable chunks, (luckily) choose the right chunk to begin the 3-step process and sequentially solve the other sub-problem chunks accordingly.
Often easier said than done though :0)


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The hardest part of problem solving is identifying the actual problem to be solved. Spotting the issue is more than half the battle.

Next, identify what kinds of rules need to be applied to this kind of problem. Is this an algebraic function? Is this a matter of constitutional law?

Next, identify the known data.

Finally, apply the appropriate rules to the known data. This will either (A) give you the solution, (B) tell you you don't have enough data (so you then go get it), or (C) tell you you don't know enough rules (so you go find someone who does, or work to discover them on your own).

That's all there is to it. Spot the issue, apply the rules/methods to the facts, and ta da!


Bwa ha ha haaaa!!
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I always use the problem solving method outlined by Georg Polya in his book "How to Solve it."

1. Understand the problem. Define the terms, draw graphs, if it will help, converse with experts, read books. This means DEFINE the problem - what are the constraints on the problem. Inately one must figure out the appropriate level of abstraction for their mental model. E.g., for thermodynamics type problems, you have to figure out "what is the system." This is the biggest part of solving real world problems and the one that is most often overlooked. Understanding the problem means clearly stating your givens and your goal(s), your assumptions, etc. Do research, some preliminary experiments, etc.

2. Plan a solution. Figure out the steps you need to take to get from the givens to the goal(s). Along the way you will figure things that you need that you don't have and you'll need to modify your list from step 1.

3. Carry out your plan. Do the work. Follow through. More research.

4. Look back. Check your results. Is the result meaningful? Does it correspond to your ballpark estimate? Does it meet all the problem constraints?

----

Now there are lots of techniques that can be used to fill out step 3:

1. Organize information
2. Draw relationships
3. Draw other diagrams as appropriate
4. Various little 'paper games' as I call them.
5. Decomposition - breaking the problem down into manageable chunks.
6. Simplification - Solve a much simpler version of the problem and see if I can solve progressively more complicated examples.
7. Similar to 6 but slightly different - use recursion.
8. Talk aloud to myself - or explain my rough thinking with other people. Even meetings can be useful, if there are no managers or salespersons present.
9. Guess and check - this is NOT taught correctly in schools by the way.

My kids were taught, for example, to just think of a wild answer and check it against equations. This is a parody of how guess and check should work. The way it SHOULD work is you consider what you know about the problem to constrain your initial guesses - othewise, you could spend forever looking for the answer. You also need to check trends.

10. Numeric solution - often easier than analytic.

11. Write a simulation.


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