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?

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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.