Here's the CIA's "Phoenix Checklist" for thinking about problems
The "Phoenix Checklist" is a set of questions developed by the CIA to define and think about a problem, and how to develop a solution.
THE PROBLEM
Why is it necessary to solve the problem?
What benefits will you receive by solving the problem?
What is the unknown?
What is it you don’t yet understand?
What is the information you have?
What isn’t the problem?
Is the information sufficient? Or is it insufficient? Or redundant? Or contradictory?
Should you draw a diagram of the problem? A figure?
Where are the boundaries of the problem?
Can you separate the various parts of the problem? Can you write them down? What are the relationships of the parts of the problem? What are the constants of the problem?
Have you seen this problem before?
Have you seen this problem in a slightly different form? Do you know a related problem?
Try to think of a familiar problem having the same or a similar unknown
Suppose you find a problem related to yours that has already been solved. Can you use it? Can you use its method?
Can you restate your problem? How many different ways can you restate it? More general? More specific? Can the rules be changed?
What are the best, worst and most probable cases you can imagine?
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THE PLAN
Can you solve the whole problem? Part of the problem?
What would you like the resolution to be? Can you picture it?
How much of the unknown can you determine?
Can you derive something useful from the information you have? Read the rest