The Extremely Fast Problem-Solving Method

1. Understand the problem.  Give what you want, and other parts of the problem a name by creating proper notation (method 5).  Fulfilling this step is essential before doing anything else.

2. If you have seen this type of problem before, then implement the method you have learned to solve problems of its class.  For example: using addition, subtraction, separation of variables to solve a PDE, etc.  Otherwise:

3. Quickly use defeasible reasoning to analyze the implications of your immediately available resources that would likely relate to finding a solution. (Use about 5 seconds to do this)  Later if you find a solution to your problem using implications (new resources) you found in this step, then you will have to return to these resources to prove them as correct and sound resources.

4. Then work forwards using the information from step 3 and from immediately available resources in the problem.  Working forwards means that you consider what steps or unspecified goals you can achieve by directly applying what you have to work with in the problem.  (Use about 5 seconds to do this)

5. Work backwards (sub-method 2d) taking into account the immediately available resources from step 3 to try and work backwards to a point found working forwards in step 4. (Use about 7-15 seconds) 

6. If more than about 20 seconds passes after beginning to implement steps 4 or 5, then use defeasible reasoning to check to see if your approach will likely take a non-negligible amount of time to implement.

If your current strategy would seemingly not be too time consuming for an extremely fast approach, then continue your strategy until you either solve the problem, or it becomes obvious that your current strategy would be too time consuming or unpromising for a super fast problem-solving approach.  Otherwise:

7. Consider how tedious and time consuming it would be to break down some or many of the defining parts of your problem into their defining parts.  If it would not be time consuming to break down some or many parts in your problem that do not have an obvious way to use for solving the problem, then break down those parts and begin this extremely fast process from step (3) or step (1).  You return to step 1 if you broke down what you want because then you have to understand your problem with respect to your new unknown.  Otherwise if breaking down the parts of the problem in question would require a non-negligible amount of time or be too tedious, then:

8. Implement the next somewhat more time consuming but simple and “fast” method below.  

        However, you should remember what was missing that prevented the previous steps from successfully solving the problem.  Do this in order to remember and take advantage of anything new you discover during your following approaches to solving the problem that could allow this first approach to work. (You should also do similarly when abandoning any approach.)  Some kind of a reminder of what was needed to make your earlier strategy work should automatically have a “neuron marker”†† in your brain that lights up when you opportunistically happen upon information that would make that “marker” idea work.