First, you identify, label and analyze it. Then you have power over it.
- By understanding your domain.
- Deducing the problem to more simpler problems.
- Applying the appropriate methods available.
In essence, the solution will eventually reveal itself.
The solution could have many possible solutions, some easier than other. Some simple and some complex, some shallow and some deeper.
If you reduce the problem to manageable chunks, which are familiar to you, you can solve the problem.
An good example is the Rubic's cube.
There are countless possibilities. You can move each plane in any direction at any time. When you move one side, the other sides move. It appears to be utter chaos.
So when setting out to solve it, the goal is to match all 6 sides. It appears impossible to conquer.
When i was 11, my brother showed me a simple pattern of movements. If you apply a series of combinations, you can alter the cube while keeping one side in tact.
So let's say you are trying to get one layer complete, the red side. That's a fairly simple task. Once that side is complete, the difficult part is that any move you make disrupts your completed layer and all is lost.
Yet when you apply this specific series of combination of movements, the end result is the four corners of your current side remain in tact, while changing the opposite side.
What does that mean, it means that you can then begin work on the opposite side of the cube, virtually keeping the original side unaffected.
So with a lot of time and experimentation, I was able to complete two opposite sides of the cube. Which mean that the four corners of each side were in the precise position to form the correct structure.
With all the corners in place, and a lot more trial and error, I was able to complete three sides. Although the original pattern helped to solve three sides, I had to learn more patterns as I went and eventually got four sides. Finally, all six sides were complete. And the problem was solved.
The reason it was solved was based on a very basic pattern of movements, when applied correctly, gradually, to allowed the structure to remain in tact without disrupting the current side,
So once you know the very basic series of movements, you know the methology of solving the cube.
And the magic and mystery dissolves into thin air.
And once the pattern is identified, labeled, and re-applied, you have cracked the code.
However, without knowing your domain, your possible cube positioning and how each move affects the downstream results, you're grasping at thin air.
I give this example to show how many seemingly impossible problems can be solved. There is a level of intelligence required, however, by learning some basic steps, reducing the complexity into simple processes, which are repeatable, a problem becomes less daunting and maybe even solvable.
And there you have it.