I typcially use a trial and error approach to problem solving when I'm dealing with a problem or challenge where I don't have a definite solution that I can use. Therefore, the best thing I can do is make a guess (with limited information) about what might work. I give that a try and if it doesn't work, I look at the result I got, make some adjustments and try again.
In a good trial and error situation, every failed attempt brings some more information that helps me improve my chances of actually getting to a solution that meets my needs or fixes my problem because each time you try, you may eliminate some of the possible solutions to your problem, narrowing the field a bit.
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