I have always wanted to become better at problem-solving, but I never had a concrete plan on how I could be better.
I came across "How to Solve It" by G. Polya, written in 1945 by a mathematician who gave 4 simple steps to solve any type of problem.
1. Understand the problem
This step seems so trivial, but it is also easy to neglect the importance of it because it is trivial. I personally have tried to solve problems without fully understanding them. I wasted many hours developing a solution that did not solve the initial problem, or missed an easier way to solve the problem.
To make sure you understand the problems, ask yourself:
Do you understand all the words in the problem?
Can you restate the problem?
Can you visualize the problem?
What is the unknown?
What is known?
What is the connection between the known and the unknown?
2. Devise a plan
When we understand the problem, we need to come up with a plan to find the unknown. This step may take a long time!
To come up with a plan, ask yourself:
Do you know a related problem? Can you use it?
Can you solve a related or smaller problem?
3. Carry out the plan
Carrying out the plan is much easier than devising a plan.
While carrying out your plan, you should check each step. If the plan does not work, go back to devising a plan.
4. Look back
After you have solved the problem, it is important to look back and examine the solution.
Ask yourself:
Can you check the result?
Can you derive the solution differently?
Can you use the solution for some other problem?
Conclusion
Even though the steps are somewhat obvious, we often neglect these steps. I have known these steps for a while now, but I still don't spend enough time on the first two steps, just out of laziness or impatience. But in the end, lack of planning almost always leads to disaster. Follow these steps and focus on the first two steps to become better at problem solving.
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