Problem solving stages

Thinking better is about knowing how to think.

Knowing how to do anything involves knowing what situations might occur, and what to do in those situations.

Problem solving is one of the most common patterns in thinking. I believe that solving a problem involves a set of recurring stages, and each stage has a recurring set of thought patterns that help overcome that stage.

Here is one possible break down of the stages of a problem:

  1. Understanding the problem
  2. Looking for a simple solution
  3. Optimizing the solution
  4. Proving that the final solution is correct and optimal

Sometimes, steps 2-4 will force returning to step 1. Perhaps for simple problems, 2 and 3 are one step, and perhaps for complex problems, there is no optimal solution, and step 3 produces an array of solutions with tradeoffs. Perhaps it’s impossible to prove that the solution is correct and optimal; perhaps there is no correct solution, but a somewhat correct one exists.

Regardless, I often find myself in the middle of a “stage” of a problem, and these stages reoccur between unrelated problems. I believe there is a lot to say about what each stage is, and what some tricks are to be better at it, and how to know you’ve completed a stage. Practicing those tricks, I believe, is an important key to being a better thinker; further, I think the process for improving in them is very similar to the process of improving at body skills, like guitar or handstands. The underlying neural process would be similar – strengthening and accelerating neural pathways through repetition.

This model came about because I noticed that it’s easy for me to keep going on something once I’ve started. For instance, beginning to write is much harder than continuing to write – there’s a lot more pressure for perfection. Mark Twain said: “The secret of getting ahead is getting started. The secret of getting started is breaking your complex, overwhelming tasks into small manageable tasks, then starting on the first one”.

So one trick that came to mind, that I think is worth practicing at the second stage of thinking, is – try wrong solutions, or try naive solutions, or try dumb solutions. Having some solutions helps understand the problem space – as you see why they don’t work – which feeds into the understanding of the problem.

I like how in thinking through the problem of “how to think better”. I tried a dumb solution – “try dumb solutions”. That forced me to consider why that may be a reasonable tactic to try, and in explaining it, I proposed that it helps understand the problem space, and noticed that understanding can feed into having more solutions. So I’ve arrived at more than one tool by looking at a simple tool.

I want to have a separate post where I explore the stages of problem solving as I currently understand them, and ongoing posts about how tricks involved in each one, and how to work on them. Here’s a summary of the ones I found in writing out this higher-level post:

  1. Understanding the problem
    1. Understand what the entities of the problem are
    2. Understand how they relate to each other (“understand the problem space”)
    3. Break down into small chunks
  2. Looking for a simple solution
    1. Try wrong solutions
    2. Try dumb/naive solutions (brute force)



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