Methods for Problem Solving

Or how to think a little differently

Karl Popper famously said “all life is problem solving”. And yet the methodologies of problem solving are very rarely analyzed. You probably know how to solve a particular class of problems; in fact, you may be excellent at solving that class of problems. But what happens when you go outside of that? How many of us have been caught on the back foot when presented with a novel problem?

The novelty I’m talking about is novelty regarding the type of problem.

If you had never studied ancient Mongolian history before and were given 2 weeks to do so, you could probably pattern match to a time when you were in school and had to cram. Maybe you chunked the concepts. Maybe you leveraged your exceptional memory and just cleared your RAM and loaded everything you could. Maybe you gave yourself memorable little stories. Whatever your method, you know the territory. Yes, the subject matter may be new, but the environment is familiar. You can pattern match because the type of problem is one in which you must memorize facts and you’ve done that before.

Now let’s say the type is truly new to you. You’re suddenly asked to find a way to start a fire. You have no tools. This is no longer a game of memorization. You must improvise. There is nothing about your cramming skills that can be used here. Can you solve the problem? What really changed in this example?

Types of problem solving

What changed was the type of problem solving that you need to do. For every problem, there is a problem solving method that is likely to be most effective. Understanding the problem solving methods enables you to be better prepared when novel situations arise. Problem solving methods fall into easy mode or hard mode.

Let’s use a common problem set to explain these methods:

You’re in charge of a brand new product. It has 100 features in it and you have 30 people who have to work on it across 4 different teams, and it needs to get launched in 6 months. Worse, you’re not starting from a clean slate. Your predecessor has muddied the waters and done a half baked version that everyone is still sort of working on but has nothing to do with what you’re tasked with. So if anything, you’re in negative territory.

Easy mode

Easy mode doesn’t detract from how useful a problem solving method is. It simply means that should you know nothing else, it’s best to start with one of these methods because they are easy to execute.

Simplification

Simplification is a problem solving method that reduces the option space and focuses on a few things. In our problem set, the chances of completing this product on time are effectively zero. This is a perfect case for the simplification method. Reduce everything to just one or two things. Only do those. Often by doing this, you find that in reality only a few things ultimately mattered. And so by simplifying, you get to the heart of the matter and cut through needless complexity.

Division

In the same problem set, let’s say you decide that in fact, you must actually do the majority of these 100 things. In this case, you take the division method. This method chunks things apart. You don’t let yourself get wrapped up into everything and instead take each chunk at a time. This gives you the focus and space to focus.

Mimicry

Now let’s say you have no idea how to even start the project. Mimicry is a good method to try; it is all about finding what others did in similar situations and mimicking them. Ok maybe your project was hard, but how did Apple launch the iPhone? How did NASA build a spaceship? How did Abraham Lincoln unite a nation? While none of these are necessarily at the same level as your problem, you can mimic their strategies to see if they would help you.

Hard mode

Hard mode methods are problem solving methods that you should typically only try when easy mode fails. It doesn’t imply any superiority; it does however imply a level of difficulty because these methods are hard to execute correctly. But if you do, you may be able to solve a problem that was previously intractable.

Explanatory power

The explanatory power method is about looking for a hypothesis that explains the most about the situation. It requires you to abstract away all the noise and look for the one thing that relates all things. To do this, you need to put on your scientist hat. Going back to our unfortunate product, you may initially assess that you need more process, more people, more time, and definitely more budget. But many projects with these things have also failed; and many projects without these things have succeeded. The explanatory power of these requirements is weak. Now consider something deeper – what really divides successful from failed products? Perhaps you realize through this analysis that successful products had a singular vision and that you’re building a chimera from 3 VPs’ opinions. This is the source of your problem. Now you have something with real explanatory power and a root problem to go and solve: creating a common vision and then get buy-in across these 3 VPs.

Inversion

Inversion is a method that requires you to invert a problem from its known state. You’ve probably heard the phrase “it’s a feature, not a bug”. This is a classic example of inversion. Maybe the state that you inherited is actually expected to happen. Maybe this product actually shouldn’t go out to market. Once you take this perspective, you start thinking a bit differently. Ok let’s say we do fail, what do we lose anyway? Maybe after evaluating you realize that you lose a shot at building a great technology. Now you’re onto something — maybe the real thing you should do after all is simply build that technology. This kind of solution naturally emerges once you go through the process of inversion.

Transformation

Transformation is approaching a problem from a different angle. Imagine you are solving a Rubik’s cube. You start on one face and then you get stuck. Do you just stay there trying stubbornly to solve this problem head on or do you switch faces? This act of switching faces is the problem solving method of transformation. In our problem set with the unfortunate product, speed-running through every single task and organizing everyone and managing all the tasks is a direct way of solving. Eventually you get exhausted and you feel like no one except you cares. Now let’s imagine you tried an indirect way; you started to pull forward a few people who showed initiative. You gave them more opportunity to shine. You give them direct responsibility over select portions. You tell them they’re so crucial to the product and you listen to their ideas. Suddenly you’re not building things alone. You’re not pulling teeth to just get status updates; you’re getting pushed status updates because the team wants to win.

Error-prone methods

The nature of the problem determines how fitting a problem solving method is. Problems arise when you use the wrong method for the problem at hand. While every single case depends on the nature of the situation, there are a few problem solving methods you should be aware of that are naturally error-prone.

Mimicry

Mimicry is a problem solving method that is often prone to errors. This is because it is generally easy to mimic actions but not results. It is very easy to bring forward mimicry solutions that are polluted versions, poor matches for the problem at hand, or simply too diluted. It’s important to remember that mimicry has to be done at the right conditions in order to generate the desired outcomes. When you apply this method, always test and iterate. Be willing to scrap things quickly.

Explanatory power

Explanatory power is another method that is particularly prone to errors. This is entirely because it is a hard method to execute. It is very easy to generalize incorrectly. Unless the problem realm that you’re involved in is science, you often do not have a way of truly falsifying your hypotheses. As a result, you have to utilize a lot of judgment to read the tea leaves if you’re right or wrong. Perhaps most importantly, you need to be rather ruthless with yourself.

This should not discourage you from using these methods. Rather, I hope that you exercise caution due to their error-prone nature. As they say, with great power comes great responsibility.