“How to Solve It” is a classic book written by George Pólya, a mathematician, providing a systematic approach to problem-solving.

While the book primarily focuses on mathematical problems, its principles extend beyond mathematics, offering a general framework and advice for approaching and solving various problems. At a high level, there are four phases:

  • Understand the Problem
  • Devise a Plan
  • Execute the Plan
  • Look Back

These high-level steps may sound like common sense, and indeed they are. However, the genius of the book lies in the precision and clarity it provides for each step.

Understand the Problem

The three elements (principals) of a problem are data, condition, and unknown. The goal of this step is to clearly understand the problem by looking at those three elements thoroughly, with a clear definition of the problem and the terms used in the problem.

  • Unknown. Problem solving is looking for the unknown, according to the data and conditions. In everyday life, it is to take action to remove the pain or achieve a gain with the constraint of money, energy and time.
  • Data. In a mathematical problem data, generally, the data is already presented. In real-life problems, we often need to collect data to understand the problem more accurately, to design and verify the solution.
  • Condition. For a technical solution, the condition is the function and non-functional requirement that must be satisfied. For project delivery, the condition is the task goal and people relationship that must both be met. For job hunting, it is the career goal and family commitment that must be met.

One exit criterion of this stage is to come up with a precise definition of the problem trying to be solved. It should include the terms used and the conditions it be must be met to consider the problem is solved successfully.

“A problem well stated is a problem half-solved.” - Charles Kettering

Devise a Plan

The main achievement in the solution of a problem is to conceive the idea of a plan. A plan is a set of high-level actions that, once performed, will lead to the obtainment of the unknown. Many heuristics can help us analyze the problem and formulate the plan.

Decomposing and Recombining. Start with the questions: What is the unknown? What is the condition? What is the data? Examine them one by one. Separate the conditions, and examine them one by one. Do the same to the data. Changing one of the triads (while keeping the other two the same) to create variants of the original problem to see if you got some insights. Don’t go into details until you have a good grasp of the problem as a whole. Otherwise, you may lost in the details.

Generalization is underrated and almost forgotten. We are used to criticizing others for overgeneralizing, which is a logical fallacy. However, generalizing is essential for abstract thinking, principle-based decision-making, and problem-solving. A general problem is often easier to solve than a specific problem, as you can get to the essence of the issue by not being distracted by the specifics. In a business example, when facing a specific issue, instead of solving that issue alone, you put in place a process to solve a category of the same issue and prevent it from happening again.

Hypothesis-based problem-solving is an integral part of systematic problem-solving and the core of the scientific approach. When confronted with a complex issue, you develop several hypotheses and then validate or invalidate them through experiments. An effective developer employs this approach when debugging an issue that may have several causes, while an ineffective developer jumps around different guesses without concluding any of them.

Working backward starts from what is required and assumes what is sought is already found. Then, inquire about the antecedent from which the desired result could be derived. Continue this process, asking about the antecedent of each preceding step until eventually coming upon something already known or easy to solve.

Humans are inclined to work towards a goal through planning and trials, which is effective at times. However, there are instances when you may not achieve what you want or get what you don’t want without proper knowledge. Our time and energy are limited. Therefore, it is important to pause, reflect, disregard sunk costs, navigate around obstacles, work backward, and ensure we are on the right track and moving towards what we truly desire.

Analogies are a cognitive tool that involves finding similarities between two situations. The format is “A:B::C:D,” reading as “A is to B as C is to D, meaning that the relationship between A and B mirrors the relationship between C and D. By drawing parallels between a known concept (C:D, base idea) and a new or less familiar one (A:B, target idea), it helps us understand the problem or explain an idea.

“If I had an hour to solve a problem I’d spend 55 minutes thinking about the problem and 5 minutes thinking about solutions.” - Albert Einstein

Execute the Plan

With a thorough understanding of the problem and a solution in mind after intensive yet intriguing mental work, this is the step to implement the plan systematically and flawlessly.

According to Polya, compared with devising the plan, carrying out the plan is much easier, and what we mainly need is patience. I think this assertion is because he is referring to mathematical problems only. For non-mathematical problems, the execution is not easier at all. To the contrary, disciplined execution is the only thing that differentiates success and failure, for both personal and business goals. Most people have a plan to go to the gym three times a week to stay fit, but how many people execute the plan? Lots of companies have a digital transformation strategy, but how many succeed? Execution is no easier than coming up with a plan.

“Everyone has a plan until they get punched in the mouth.” - Mike Tyson

Looking Back

The last step is to reflect on the solution to ensure its correctness and completeness. Equally important, if not more so, is to reflect on the path that led to its solution to consolidate the knowledge and develop the ability to solve further problems.

“An unexamined life is not worth living”. - Socrates

Challenges to Clear Thinking

Nothing suggests that with the simple four steps, we are now rational, disciplined, and clear thinkers. Far from that.

In my view, the major obstacles to clear thinking include, but are not limited to:

  • Cognitive Bias
  • Prejudice
  • Illogical reasoning

The first was never to accept anything as true if I had not evident knowledge of its being so; that is, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgement than what is presented to my mind so clearly and distinctly as to exclude all ground of doubt. - Decarte

But the #1 obstacle to clear thinking is when emotions get the better of you. I’m sure every one of us has occasions we regretted, wishing we could have done better in the past. That is when your prefrontal cortex relinquishes control to your limbic system.

May we all think clearly.