Problem Solving as a Process

How to solve your problem(s) step by step according to...

“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

One of the most influential sources of information, procedures, and methods on how to solve problems is the Hungarian mathematician George Pólya (1887-1985). His small volume on problem solving, How to Solve It (1945), continues to be one of the most useful books on the subject, and has sold over a million copies worldwide.

Mentioned in the preface of his book is the term “heuristic” that he refers to as “serious study of methods of solution.” Heuristics is the systematic applications of procedures (or more generally, asking the right questions) to employ in the development of solutions to problems (from Pólya’s writing, those mostly arising in mathematics). However, these heuristics can easily be applied to all kinds and types of problems, including those of a personal nature.

I have only briefly introduced here George Pólya and his amazing work. In following newsletters, I will examine more in depth his lifetime of work on problem solving.

I would like to delineate three early and crucial concepts from How to Solve It:

1. Examine and understand the problem.

   1. Examine what you know and what you need to know about your problem. Define the true nature and scope of the problem. What problem are you really solving? For instance, you are not sleeping well. Look at why you may not be sleeping well. Consult a doctor. Not sleeping well may be a symptom of a larger problem (for example, sleep apnea).

   2. Is there data about the problem that might inform your understanding of where to look for a solution? Data driven solutions are more reliable. Say you suspect you may have sleep apnea. Look for reliable information and data (research from experts and multiple sources) on the condition. The data that exists may point towards a solution (hypothetically, let’s say 55% of individuals with sleep apnea benefit and reliably sleep better with the help of a nighttime breathing machine). This data might point towards a workable solution. However, further investigation might be necessary to confirm any conclusions that might be drawn from this (or any) data.

   3. What conditions and constraints (money, time, knowledge) exist surrounding the problem? What limits do you face? What are the boundaries of what can be achieved or what solution is possible? Once you know sleep apnea is at least one of the causes of your not sleeping well, a few other questions need to be considered: How much will such a machine cost? Is it covered by insurance? Can you sleep comfortably with a mask and a breathing tube?

   The nice thing about heuristics is that they can be applied to almost any type of problem. The example above is simple, but still illustrates how asking the right questions can lead to better solutions.

2. Come up with a preliminary plan and get going.

   1. Is your problem one that is recurring? Have you encountered a related or similar problem before whose solution can be utilized or implemented? Look for information related to your problem; or, if your problem is or seems unique, gather together pieces of the puzzle (metaphorically speaking) to see how they might fit together to offer insights.

   2. Similar problems often have similar solutions. Look for commonalities and see if prior solutions point you in a profitable direction. Can you restate the problem in a different way to make it more solvable?

   3. Chart a initial plan: Point A to Point B. Any advancement in that direction? You may not know where exactly the solution will be, but advancing up a mountain (hill-climbing) often requires step by step planning. Knocking down problem obstacles requires boldness and patience, creativity and planning, leaps and shuffles.

   Procrastination, frustration, and reliance on too much research can hamper, delay, and destroy effective problem solving. If the problem has merit, if the problem requires a timely solution, if the problem is actually solvable, move forward. Be on guard against problems that offer unicorn solutions (if I only bought enough lottery tickets I could be rich). The solutions that are real are attainable in the space that you inhabit. Miracle solutions happen, but are rare. Accidental solutions also happen, but the foundation already probably existed. Unexpected solutions are the happiest solutions of all, but do not count on those.

3. Look back at how you approached the problem, and how you might use what you have learned or the solution/methods you have developed to solve future problems.

   1. Check and double check your solution. Is it the only possible one? Is the solution logical? Are there flaws in your reasoning? Is your solution the right approach? Have all the conditions for a solution been met? Is there an equally good or even superior solution waiting to be discovered later, perhaps?

   2. How is the solution received by others? Who might be happy or unhappy? What are/will be the costs to implement the solution? How long might the solution take to work? Is the method you choose to use inefficient, inelegant, inelastic?

   3. Discuss your solution with others (if possible). Seek insight and input from trusted people. Problem solvers often have a community of people they often consult or confide. Do not be shy to talk about your problem and how you came up with a solution. You can find great support among those with similar interests or concerns. There is a lot of wisdom out in the world waiting to be shared.

A final question: Will the solution to your problem lead to, or create other, even more serious problems? This should be of some consideration, even if the current benefits of the solution outweigh the current costs, because some problems only have a temporary solution, and eventually get worse, festering like an open wound, causing much more serious damage at a later time. Beware of easily attainable solutions!

There is so much more to discover about problem solving in reading George Pólya. This summary of just a few of his methods will hopefully whet your appetite for more if you are not already familiar with his work. If your interest is piqued, please refer to his books, as he was a master problem solver. His insights into problem solving, in many ways, revolutionized the field, and we problem solvers owe him a kind thank you!

Happy Problem Solving!

Evan