Problem-solving is one of those skills that is in high demand. Many employers rate it as one of the most important traits they look for in prospective employees. It is also usually listed as an important learning outcome in many of the classes you in take in college including math classes, Computer classes, and even this class! But, it is often not taught at all or very well.

One reason why this is the case is because of a confusion relating to what kinds of problems are being solved. It is often assumed that by practicing any kind of problems for which you don’t have an answer you will learn the skills appropriate to solve any problem. But, this is simply not true. Since there are different types of problems learning how to solve one type won’t necessarily help you build the skills you need to solve the other type. So, let’s begin by distinguishing two types of problems: puzzles and mysteries.

In his book Curious: The Desire to Know and Why Your Future Depends on It, Ian Leslie defines these two types of problems very well: puzzles and mysteries.

“Puzzles have definite answers. Puzzles are orderly; they have a beginning and an end. Once the missing information is found, it’s not a puzzle anymore.” Most of the problems you encounter in your college math courses are in reality puzzles. They have definite answers and are orderly. Also, the information you need to solve them is right there in the question! And, if you need extra help you can just turn back to the chapter in the text which discusses how to solve these particular type of problems.

Many “logic puzzle” questions are (obviously) also just puzzles. While they seem more complex in reality they are the same as your math problems. They have definite answers and are orderly. Here are a couple of examples:

You have eight billiard balls. One of them is “defective,” meaning that it weighs more than the others. How do you tell, using a balance, which ball is defective in two weighing?

You have five jars of pills. All the pills in one jar only are “contaminated.” The only way to tell which pills are contaminated is by weight. A regular pill weighs 10 grams; a contaminated pill is 9 grams. You are given a scale and allowed to make just one measurement with it. How do you tell which jar is contaminated?

Another important characteristic of puzzles is that you can quite often Google the answer for them! Go ahead try and figure these two out and if you have trouble just Google the answer.

Now, here’s the question. Are these kinds of problems “real?” In other words, are these the kinds of problems you’re likely to run into in your everyday life? Are they the kinds of problems you will run into at work? I doubt it. Another question then: Is learning how to solve these kinds of problems a good preparation for learning to face real world problems? Again, I doubt it.

So, the second type of problem Leslie defines is mysteries. “Mysteries are murkier; less neat. They pose questions that can’t be answered definitively because the answers often depend on a highly complex and interrelated set of factors, both known and unknown.” In other words, the exact kind of problems you’re likely to run into in real life and at work.

So, how do you solve a mystery? Well, if you’ve understood the distinction between puzzles and mysteries you can probably guess what I’m about to say. There’s no easy method which works for all mysteries. Their very ambiguity and lack of clarity insures that this is so. But, there are things you do can do to improve your ability to solve these kinds of problems. Here are a few steps to take.

- Practice solving mysteries. Like any other skill the more you practice solving these kinds of problems the better you will become at solving them. And, it should be easy to find such problems as they crop up in everyday life all of the time. Here are some possible examples:

[A] How can I achieve a better balance between all my responsibilities including work, college, and family?

[B] How can I find a career that will allow me to earn enough money to support myself and my family and also allow me to grow and build my skills and talents?

I know what you’re thinking. Sure, these are real world problems and I’ve even faced some of them but how can I build the skills I need to solve these problems before taking these problems on? It does no good to practice on these very difficult problems.

So, to prepare for solving these kinds of problems here are some other potential helpful steps.

- Learn as much as you can about as many topics as you can. Solving mysteries often involves drawing on knowledge from a variety of sources. It is quite likely that many of the things you’re now learning (even those you think are irrelevant) may turn out to be helpful at some point in solving a problem. So, take advantage of the opportunity to really learn about Reasoning,Computers, mathematics, and all the other subjects you’re learning now. That time will pay off.
- Make connections. A lot of problems are solved by finding interesting, creative connections between seemingly unrelated topics. A good example here is Steve Jobs’ application of his knowledge of calligraphy to the Apple operating system. Another is the psychiatrist Jeffrey Schwartz’s development of a treatment for OCD (obsessive compulsive disorder) by combining Buddhism and Austrian economics.
- Read books about mysteries, problem solving, and even mystery novels. Sherlock Holmes is a great place to start. Reading the Conan Doyle’s stories of the great detective reveal some basic principles of problem solving which can apply to everyday life. Daniel Smith’s book How to Think Like Sherlock is another good resource.
- Solve simpler mysteries first. Rather than taking on the more complex type of real world problems mentioned above, begin with simpler, but still real, problems. Never mind solving your work-life balance problem right off. Start with solving this problem: How can I keep from losing my phone every time I get ready to go somewhere?
- Adopt a problem-solving mindset. Be observant of your surroundings and attuned to what you can do to improve how you live, work, or do simple things. Thomas Edison exemplifies this mindset very well. He often presented his lab assistants with the following challenge. He would hand them some ordinary item (like an iron or a fountain pen) and say “There’s a better way. Find it.” Adopt that mentality in your life. Whatever you’re doing ask whether there is a better way: easier, more efficient, more effective.
- Learn about design thinking. Lastly, you may want to learn about design thinking. I’ve made a few resources available that provide a brief introduction to the basic ideas of design. The important feature is to solve problems with the end user in mind. When you’re trying to solve a problem be sure you understand for whom you are solving it and what their needs are. That will allow you to focus on the best solutions given what they’re facing.
- Identify the problem: In simple terms, you need to identify the nature of the problem and deconstructed and develop an effective set of actions to address the challenges. Furthermore, in some challenging situations, several students are overwhelmed with emotions and they just see big obstacles or trouble. But great problem solvers generally identify the roots of the problematic situation.
- Define the main elements of the issue: You need to break down the problem into small pieces or smaller and manageable parts by defining the major elements of the problem. It is an important step and skill to develop both managerial and psychologically instead of just facing a giant or a scary impossible mountain.
- Understand possible situations: Finding possible solutions is quite challenging in the problem solving process as on the surface it looks like most of the work is done already and the ultimate goal is closed. But in reality students need to look for simplistic ways to address these elements of the problems. They need to find the most effective ways and turn them into an opportunity to make a strong success story.

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