# 4.2 Problem Solving Methods: Definition & Types

There’s more than one way to solve a problem. In this lesson, we’ll review the five most common methods: trial and error, difference reduction, means-ends analysis, working backwards, and analogies.

## What Are Problem Solving Methods?

Problem solving skills are among the most valued skills in the workforce today because they can be applied to dozens of situations. A person with a physics degree might get hired as a computer programmer because of their problem solving skills. Or an industrial engineer might have an easier time getting a job as an urban planner because they used problem solving skills at their previous job.

Problem solving methods are the steps we use to find solutions to problems and issues. Humans are naturally quite good at problem solving, and we often use sophisticated methods that we don’t even know we’re using to try to get to the answer. Learning about the methods will enable you to recognize the approaches you already use and identify other approaches that could be useful for you. Then, you will have several tools to help you strategize solutions to difficult problems.

## Trial and Error

Trial and error is a way of solving problems through repeated attempts, trying something different every time until you are successful. Although this approach sounds random, problem solving through trial and error is efficient only when you can base your attempts on some prior knowledge and information.

For example, a programmer using a new language knows that quotes should surround pieces of text but is unsure whether that language uses single quotes or double quotes. Rather than look it up, it will be quicker just to try both (which would be the trial), since there are only two possibilities. If single quotes are incorrect (which would be an error), then the programmer will try again with double quotes.

But, if you have no knowledge of how programming languages work at all, then you’re out of luck. No amount of playing around with random bits of text is likely to get you to a working computer program. So when there are many, even unlimited, options, other problem-solving methods are sometimes best.

## Difference Reduction

Difference reduction requires you to break down a large task into smaller steps. The first thing you do is ask yourself what step will take you from where you are to as close as possible to the final goal. You take that step and repeat the process until you finally reach the goal.

For example, if you need to get from the street to the inside of your home, you might have to:

1. Unlock the gate
2. Swing open the gate
3. Walk to the house
4. Unlock the house
5. Open the door

Sometimes difference reduction is not the quickest way to get to your goal – sometimes you have to take one step backwards to take a step forwards. For example, the step that will get you closest to being inside your home might be to walk to the door. But if you’re locked out of the house, you might first need to visit the neighbor for the spare key.

## Means-Ends Analysis

With means-ends analysis you compare your current situation and the situation you want to arrive at, identify the most significant difference between those two situations, and then create a sub-goal to remove that difference.

If you want to work as a doctor, the most significant difference between where you are and where you want to be is having a job as a doctor – that’s what would have to be different in your life to make that happen. Gradually, you’ll come to the conclusion that you don’t yet have the knowledge or the degree necessary, but the biggest difference in your actual life is the job.

Means-ends analysis is easier to explain using examples. Let’s say that your house is messy. Your goal is for it to be tidy. Here are the steps you would go through to complete a means-ends analysis:

• Step 1: What’s the biggest difference between these two situations? Nothing is where it should be.
• Step 2: What would change this? Moving objects to where they belong, throwing them away, or hiding them so they are no longer in view.
• Step 3: You decide to move the objects to where they belong. But not everything has particular place that it belongs, like the nice vase your mother just bought you. So you create a new sub-goal: you want each object in your house to have a place it belongs.
• Step 4: What’s the biggest difference between these two situations? There isn’t enough storage space for everything.
• Step 5: What would cause there to be enough storage space? Reorganizing things to make a space for each object, buying a storage box or cupboard, or moving house.
• Step 6: You decide to buy a new storage box. But you don’t have any money, so you create a new sub-goal: you want to have some money.
• Step 7: Now, what’s the biggest difference between these two situations?

And on and on the process continues. While this sounds complicated, means-end analysis is something you do all the time quickly, without realizing it.

Means-ends analysis might sound quite similar to difference reduction, and it’s true that they have a lot in common. But difference reduction doesn’t provide an answer for what to do if removing the biggest difference isn’t currently possible. Means-ends analysis provides a way to solve sub-problems as and when they come up.

## Working Backwards

Working backwards involves examining the result you want and figuring out the steps that would lead to that result. In a lot of real-life situations, working backwards just doesn’t make sense. But, it can work very well in mathematical proofs because the math result you want can be rearranged to get closer to what you start with.

Let’s go back to the example where you want to work as a doctor. Rather than jumping right to the biggest difference – a job as a doctor, it might make sense to work backwards. You need to get a job as a doctor, which requires a 3 – 7 year residency, which you can’t get into unless you’ve completed a doctorate in medicine, which in turn requires a bachelor’s degree in science. So working backwards, perhaps your first step is to research the admission requirements for a science degree.

## Analogies

Last of all, we can use analogies, when you use a situation or idea to symbolically represent another, such as a story. Sometimes this can help you come up with a solution that isn’t obvious.

The classic example of an analogy problem solving is the issue of how to destroy a cancerous tumor by using radiation that also destroys healthy cells. If the radiation has enough energy to destroy the cancer, it will destroy healthy cells. And if it doesn’t have enough energy, it won’t destroy the cancer. It seems hopeless, but using the following story, or analogy, can help people with no medical background figure out the solution.

The story goes that an army wants to conquer a fortress. The roads to that fortress are mined and can be passed safely only by small numbers of people, which won’t be enough to conquer the fortress. But if the whole army goes in together, it will be killed by the mines. The solution is to split up the army into small groups and use every path to the fortress, so that each small group can reach the fortress. The story allows people to quickly come to the conclusion that attacking the cancer with radiation from many different directions will allow the healthy cells to be protected.

## Lesson Summary

Problem solving is a highly sought-after skill. There are many techniques to problem solving. Examples include trial and error, difference reduction, means-ends analysis, working backwards, and analogies.

• Trial and error requires you to try various things over and over until you come up with the correct solution.
• With difference reduction you break things down into sub-goals and steps, taking the step that will get you closest your goal each time.
• If you use means-ends analysis, you ask yourself what the biggest difference is between your current situation and goal, and then ask yourself how you can change that difference. This will often involve creating sub-steps along the way.
• Working backwards involves starting with the end result and figuring out the steps you need to take to get to that goal.
• Finally, analogies are symbols or stories that represent something else and which help you discover creative ideas that might not come to mind otherwise.