Solving Problems

Learning Objectives

  • Describe problem solving strategies, including algorithms and heuristics
  • Explain some common roadblocks to effective problem solving, including choice blindness

People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

Problem-Solving Strategies

When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them. For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

Table 1. Problem-Solving Strategies
Method Description Example
Trial and error Continue trying different solutions until problem is solved Restarting phone, turning off WiFi, turning off bluetooth in order to determine why your phone is malfunctioning
Algorithm Step-by-step problem-solving formula Instruction manual for installing new software on your computer
Heuristic General problem-solving framework Working backwards; breaking a task into steps

Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

  • When one is faced with too much information
  • When the time to make a decision is limited
  • When the decision to be made is unimportant
  • When there is access to very little information to use in making the decision
  • When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Watch It

What problem-solving method could you use to solve Einstein’s famous riddle?

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Everyday Connections: Solving Puzzles

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (Figure 1) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

A four column by four row Sudoku puzzle is shown. The top left cell contains the number 3. The top right cell contains the number 2. The bottom right cell contains the number 1. The bottom left cell contains the number 4. The cell at the intersection of the second row and the second column contains the number 4. The cell to the right of that contains the number 1. The cell below the cell containing the number 1 contains the number 2. The cell to the left of the cell containing the number 2 contains the number 3.

Figure 1. How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

Here is another popular type of puzzle that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

A square shaped outline contains three rows and three columns of dots with equal space between them.

Figure 2. Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

Take a look at the “Puzzling Scales” logic puzzle below (Figure 3). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

A puzzle involving a scale is shown. At the top of the figure it reads: “Sam Loyds Puzzling Scales.” The first row of the puzzle shows a balanced scale with 3 blocks and a top on the left and 12 marbles on the right. Below this row it reads: “Since the scales now balance.” The next row of the puzzle shows a balanced scale with just the top on the left, and 1 block and 8 marbles on the right. Below this row it reads: “And balance when arranged this way.” The third row shows an unbalanced scale with the top on the left side, which is much lower than the right side. The right side is empty. Below this row it reads: “Then how many marbles will it require to balance with that top?”

Figure 3. The puzzle reads, “Since the scales now balance…and balance when arranged this way, then how many marbles will it require to balance with that top?

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Pitfalls to Problem-Solving

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now. Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

Link to Learning

Check out this Apollo 13 scene where the group of NASA engineers are given the task of overcoming functional fixedness.

Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

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In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. This bias proves that first impressions do matter and that we tend to look for information to confirm our initial judgments of others.

Watch It

Watch this video from the Big Think to learn more about the confirmation bias.

Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision. To use a common example, would you guess there are more murders or more suicides in America each year? When asked, most people would guess there are more murders. In truth, there are twice as many suicides as there are murders each year. However, murders seem more common because we hear a lot more about murders on an average day. Unless someone we know or someone famous takes their own life, it does not make the news. Murders, on the other hand, we see in the news every day. This leads to the erroneous assumption that the easier it is to think of instances of something, the more often that thing occurs.

Watch It

Watch the following video for an example of the availability heuristic.

Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in Table 2 below.

Table 2. Summary of Decision Biases
Bias Description
Anchoring Tendency to focus on one particular piece of information when making decisions or problem-solving
Confirmation Focuses on information that confirms existing beliefs
Hindsight Belief that the event just experienced was predictable
Representative Unintentional stereotyping of someone or something
Availability Decision is based upon either an available precedent or an example that may be faulty

Link to Learning

Learn more about heuristics and common biases through the article, “8 Common Thinking Mistakes Our Brains Make Every Day and How to Prevent Them” by Belle Beth Cooper.

You can also watch this clever music video explaining these and other cognitive biases.

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Think It Over

Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

Psych in Real Life: Choice Blindness

Some choices are easy (“Do you want pepperoni or anchovies on your pizza?”) and some choices are hard (“Are you going to get Amazon Echo or Google Home?”), but most of us like to think that we “know our own mind”—that is, when we finally make a choice, we are clear about our decision. Research by psychologists in Sweden shows that this confidence in our own self-knowledge may not always be justified.

Choice blindness is the failure to recall a choice immediately after we have made that choice. If you go to an ice cream store, order a chocolate cone, and then accept a strawberry cone without noticing, that is choice blindness. If you go to an electronics store, select the new 55-inch Vizio television, and then fail to notice when they bring out (and expect you to pay for) the far more expensive 55-inch Sony television, that is choice blindness. If you order a burger and fries, and then don’t notice when soup-and-salad is placed in front of you, that is choice blindness.

As you have seen, Johannson, Hall, and their colleagues[1] found a method for inducing choice blindness in a laboratory setting, but they wanted to do more than simply demonstrate that people sometimes forget their choices. As psychological scientists, their goal is to explore an interesting phenomenon (i.e., choice blindness) to understand why it happens and to see if it tells us anything new about the way our minds work.

The Attraction Preference Experiment

You can learn the basics of the experiment conducted by Petter Johannson, Lars Hall and their colleagues by watching the following video[2].

Johannson and Hall were curious to see how often people noticed that there was a mismatch between their choice and the picture they were told they had chosen. Here’s how the experiment worked. Imagine that you are sitting across a table from an experimenter, who is dressed in a long sleeved black shirt. He shows you a pair of pictures of head-and-shoulder shots of two males or two females. On each trial, you indicate which of the two people in the pictures you find more attractive. After you make your choice, the experimenter hands you the card you just pointed at and asks you to explain why you preferred this person.

Except that this didn’t always happen this way. Using a magician’s trick, on some trials, when the experimenter handed you the card, he actually handed you the card you did NOT choose.

Watch this video to see the experimenter’s explain it.

The researchers tested 120 college students (70 female, 50 male). The pictures were all of women. As the video showed, they made their choice and then immediately explained the reasons for their preference. Only 13% of the switches were detected immediately. Approximately 10% more switches were mentioned “retrospectively”, where a participant initially justified choosing the switched face, but later indicated some suspicion that the wrong picture had been presented. Most participants who detected a switch attributed it to a technical error rather than suspecting that it was part of the research procedure.

But is it Real? The Value of Replication

The video you just watched described an experiment with a surprising result: more than 75% of the time, people make a choice and then, without indicating that anything is amiss, they proceed to justify a choice they did not make. But how solid is this study and how much can we believe these results? Maybe the choice blindness experiment reported real results, but (even assuming that the experimenters were completely honest and careful) could this have just been a weird outcome that will never happen again? In other words, is this a reliable result or just a fluke?

There is only one way to determine if a phenomenon is reliable, and that is replication. If you can’t replicate an effect, then you shouldn’t waste people’s time reading about it in a scientific paper.

There are at least three different types of replication.

  1. Direct Replication: Conduct exactly the same study again, usually with new participants from the same population as the original study. A successful replication would produce results similar to those in the original study.
  2. Systematic Replication: Conduct a study that is similar to the original one, but using slightly different methods or stimuli.
  3. Conceptual Replication: Conduct a very different study that still tests the original idea. In the current context, a conceptual replication would test the choice blindness idea using a method that did not involve choosing attractive people.

So, can you believe the choice blindness phenomenon?

Case #1

In the years just before they published their 2005 study, the experimenters conducted two similar studies. For these studies, the pictures were presented on a computer screen, and the computer switched the pictures on the critical trials, so no magic was necessary. The results were very similar to the results of the study reported in the video above.

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Case #2

When the BBC (British Broadcasting Corporation) made the video, they reconstructed the experiment in a form very similar to the original. They reported that 80% of the participants did not notice any switching of pictures—a result very similar to the original. Unfortunately, without a published report of the study, it is impossible to know if the scientific standards of the original study had been maintained.

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Case #3

In 2014, researchers at the National University of Singapore reported a study similar to the experiment shown in the video. The stimuli were presented using a computer rather than a live experimenter. In addition to choosing one of the two faces, the participants rated their confidence in their choice and they typed their explanation of their preference. The faces were all of Caucasian women (as in the original study), but the participants were all of Asian descent (ethnic backgrounds: Chinese, Indian, and Vietnamese). Their results were similar to those of the original study.

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Case #4

Here is video showing another study by Johannson and Hall. The video has no sound—only subtitles.

Before an election, researchers polled people about their political preferences, selecting either right-wing or left-wing policies. The researchers secretly copied down the opposite of their responses and had the participants explain their answers. Fascinatingly, many people defended the views they said to have disagreed with.

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Link to Learning

Visit this link to watch another video related about conceptual replication, this time related to taste.

From Phenomenon to Scientific Exploration

What you saw in the video is what a scientist would call a phenomenon—that is, a behavior that happens under certain conditions. The video showed that, if an experimenter is tricky enough, he or she can get people to justify choices that they never made. If you find this phenomenon interesting, then it may be worth your time to try to find out why it happens. (If you didn’t think it was interesting, then you will probably move on to find something that inspires you.)

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Any of the choices in the list above could explain—fully or in part—the choice blindness phenomenon, but each idea would need to be tested. That is where the science comes in. The starting point for science is something interesting (a surprising phenomenon). If we are motivated to ask why something happened, then we jump into the real work of science: exploring possible explanations.

The next scientific step systematically (i.e., carefully and with specific purposes) changes elements of the procedures or stimuli to see how these changes affect the results. Remember that our dependent variable is the probability that the change in faces will be detected. So now we try to learn more about change blindness by seeing how changing specific details (independent variables) either increase or decrease people’s likelihood of noticing the switch in faces.

Two Variables: Time and Similarity

In the 2005 study, Johansson and Hall looked at two interesting variables that might influence detection of the mismatch. First, how rushed were the participants to make their decision? They gave some people only 2 seconds to choose the more attractive person. Others were given 5 seconds, and another group was given as long as people wanted (free choice). Should more time make someone more likely or less likely to notice that they have been given the picture they did not choose?

The second variable was how similar the two faces were to one another. In some cases, the two faces were similar to each other in general features, while in other cases the two faces were more distinctly different. If the two faces are quite different, how should that affect your ability to notice?

Two sets of images. One shows incredibly similar faces of caucasian women, while the next pair shows dissimilar female faces.

Figure 4. Johansson and Hall wanted to know if people were more likely to notice a similar or dissimilar image when shown a picture they did not chose.

The Results

If we put the two manipulated variables (time and similarity) together, that gives us six conditions:

Graph showing the similarity of two faces and the time time choose variables. In any given situation, participates had either 2 seconds to choose similar faces, 2 seconds to choose dissimilar faces, 5 seconds to choose similar or dissimilar faces, and unlimited time to choose similar or dissimilar faces.

Figure 5. The six conditions of the experiment show that people were shown either similar or dissimilar faces, or given various amounts of time.

Try It

In the figure below, adjust the bars to fit your predictions about how often people would notice the picture switch. Higher bars mean people more often noticed that the cards had been switched. Lower bars mean that people made one choice and didn’t notice when they were given the wrong picture. This isn’t easy because you need to take account of the two variables: (1) amount of time looking at the pictures before your choice and (2) similarity of the faces in the pictures.

Most people make predictions that put the red bars lowest, the purple bars in the middle, and the green bars highest. This supports the idea that the more time you have to look at the pictures, the more likely you are to notice that the picture you have chosen is not the one the experimenter gave you.

People also expect that the switch will be more noticeable if the faces are dissimilar. For example, if we look at the green bars with unlimited time, it makes sense that people will generally notice when the faces have been switched on them, and this is much greater when the two faces are very different (dissimilar condition) than when they are similar (similar condition).

Click here to see the what most people expect the results to be.

What Do These Results Tell Us?

With just these results, we are still a long way from understanding choice blindness. The experiment you just read takes us a couple of steps in the right direction. First, the similarity of the faces is (surprisingly) not a particularly influential factor. This does not mean that the case is closed and similarity is unimportant, but it does suggest that confusion due to similarity may not be the whole story.

The amount of time participants had to choose did have a big influence on detection of a switch in faces. When the participants were rushed (2 second condition), the chance of detecting a change was very slight. Given 5 seconds, detection improved, but not by a great amount. Unlimited time to choose made a substantial difference, but detection was still only around 25%. These results suggest that time to choose may be an important factor, but it is not the whole story. Furthermore, we are still not sure what it was about the extra time that led to improved detection. Did more time allow the participants to remember the faces better? Or perhaps their memory for faces was not improved, but they had more time to think of reasons they preferred one person over the other (her earrings, the way her hair flowed, a look in her eyes). These preferred features could signal to them that something was missing when the wrong picture was presented.

If you explore the research literature on choice blindness, you will find that the phenomenon has been studied from many angles. Experiments have been conducted in university laboratories and on the streets of a city in the Netherlands. Choice blindness in the video involved remembering what someone looked like, but choices involving sound, taste, and smell have also produced choice blindness. Even people’s judgments about their own personality and preferences is open to choice blindness. We don’t fully understand when and why choice blindness occurs, but it is an intriguing phenomenon, open to scientific curiosity.

A Final Thought

In a TED talk from 2016, Petter Johannson describes choice blindness to an audience. At the end he acknowledges that choice blindness can make people look silly or worse, but he also believes that this research provides us with an insight about people that may be reason for hope in a world seemingly full of discord and bereft of compromise.

Here are the closing lines from his TED talk:

This [choice blindness] may all seem a bit disturbing. But if you want to look at it from a positive direction, it could be seen as showing: Okay, so we’re all a little bit more flexible than we think. We can change our minds. Our attitudes are not set in stone. And we can also change the minds of others if we can only get them to engage with the issue and see it from the opposite view. … Getting rid of the need to stay consistent is actually a huge relief and makes [social] life so much easier to live.

So the conclusion must be, “Know that you don’t know yourself. Or at least not as well as you think you do.”


algorithm: problem-solving strategy characterized by a specific set of instructions
anchoring bias: faulty heuristic in which you fixate on a single aspect of a problem to find a solution
availability heuristic: faulty heuristic in which you make a decision based on information readily available to you
confirmation bias: faulty heuristic in which you focus on information that confirms your beliefs
functional fixedness: inability to see an object as useful for any other use other than the one for which it was intended
heuristic: mental shortcut that saves time when solving a problem
hindsight bias: belief that the event just experienced was predictable, even though it really wasn’t
mental set: continually using an old solution to a problem without results
problem-solving strategy: method for solving problems
representative bias: faulty heuristic in which you stereotype someone or something without a valid basis for your judgment
trial and error: problem-solving strategy in which multiple solutions are attempted until the correct one is found
working backwards: heuristic in which you begin to solve a problem by focusing on the end result

  1. Petter Johannson, Lars Hall, Sverker Sikström, & Andreas Olsson. (2005). Failure to detect mismatches between intention and outcome in a simple decision task. Science, 310 (7 October 2005), 116-119.
  2. The video is a segment from a BBC video from the science series called Horizons. This particular show was about decision making
  3. The results are more complex than the figure suggests. The data shown above are limited to first detections of the switch in pictures. After people notice that there has been a switch, they tend to be a bit suspicious and they are more vigilant about noticing changes. If all trials are taken into account, the data are still similar to these, but not quite as pretty. See the original paper for all the details.