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Article • 11 min read

Getting to the Root of a Problem Quickly

By the Mind Tools Content Team

Have you ever had a problem that refused to go away? No matter what you did, sooner or later it would return, perhaps in another form.

Stubborn or recurrent problems are often symptoms of deeper issues. "Quick fixes" may seem convenient, but they often solve only the surface issues and waste resources that could otherwise be used to tackle the real cause.

In this article and in the video, below, we look at the 5 Whys technique (sometimes known as 5Y). This is a simple but powerful tool for cutting quickly through the outward symptoms of a problem to reveal its underlying causes – so that you can deal with it once and for all.

Origins of the 5 Whys Technique

Sakichi Toyoda, the Japanese industrialist, inventor, and founder of Toyota Industries, developed the 5 Whys technique in the 1930s. It became popular in the 1970s, and Toyota still uses it to solve problems today.

Toyota has a "go and see" philosophy. This means that its decision making is based on an in-depth understanding of what's actually happening on the shop floor , rather than on what someone in a boardroom thinks might be happening.

The 5 Whys technique is true to this tradition, and it is most effective when the answers come from people who have hands-on experience of the process or problem in question.

The method is remarkably simple: when a problem occurs, you drill down to its root cause by asking "Why?" five times. Then, when a counter-measure becomes apparent, you follow it through to prevent the issue from recurring.

The 5 Whys uses "counter-measures," rather than "solutions." A counter-measure is an action or set of actions that seeks to prevent the problem from arising again, while a solution may just seek to deal with the symptom. As such, counter-measures are more robust, and will more likely prevent the problem from recurring.

When to Use a 5 Whys Analysis

You can use 5 Whys for troubleshooting, quality improvement, and problem solving, but it is most effective when used to resolve simple or moderately difficult problems.

It may not be suitable if you need to tackle a complex or critical problem. This is because 5 Whys can lead you to pursue a single track, or a limited number of tracks, of inquiry when, in fact, there could be multiple causes. In cases like these, a wider-ranging method such as Cause and Effect Analysis or Failure Mode and Effects Analysis may b e more effective.

This simple 5 Whys technique, however, can often direct you quickly to the root cause of a problem. So, whenever a system or process isn't working properly, give it a try before you embark on a more in-depth approach – and certainly before you attempt to develop a solution.

The tool's simplicity gives it great flexibility, too, and 5 Whys combines well with other methods and techniques, such as Root Cause Analysis . It is often associated with Lean Manufacturing , where it is used to identify and eliminate wasteful practices. It is also used in the analysis phase of the Six Sigma quality improvement methodology.

How to Use the 5 Whys

The model follows a very simple seven-step process: [1]

1. Assemble a Team

Gather together people who are familiar with the specifics of the problem, and with the process that you're trying to fix. Include someone to act as a facilitator , who can keep the team focused on identifying effective counter-measures.

2. Define the Problem

If you can, observe the problem in action. Discuss it with your team and write a brief, clear problem statement that you all agree on. For example, "Team A isn't meeting its response time targets" or "Software release B resulted in too many rollback failures."

Then, write your statement on a whiteboard or sticky note, leaving enough space around it to add your answers to the repeated question, "Why?"

3. Ask the First "Why?"

Ask your team why the problem is occurring. (For example, "Why isn't Team A meeting its response time targets?")

Asking "Why?" sounds simple, but answering it requires serious thought. Search for answers that are grounded in fact: they must be accounts of things that have actually happened, not guesses at what might have happened.

This prevents 5 Whys from becoming just a process of deductive reasoning, which can generate a large number of possible causes and, sometimes, create more confusion as you chase down hypothetical problems.

Your team members may come up with one obvious reason why, or several plausible ones. Record their answers as succinct phrases, rather than as single words or lengthy statements, and write them below (or beside) your problem statement. For example, saying "volume of calls is too high" is better than a vague "overloaded."

4. Ask "Why?" Four More Times

For each of the answers that you generated in Step 3, ask four further "whys" in succession. Each time, frame the question in response to the answer you've just recorded.

Try to move quickly from one question to the next, so that you have the full picture before you jump to any conclusions.

The diagram, below, shows an example of 5 Whys in action, following a single lane of inquiry.

Figure 1: 5 Whys Example (Single Lane)

solve problems quickly

The 5 Whys method also allows you to follow multiple lanes of inquiry. An example of this is shown in Figure 2, below.

In our example, asking "Why was the delivery late?" produces a second answer (Reason 2). Asking "Why?" for that answer reveals a single reason (Reason 1), which you can address with a counter-measure.

Similarly, asking "Why did the job take longer than expected?" has a second answer (Reason 2), and asking "Why?" at this point reveals a single reason (Reason 1). Another "Why?" here identifies two possibilities (Reasons 1 and 2) before a possible counter-measure becomes evident.

There is also a second reason for "Why we ran out of printer ink" (Reason 2), and a single answer for the next "Why?" (Reason 1), which can then be addressed with a counter-measure.

Figure 2: 5 Whys Example (Multiple Lanes)

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Step 5. Know When to Stop

You'll know that you've revealed the root cause of the problem when asking "why" produces no more useful responses, and you can go no further. An appropriate counter-measure or process change should then become evident. (As we said earlier, if you're not sure that you've uncovered the real root cause, consider using a more in-depth problem-solving technique like Cause and Effect Analysis , Root Cause Analysis , or FMEA .)

If you identified more than one reason in Step 3, repeat this process for each of the different branches of your analysis until you reach a root cause for each one.

The "5" in 5 Whys is really just a " rule of thumb ." In some cases, you may need to ask "Why?" a few more times before you get to the root of the problem.

In other cases, you may reach this point before you ask your fifth "Why?" If you do, make sure that you haven't stopped too soon, and that you're not simply accepting "knee-jerk" responses.

The important point is to stop asking "Why?" when you stop producing useful responses.

As you work through your chain of questions, you may find that someone has failed to take a necessary action. The great thing about 5 Whys is that it prompts you to go further than just assigning blame , and to ask why that happened. This often points to organizational issues or areas where processes need to be improved.

6. Address the Root Cause(s)

Now that you've identified at least one root cause, you need to discuss and agree on the counter-measures that will prevent the problem from recurring.

7. Monitor Your Measures

Keep a close watch on how effectively your counter-measures eliminate or minimize the initial problem. You may need to amend them, or replace them entirely. If this happens, it's a good idea to repeat the 5 Whys process to ensure that you've identified the correct root cause.


A similar question-based approach known as "appreciation" can help you to uncover factors in a situation that you might otherwise miss.

It was originally developed by the military to assist commanders in gaining a comprehensive understanding of any fact, problem or situation. But you can also apply it in the workplace.

Starting with a fact, you first ask the question, "So what?" – in other words, what are the implications of that fact? Why is this fact important?

You then continue asking that question until you've drawn all possible conclusions from it.

The major difference between this and the 5 Whys technique is that appreciation is often used to get the most information out of a simple fact or statement, while 5 Whys is designed to drill down to the root of a problem.

5 Whys Infographic

See our infographic on the 5 Whys and use it to get to the root of your problems!

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Bear in mind that appreciation can restrict you to one line of thinking. For instance, once you've answered your first "So what?" question, you might follow a single line of inquiry to its conclusion. To avoid this, repeat the appreciation process several times over to make sure that you've covered all bases.

The 5 Whys strategy is a simple, effective tool for uncovering the root of a problem. You can use it in troubleshooting, problem-solving, and quality-improvement initiatives.

Start with a problem and ask why it is occurring. Make sure that your answer is grounded in fact, and then ask the question again. Continue the process until you reach the root cause of the problem, and you can identify a counter-measure that will prevent it from recurring.

Bear in mind that this questioning process is best suited to simple or moderately difficult problems. Complex problems may benefit from a more detailed approach, although using 5 Whys will still give you useful insights.

[1] Pojasek, R. (2000). 'Asking "Why?" Five Times,' Environmental Quality Management , Volume 10, Issue 1, 79–84. Available here . [Accessed July 1, 2022.]

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10 Ways to Do Fast Math: Tricks and Tips for Doing Math in Your Head

You don’t have to be a math teacher to know that a lot of students—and likely a lot of parents (it’s been awhile!)—are intimidated by math problems, especially if they involve large numbers. Learning techniques on how to do math quickly can help students develop greater confidence in math , improve math skills and understanding, and excel in advanced courses.

If it’s your job to teach those, here’s a great refresher.

Fast math tricks infographic. Learning techniques on how to do math quickly can help students develop greater confidence in math, improve math skills and understanding, and excel in advanced courses. Add large numbers. Subtract 1,000. Multiplying 5 times any number. Division tricks. Multiplying by 9. Percentage. Square a 2-digit number ending in 5. Tough multiplication. Multiplying numbers ending in zero. 10 and 11 multiplication tricks.

Fast math tricks infographic

10 tricks for doing fast math

Here are 10 fast math strategies students (and adults!) can use to do math in their heads. Once these strategies are mastered, students should be able to accurately and confidently solve math problems that they once feared solving.

1. Adding large numbers

Adding large numbers just in your head can be difficult. This method shows how to simplify this process by making all the numbers a multiple of 10. Here is an example:

While these numbers are hard to contend with, rounding them up will make them more manageable. So, 644 becomes 650 and 238 becomes 240.

Now, add 650 and 240 together. The total is 890. To find the answer to the original equation, it must be determined how much we added to the numbers to round them up.

650 – 644 = 6 and 240 – 238 = 2

Now, add 6 and 2 together for a total of 8

To find the answer to the original equation, 8 must be subtracted from the 890.

890 – 8 = 882

So the answer to 644 +238 is 882.

2. Subtracting from 1,000

Here’s a basic rule to subtract a large number from 1,000: Subtract every number except the last from 9 and subtract the final number from 10

For example:

1,000 – 556

Step 1: Subtract 5 from 9 = 4

Step 2: Subtract 5 from 9 = 4

Step 3: Subtract 6 from 10 = 4

The answer is 444.

3. Multiplying 5 times any number

When multiplying the number 5 by an even number, there is a quick way to find the answer.

For example, 5 x 4 =

When multiplying an odd number times 5, the formula is a bit different.

For instance, consider 5 x 3.

4. Division tricks

Here’s a quick way to know when a number can be evenly divided by these certain numbers:

5. Multiplying by 9

This is an easy method that is helpful for multiplying any number by 9. Here is how it works:

Let’s use the example of 9 x 3.

Step 1 : Subtract 1 from the number that is being multiplied by 9.

3 – 1 = 2

The number 2 is the first number in the answer to the equation.

Step 2 : Subtract that number from the number 9.

9 – 2 = 7

The number 7 is the second number in the answer to the equation.

So, 9 x 3 = 27

6. 10 and 11 times tricks

The trick to multiplying any number by 10 is to add a zero to the end of the number. For example, 62 x 10 = 620.

There is also an easy trick for multiplying any two-digit number by 11. Here it is:

Take the original two-digit number and put a space between the digits. In this example, that number is 25.

Now add those two numbers together and put the result in the center:

2_(2 + 5)_5

The answer to 11 x 25 is 275.

If the numbers in the center add up to a number with two digits, insert the second number and add 1 to the first one. Here is an example for the equation 11 x 88

(8 + 1)_6_8

There is the answer to 11 x 88: 968

7. Percentage

Finding a percentage of a number can be somewhat tricky, but thinking about it in the right terms makes it much easier to understand. For instance, to find out what 5% of 235 is, follow this method:

8. Quickly square a two-digit number that ends in 5

Let’s use the number 35 as an example.

35 squared = [3 x (3 + 1)] & 25

[3 x (3 + 1)] = 12

12 & 25 = 1225

35 squared = 1225

9. Tough multiplication

When multiplying large numbers, if one of the numbers is even, divide the first number in half, and then double the second number. This method will solve the problem quickly. For instance, consider

Step 1: Divide the 20 by 2, which equals 10. Double 120, which equals 240.

Then multiply your two answers together.

10 x 240 = 2400

The answer to 20 x 120 is 2,400.

10. Multiplying numbers that end in zero

Multiplying numbers that end in zero is actually quite simple. It involves multiplying the other numbers together and then adding the zeros at the end. For instance, consider:

Step 1: Multiply the 2 times the 4

Step 2: Put all four of the zeros after the 8

200 x 400= 80,000

Practicing these fast math tricks can help both students and teachers improve their math skills and become secure in their knowledge of mathematics—and unafraid to work with numbers in the future.

You may also like to read

From our blog

How to Solve Math Problems Faster: 15 Techniques to Show Students

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“Test time. No calculators.”

You’ll intimidate many students by saying this, but teaching techniques to solve math problems with ease and speed can make it less daunting.

This can also  make math more rewarding . Instead of relying on calculators, students learn strategies that can improve their concentration and estimation skills while building number sense. And, while there are educators who  oppose math “tricks”  for valid reasons, proponents point to benefits such as increased confidence to handle difficult problems.

Here are 15 techniques to show students,  helping them solve math problems faster:

Addition and Subtraction

1. two-step addition.

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Many students struggle when learning to add integers of three digits or higher together, but changing the process’s steps can make it easier.

The first step is to  add what’s easy.  The second step is to  add the rest.

Let’s say students must find the sum of 393 and 89. They should quickly see that adding 7 onto 393 will equal 400 — an easier number to work with. To balance the equation, they can then subtract 7 from 89.

Broken down, the process is:

With this fast technique, big numbers won’t look as scary now.

2. Two-Step Subtraction

There’s a similar method for subtraction.

Remove what’s easy. Then remove what’s left.

Suppose students must find the difference of 567 and 153. Most will feel that 500 is a simpler number than 567. So, they just have to take away 67 from the minuend — 567 — and the subtrahend — 153 — before solving the equation.

Here’s the process:

Instead of two complex numbers, students will only have to tackle one.

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3. Subtracting from 1,000

You can  give students confidence  to handle four-digit integers with this fast technique.

To subtract a number from 1,000, subtract that number’s first two digits from 9. Then, subtract the final digit from 10.

Let’s say students must solve 1,000 – 438.  Here are the steps:

This also applies to 10,000, 100,000 and other integers that follow this pattern.

Multiplication and Division

4. doubling and halving.

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When students have to multiply two integers, they can speed up the process when one is an even number. They just need to  halve the even number and double the other number.

Students can stop the process when they can no longer halve the even integer, or when the equation becomes manageable.

Using 33 x 48 as an example,  here’s the process:

The only prerequisite is understanding the 2 times table.

5. Multiplying by Powers of 2

This tactic is a speedy variation of doubling and halving.

It simplifies multiplication if a number in the equation is a power of 2, meaning it works for 2, 4, 8, 16 and so on.

Here’s what to do:  For each power of 2 that makes up that number, double the other number.

For example, 9 x 16 is the same thing as 9 x (2 x 2 x 2 x 2) or 9 x 24. Students can therefore double 9 four times to reach the answer:

Unlike doubling and halving, this technique demands an understanding of exponents along with a strong command of the 2 times table.

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6. Multiplying by 9

For most students, multiplying by 9 — or 99, 999 and any number that follows this pattern — is difficult compared with multiplying by a power of 10.

But there’s an easy tactic to solve this issue, and  it has two parts.

First, students round up the 9  to 10. Second, after solving the new equation, they subtract the number they just multiplied by 10 from the answer.

For example, 67 x 9 will lead to the same answer as 67 x 10 – 67. Following the order of operations will give a result of 603. Similarly, 67 x 99 is the same as 67 x 100 – 67.

Despite more steps, altering the equation this way is usually faster.

7. Multiplying by 11

solve problems quickly

There’s an easier way for multiplying two-digit integers by 11.

Let’s say students must find the product of 11 x 34.

The idea is to put a space between the digits, making it 3_4. Then, add the two digits together and put the sum in the space.

The answer is 374.

What happens if the sum is two digits? Students would put the second digit in the space and add 1 to the digit to the left of the space.  For example:

It’s multiplication without having to multiply.

8. Multiplying Even Numbers by 5

This technique only requires basic division skills.

There are two steps,  and 5 x 6 serves as an example. First, divide the number being multiplied by 5 — which is 6 — in half. Second, add 0 to the right of number.

The result is 30, which is the correct answer.

It’s an ideal, easy technique for students mastering the 5 times table.

9. Multiplying Odd Numbers by 5

This is another time-saving tactic that works well when teaching students the 5 times table.

This one has three steps,  which 5 x 7 exemplifies.

First, subtract 1 from the number being multiplied by 5, making it an even number. Second, cut that number in half — from 6 to 3 in this instance. Third, add 5 to the right of the number.

The answer is 35.

Who needs a calculator?

10. Squaring a Two-Digit Number that Ends with 1

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Squaring a high two-digit number can be tedious, but there’s a shortcut if 1 is the second digit.

There are four steps to this shortcut,  which 812 exemplifies:

This work-around eliminates the difficulty surrounding the second digit, allowing students to work with multiples of 10.

11. Squaring a Two-Digit Numbers that Ends with 5

Squaring numbers ending in 5 is easier, as there are  only two parts of the process.

First, students will always make 25 the product’s last digits.

Second, to determine the product’s first digits, students must multiply the number’s first digit — 9, for example — by the integer that’s one higher — 10, in this case.

So, students would solve 952 by designating 25 as the last two digits. They would then multiply 9 x 10 to receive 90. Putting these numbers together, the  result is 9,025.

Just like that, a hard problem becomes easy multiplication for many students.

12. Calculating Percentages

Cross-multiplication is an  important skill  to develop, but there’s an easier way to calculate percentages.

For example, if students want to know what 65% of 175 is, they can multiply the numbers together and move the decimal place two digits to the left.

The result is 113.75, which is indeed the correct answer.

This shortcut is a useful timesaver on tests and quizzes.

13. Balancing Averages

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To determine the average among a set of numbers, students can balance them instead of using a complex formula.

Suppose a student wants to volunteer for an average of 10 hours a week over a period of four weeks. In the first three weeks, the student worked for 10, 12 and 14 hours.

To determine the number of hours required in the fourth week, the student must  add how much he or she surpassed or missed the target average  in the other weeks:

To learn the number of hours for the final week, the student must  subtract the sum from the target average:

With practice, this method may not even require pencil and paper. That’s how easy it is. 

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Word Problems

14. identifying buzzwords.

Students who struggle to translate  word problems  into equations will benefit from learning how to spot buzzwords — phrases that indicate specific actions.

This isn’t a trick. It’s a tactic.

Teach students to look for these buzzwords,  and what skill they align with in most contexts:

Be sure to include buzzwords that typically appear in their textbooks (or other classroom  math books ), as well as ones you use on tests and assignments.

As a result, they should have an  easier time processing word problems .

15. Creating Sub-Questions

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For complex word problems, show students how to dissect the question by answering three specific sub-questions.

Each student should ask him or herself:

These sub-questions help students avoid overload.

Instead of writing and analyzing each detail of the question, they’ll be able to identify key information. If you identify students who are struggling with these, you can use  peer learning  as needed.  

For more fresh approaches to teaching math in your classroom, consider treating your students to a range of  fun math activities .

Final Thoughts About these Ways to Solve Math Problems Faster

Showing these 15 techniques to students can give them the  confidence to tackle tough questions .

They’re also  mental math  exercises, helping them build skills related to focus, logic and critical thinking.

A rewarding class equals an  engaging class . That’s an easy equation to remember.

> Create or log into your teacher account on Prodigy  — a free, adaptive math game that adjusts content to accommodate player trouble spots and learning speeds. Aligned to US and Canadian curricula, it’s loved by more than 500,000 teachers and 15 million students.

What Are Heuristics?

These mental shortcuts can help people make decisions more efficiently

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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Steven Gans, MD is board-certified in psychiatry and is an active supervisor, teacher, and mentor at Massachusetts General Hospital.

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Verywell / Cindy Chung 

How to Make Better Decisions

Heuristics are mental shortcuts that allow people to solve problems and make judgments quickly and efficiently. These rule-of-thumb strategies shorten decision-making time and allow people to function without constantly stopping to think about their next course of action.

However, there are both benefits and drawbacks of heuristics. While heuristics are helpful in many situations, they can also lead to  cognitive biases . Becoming aware of this might help you make better and more accurate decisions.

Press Play for Advice On Making Decisions

Hosted by Editor-in-Chief and therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares a simple way to make a tough decision. Click below to listen now.

Follow Now : Apple Podcasts / Spotify / Google Podcasts

The History and Origins of Heuristics

Nobel-prize winning economist and cognitive psychologist Herbert Simon originally introduced the concept of heuristics in psychology in the 1950s. He suggested that while people strive to make rational choices, human judgment is subject to cognitive limitations. Purely rational decisions would involve weighing all the potential costs and possible benefits of every alternative.

But people are limited by the amount of time they have to make a choice as well as the amount of information they have at their disposal. Other factors such as overall intelligence and accuracy of perceptions also influence the decision-making process.

During the 1970s, psychologists Amos Tversky and Daniel Kahneman presented their research on cognitive biases. They proposed that these biases influence how people think and the judgments people make.

As a result of these limitations, we are forced to rely on mental shortcuts to help us make sense of the world. Simon's research demonstrated that humans were limited in their ability to make rational decisions, but it was Tversky and Kahneman's work that introduced the study of heuristics and the specific ways of thinking that people rely on to simplify the decision-making process.

How Heuristics Are Used

Heuristics play important roles in both  problem-solving  and  decision-making , as we often turn to these mental shortcuts when we need a quick solution.

Here are a few different theories from psychologists about why we rely on heuristics.

In order to cope with the tremendous amount of information we encounter and to speed up the decision-making process, our brains rely on these mental strategies to simplify things so we don't have to spend endless amounts of time analyzing every detail.

You probably make hundreds or even thousands of decisions every day. What should you have for breakfast? What should you wear today? Should you drive or take the bus? Fortunately, heuristics allow you to make such decisions with relative ease and without a great deal of agonizing.

There are many heuristics examples in everyday life. When trying to decide if you should drive or ride the bus to work, for instance, you might remember that there is road construction along the bus route. You realize that this might slow the bus and cause you to be late for work. So you leave earlier and drive to work on an alternate route.

Heuristics allow you to think through the possible outcomes quickly and arrive at a solution.

Are Heuristics Good or Bad?

Heuristics aren't inherently good or bad, but there are pros and cons to using them to make decisions. While they can help us figure out a solution to a problem faster, they can also lead to inaccurate judgments about other people or situations.

Types of Heuristics

There are many different kinds of heuristics. While each type plays a role in decision-making, they occur during different contexts. Understanding the types can help you better understand which one you are using and when.


The availability heuristic  involves making decisions based upon how easy it is to bring something to mind. When you are trying to make a decision, you might quickly remember a number of relevant examples. Since these are more readily available in your memory, you will likely judge these outcomes as being more common or frequently occurring.

For example, if you are thinking of flying and suddenly think of a number of recent airline accidents, you might feel like air travel is too dangerous and decide to travel by car instead. Because those examples of air disasters came to mind so easily, the availability heuristic leads you to think that plane crashes are more common than they really are.


The familiarity heuristic refers to how people tend to have more favorable opinions of things, people, or places they've experienced before as opposed to new ones. In fact, given two options, people may choose something they're more familiar with even if the new option provides more benefits.


The representativeness heuristic  involves making a decision by comparing the present situation to the most representative mental prototype. When you are trying to decide if someone is trustworthy, you might compare aspects of the individual to other mental examples you hold.

A soft-spoken older woman might remind you of your grandmother, so you might immediately assume that she is kind, gentle, and trustworthy. However, this is an example of a heuristic bias, as you can't know someone trustworthy based on their age alone.

The affect heuristic involves making choices that are influenced by the emotions that an individual is experiencing at that moment. For example, research has shown that people are more likely to see decisions as having benefits and lower risks when they are in a positive mood. Negative emotions, on the other hand, lead people to focus on the potential downsides of a decision rather than the possible benefits.

The anchoring bias involves the tendency to be overly influenced by the first bit of information we hear or learn. This can make it more difficult to consider other factors and lead to poor choices. For example, anchoring bias can influence how much you are willing to pay for something, causing you to jump at the first offer without shopping around for a better deal.

Scarcity is a principle in heuristics in which we view things that are scarce or less available to us as inherently more valuable. The scarcity heuristic is one often used by marketers to influence people to buy certain products. This is why you'll often see signs that advertise "limited time only" or that tell you to "get yours while supplies last."

Trial and Error

Trial and error is another type of heuristic in which people use a number of different strategies to solve something until they find what works. Examples of this type of heuristic are evident in everyday life. People use trial and error when they're playing video games, finding the fastest driving route to work, and learning to ride a bike (or learning any new skill).

Difference Between Heuristics and Algorithms

Though the terms are often confused, heuristics and algorithms are two distinct terms in psychology.

Algorithms are step-by-step instructions that lead to predictable, reliable outcomes; whereas heuristics are mental shortcuts that are basically best guesses. Algorithms always lead to accurate outcomes, whereas, heuristics do not.

Examples of algorithms include instructions for how to put together a piece of furniture or a recipe for cooking a certain dish. Health professionals also create algorithms or processes to follow in order to determine what type of treatment to use on a patient.

How Heuristics Can Lead to Bias

While heuristics can help us solve problems and speed up our decision-making process, they can introduce errors. As in the examples above, heuristics can lead to inaccurate judgments about how commonly things occur and about how representative certain things may be.

Just because something has worked in the past does not mean that it will work again, and relying on a heuristic can make it difficult to see alternative solutions or come up with new ideas.

Heuristics can also contribute to stereotypes and  prejudice . Because people use mental shortcuts to classify and categorize people, they often overlook more relevant information and create stereotyped categorizations that are not in tune with reality.

While heuristics can be a useful tool, there are ways you can improve your decision-making and avoid cognitive bias at the same time.

We are more likely to make an error in judgment if we are trying to make a decision quickly or are under pressure to do so. Whenever possible, take a few deep breaths . Do something to distract yourself from the decision at hand. When you return to it, you may find you have a fresh perspective, or notice something you didn't before.

Identify the Goal

We tend to focus automatically on what works for us and make decisions that serve our best interest. But take a moment to know what you're trying to achieve. Are there other people who will be affected by this decision? What's best for them? Is there a common goal that can be achieved that will serve all parties?

Process Your Emotions

Fast decision-making is often influenced by emotions from past experiences that bubble to the surface. Is your decision based on facts or emotions? While emotions can be helpful, they may affect decisions in a negative way if they prevent us from seeing the full picture.

Recognize All-or-Nothing Thinking

When making a decision, it's a common tendency to believe you have to pick a single, well-defined path, and there's no going back. In reality, this often isn't the case.

Sometimes there are compromises involving two choices, or a third or fourth option that we didn't even think of at first. Try to recognize the nuances and possibilities of all choices involved, instead of using all-or-nothing thinking .

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Marewski JN, Gigerenzer G. Heuristic decision making in medicine .  Dialogues Clin Neurosci . 2012;14(1):77–89. PMID: 22577307

Schwikert SR, Curran T. Familiarity and recollection in heuristic decision making .  J Exp Psychol Gen . 2014;143(6):2341-2365. doi:10.1037/xge0000024

Finucane M, Alhakami A, Slovic P, Johnson S. The affect heuristic in judgments of risks and benefits . J Behav Decis Mak . 2000; 13(1):1-17. doi:10.1002/(SICI)1099-0771(200001/03)13:1<1::AID-BDM333>3.0.CO;2-S

Cheung TT, Kroese FM, Fennis BM, De Ridder DT. Put a limit on it: The protective effects of scarcity heuristics when self-control is low . Health Psychol Open . 2015;2(2):2055102915615046. doi:10.1177/2055102915615046

Mohr H, Zwosta K, Markovic D, Bitzer S, Wolfensteller U, Ruge H. Deterministic response strategies in a trial-and-error learning task . Inman C, ed. PLoS Comput Biol. 2018;14(11):e1006621. doi:10.1371/journal.pcbi.1006621

Lang JM, Ford JD, Fitzgerald MM.  An algorithm for determining use of trauma-focused cognitive-behavioral therapy .  Psychotherapy   (Chic) . 2010;47(4):554-69. doi:10.1037/a0021184

Bigler RS, Clark C. The inherence heuristic: A key theoretical addition to understanding social stereotyping and prejudice. Behav Brain Sci . 2014;37(5):483-4. doi:10.1017/S0140525X1300366X

del Campo C, Pauser S, Steiner E, et al.  Decision making styles and the use of heuristics in decision making .  J Bus Econ.  2016;86:389–412. doi:10.1007/s11573-016-0811-y

Marewski JN, Gigerenzer G. Heuristic decision making in medicine .  Dialogues Clin Neurosci . 2012;14(1):77-89. doi:10.31887/DCNS.2012.14.1/jmarewski

Zheng Y, Yang Z, Jin C, Qi Y, Liu X. The influence of emotion on fairness-related decision making: A critical review of theories and evidence .  Front Psychol . 2017;8:1592. doi:10.3389/fpsyg.2017.01592

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By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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35 problem-solving techniques and methods for solving complex problems

Problem solving workshop

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All teams and organizations encounter challenges as they grow. There are problems that might occur for teams when it comes to miscommunication or resolving business-critical issues . You may face challenges around growth , design , user engagement, and even team culture and happiness. In short, problem-solving techniques should be part of every team’s skillset.

Problem-solving methods are primarily designed to help a group or team through a process of first identifying problems and challenges , ideating possible solutions , and then evaluating the most suitable .

Finding effective solutions to complex problems isn’t easy, but by using the right process and techniques, you can help your team be more efficient in the process.

So how do you develop strategies that are engaging, and empower your team to solve problems effectively?

In this blog post, we share a series of problem-solving tools you can use in your next workshop or team meeting. You’ll also find some tips for facilitating the process and how to enable others to solve complex problems.

Let’s get started! 

How do you identify problems?

How do you identify the right solution.

Complete problem-solving methods

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve. 

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward. 

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.  

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.  

Try different approaches  

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally 

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator 

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design the right agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

SessionLab makes it easy to plan a process to solve important problems. You can find methods fit for your purpose in the library and add them to your agenda. You’ll even find templates designed by expert facilitators to help you kickstart your workshop design.

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

Design Sprint 2.0

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on. 

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages. 

Lightning Decision Jam (LDJ)   #action   #decision making   #problem solving   #issue analysis   #innovation   #design   #remote-friendly   The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design. 

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition   #problem solving   #idea generation   #creativity   #online   #remote-friendly   A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys 

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges. 

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results. 

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys   #hyperisland   #innovation   This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold. 

World Cafe   #hyperisland   #innovation   #issue analysis   World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD)   #idea generation   #liberating structures   #action   #issue analysis   #remote-friendly   DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology   #action plan   #idea generation   #problem solving   #issue analysis   #large group   #online   #remote-friendly   Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed. 

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.  

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It!   #gamestorming   #problem solving   #action   Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed. 

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable. 

The Creativity Dice   #creativity   #problem solving   #thiagi   #issue analysis   Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around. 

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish. 

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis   #problem solving   ##root cause analysis   #decision making   #online facilitation   A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree 

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them. 

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree   #define intentions   #create   #design   #issue analysis   A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward. 

SWOT analysis   #gamestorming   #problem solving   #action   #meeting facilitation   The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results. 

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause. 

Agreement-Certainty Matrix   #issue analysis   #liberating structures   #problem solving   You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic .  A problem is simple when it can be solved reliably with practices that are easy to duplicate.  It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably.  A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail.  Chaotic is when the context is too turbulent to identify a path forward.  A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.”  The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process. 

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID   #gamestorming   #project planning   #issue analysis   #problem solving   When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!   

Speed Boat   #gamestorming   #problem solving   #action   Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How   #idea generation   #issue analysis   #problem solving   #online   #creative thinking   #remote-friendly   A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills. 

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO! 

LEGO Challenge   #hyperisland   #team   A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems. 

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken. 

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What?   #issue analysis   #innovation   #liberating structures   You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists  

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists   #vision   #big picture   #issue analysis   #remote-friendly   This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions 

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

21. Mindspin  

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly. 

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation. 

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex. 

MindSpin   #teampedia   #idea generation   #problem solving   #action   A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result. 

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution. 

Improved Solutions   #creativity   #thiagi   #problem solving   #action   #team   You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged. 

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch   #design sprint   #innovation   #idea generation   #remote-friendly   The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper,  Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change. 

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.   

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change. 

15% Solutions   #action   #liberating structures   #remote-friendly   You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference.  15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change.  With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process. 

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud. 

How-Now-Wow Matrix   #gamestorming   #idea generation   #remote-friendly   When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice. 

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them. 

Impact and Effort Matrix   #gamestorming   #decision making   #action   #remote-friendly   In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action? 

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus. 

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively. 

Dotmocracy   #action   #decision making   #group prioritization   #hyperisland   #remote-friendly   Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute. 

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out   #team   #opening   #closing   #hyperisland   #remote-friendly   Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together  

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start. 

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems. 

Doodling Together   #collaboration   #creativity   #teamwork   #fun   #team   #visual methods   #energiser   #icebreaker   #remote-friendly   Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team! 

Show and Tell   #gamestorming   #action   #opening   #meeting facilitation   Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible. 

Constellations   #trust   #connection   #opening   #coaching   #patterns   #system   Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic. 

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree   #thiagi   #opening   #perspectives   #remote-friendly   With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space. 

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round. 

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them. 

One breath feedback   #closing   #feedback   #action   This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix 

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward. 

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved. 

Who/What/When Matrix   #gamestorming   #action   #project planning   With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out! 

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised. 

Response Cards   #debriefing   #closing   #structured sharing   #questions and answers   #thiagi   #action   It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you! 

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thank you very much for these excellent techniques

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Certainly wonderful article, very detailed. Shared!

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Reach a solution faster with these problem-solving techniques

Georgina Guthrie

Georgina Guthrie

May 20, 2021

This post was originally published on October 18, 2019, and updated most recently on May 20, 2021.

There are three common approaches to any problem. One: Panic. Two: Bury your head in the sand. And three: Tackle it. While we all succumb to option one or two from time to time, let’s focus on the problem-solving techniques that will get you to option three.

Learning to overcome problems effectively is one of the most valuable things you can learn for both your professional and personal life. If you hold a senior or managerial position, then you’ll not only need to know how to solve personal challenges but also to figure out how to make decisions on behalf of your team or organization. These larger problems often need to be turned into projects.

Whether your project is personal or organizational, big or small, using a methodical approach will help tackle it more effectively. First, let’s take a look at what problem-solving is.

What is problem-solving?

Solving a problem involves strategically working through every aspect of an issue to reach a solution.

First, you need to define the problem. Then, you need to evaluate potential fixes. After that comes implementation, and finally, confirmation that the problem has been resolved.

This process can be done individually or as a group. Collective problem solving is more common in business scenarios because workplace decisions usually affect more than one person.

How to solve any problem in 5 steps

These stages can help anyone start solving an issue. They also come in handy during times of stress because they give you a clear route to follow.

1. Define the problem

It sounds like a no-brainer, but it’s not always as clear-cut as you might think — especially when there are multiple stages of factors.

Say, for example, the issue is a missed deadline. It might not be as simple as turning to the person responsible for delivery. There may have been a chain of events that had just as valid of an impact. First, define the nature of the issue —what are the signs something’s wrong? Then work your way back through the potential causes.

You don’t have to be concrete here, simply keep your options open and evaluate everything. If you need to involve other people to find out what’s gone wrong, keep your tone non-accusatory . People can clam up and blame others when they feel under threat. To stop that happening, reiterate it’s not about blame; it’s about finding a solution.

There are diagrams you can use to help you out here. A fishbone diagram (aka a ‘cause and effect diagram,’ is one method that can help you locate the route cause.

The five whys approach

Another option is an exercise called ‘five whys,’ which involves asking employees to methodically dig deeper into the problem than they might otherwise.

Simply start with the question ‘why did x happen,’ and then ask ‘why is that?’ five or more times to unearth more details. Obviously, asking this in person makes you sound a little interrogatory, so you might consider creating a form for the exercise. If you really prefer in-person interaction, let people know what you’re doing ahead of time. Mix up your ‘why is that’ with similar variations. And remember to smile and keep the tone light. This is about reaching a solution together, not blame.

2. Find a solution

This could be something you work through on your own. But, if you’re operating within an organization, it may be better to solve the issue as a small group.

Your solution really depends on the problem you have. But for the best chance of success, come up with as many options as possible, then narrow your selection down to three or so. We’ll go into more detail about how to come up with solutions a little later on in the article.

3. Evaluate your options

Once you’ve chosen your favorite solutions, evaluate each one and decide on the best route (that includes a primary solution and a contingency plan). You may want to involve relevant colleagues to help you reach a decision — especially if your choice will impact different departments.

4. Implement your plan

Once you’ve set the wheels in motion, you need to keep a close eye on how your chosen solution is performing. Does it fix the issue, or do you need to implement your contingency plan ?

If you’re managing a team, then helping everyone feel organized is crucial if you want to keep stress to a minimum. Project management software is a good option here because it means you and your team can track progress in real-time, share updates, and collaborate more freely, ironing out barriers that could lead to confusion.

5. Assess the project’s success

As an optional fifth and final stage, you can evaluate your chosen route to see whether it was effective, either as a post-mortem meeting  or a via some number crunching — whatever works for you.

Evaluating everything post-event gives you a better understanding of what went wrong and how well you managed it — which can help you if something similar happens again.

Two problem-solving techniques you need to know

Now you know the steps involved in problem-solving, here are some of the problem-solving techniques you can use to help you define your solution.

1. Creative Problem Solving (CPS)

CPS isn’t just about coming up with ad-hoc ideas. It’s a legitimate process formulated by Alex Faickney Osborn — the father of traditional brainstorming — and academic Sid Parnes , designed to help teams think more creatively.

3 key phases make up the CPS method.

2. Process-oriented problem solving

This is a formally defined approach that can be scaled to fit the task. The good thing about this method is that the journey to fixing the problem is already defined, which makes that initial jumping-off point a little less intimidating. There are several routes you can take, but we’ll focus on the three most popular options.

Common barriers to problem-solving

Ever heard of reproductive thinking ? No, it’s nothing to do with the birds and the bees. It’s a term coined by psychologists to describe how people reproduce past experiences to help them deal with current problems.

Problems arise when the mind becomes so focused on one particular solution that it can’t comprehend any other route — something that’s known as mental entrenchment . This usually happens when you’re drawing too heavily from past experience: You want to do something you know worked previously, even if it has little relation to your current issue.

Keep your mind open and pay attention to any biases you may have developed. The best way to do this is to get a second opinion and listen to what others think. Their fresh perspective may help illuminate routes you hadn’t previously considered.

Other barriers include:

Final thoughts

Problems are an inherent part of working life, and when things go wrong, it’s natural to feel stressed and confused. The secret to keeping a calm head is having pre-defined steps in place before things go belly up — so that when they do, you don’t need to panic and scramble around for a solution. If you approach each task with an open mind, the right project management tools , and a methodical plan, you’ll soon learn to take issues big and small in your stride.

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How to Solve Problems

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To bring the best ideas forward, teams must build psychological safety.

Teams today aren’t just asked to execute tasks: They’re called upon to solve problems. You’d think that many brains working together would mean better solutions, but the reality is that too often problem-solving teams fall victim to inefficiency, conflict, and cautious conclusions. The two charts below will help your team think about how to collaborate better and come up with the best solutions for the thorniest challenges.

First, think of the last time you had to solve a problem. Maybe it was a big one: A major trade route is blocked and your product is time sensitive and must make it to market on time. Maybe it was a small one: A traffic jam on your way to work means you’re going to be late for your first meeting of the day. Whatever the size of the impact, in solving your problem you moved through five stages, according to “ Why Groups Struggle to Solve Problems Together ,” by Al Pittampalli.

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Pittampalli finds that most of us, when working individually, move through these stages intuitively. It’s different when you’re working in a team, however. You need to stop and identify these different stages to make sure the group is aligned. For example, while one colleague might join a problem-solving discussion ready to evaluate assumptions (Stage 3), another might still be defining the problem (Stage 1). By defining each stage of your problem-solving explicitly, you increase the odds of your team coming to better solutions more smoothly.

This problem-solving technique gains extra power when applied to Alison Reynold’s and David Lewis’ research on problem-solving teams. In their article, “ The Two Traits of the Best Problem-Solving Teams ,” they find that highly effective teams typically have a pair of common features: They are cognitively diverse and they are psychologically safe. They also exhibit an array of characteristics associated with learning and confidence; these teammates tend to be curious, experimental, and nurturing, for example.

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As you and your colleagues consider these ideas, think about the last problem you had to solve as a team. First, map out what you remember from each step of your problem-solving. Were all of you on the same page at each stage? What aspects of the problem did you consider — or might you have missed — as a result? What can you do differently the next time you have a problem to solve? Second, ask where your team sees themselves on the chart. What kinds of behaviors could your team adopt to help you move into that top-right quadrant?

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Reviewed by Psychology Today Staff

A heuristic is a mental shortcut that allows an individual to make a decision, pass judgment, or solve a problem quickly and with minimal mental effort. While heuristics can reduce the burden of decision-making and free up limited cognitive resources, they can also be costly when they lead individuals to miss critical information or act on unjust biases.

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As humans move throughout the world, they must process large amounts of information and make many choices with limited amounts of time. When information is missing, or an immediate decision is necessary, heuristics act as “rules of thumb” that guide behavior down the most efficient pathway.

Heuristics are not unique to humans; animals use heuristics that, though less complex, also serve to simplify decision-making and reduce cognitive load.

Generally, yes. Navigating day-to-day life requires everyone to make countless small decisions within a limited timeframe. Heuristics can help individuals save time and mental energy, freeing up cognitive resources for more complex planning and problem-solving endeavors.

The human brain and all its processes—including heuristics— developed over millions of years of evolution . Since mental shortcuts save both cognitive energy and time, they likely provided an advantage to those who relied on them.

Heuristics that were helpful to early humans may not be universally beneficial today . The familiarity heuristic, for example—in which the familiar is preferred over the unknown—could steer early humans toward foods or people that were safe, but may trigger anxiety or unfair biases in modern times.


The study of heuristics was developed by renowned psychologists Daniel Kahneman and Amos Tversky. Starting in the 1970s, Kahneman and Tversky identified several different kinds of heuristics, most notably the availability heuristic and the anchoring heuristic.

Since then, researchers have continued their work and identified many different kinds of heuristics, including:

Familiarity heuristic

Fundamental attribution error

Representativeness heuristic


The anchoring heuristic, or anchoring bias , occurs when someone relies more heavily on the first piece of information learned when making a choice, even if it's not the most relevant. In such cases, anchoring is likely to steer individuals wrong .

The availability heuristic describes the mental shortcut in which someone estimates whether something is likely to occur based on how readily examples come to mind . People tend to overestimate the probability of plane crashes, homicides, and shark attacks, for instance, because examples of such events are easily remembered.

People who make use of the representativeness heuristic categorize objects (or other people) based on how similar they are to known entities —assuming someone described as "quiet" is more likely to be a librarian than a politician, for instance. 

Satisficing is a decision-making strategy in which the first option that satisfies certain criteria is selected , even if other, better options may exist.


Heuristics, while useful, are imperfect; if relied on too heavily, they can result in incorrect judgments or cognitive biases. Some are more likely to steer people wrong than others.

Assuming, for example, that child abductions are common because they’re frequently reported on the news—an example of the availability heuristic—may trigger unnecessary fear or overprotective parenting practices. Understanding commonly unhelpful heuristics, and identifying situations where they could affect behavior, may help individuals avoid such mental pitfalls.

Sometimes called the attribution effect or correspondence bias, the term describes a tendency to attribute others’ behavior primarily to internal factors—like personality or character— while attributing one’s own behavior more to external or situational factors .

If one person steps on the foot of another in a crowded elevator, the victim may attribute it to carelessness. If, on the other hand, they themselves step on another’s foot, they may be more likely to attribute the mistake to being jostled by someone else .

Listen to your gut, but don’t rely on it . Think through major problems methodically—by making a list of pros and cons, for instance, or consulting with people you trust. Make extra time to think through tasks where snap decisions could cause significant problems, such as catching an important flight.

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How to Solve Math Problems

Last Updated: May 16, 2023 Approved

This article was co-authored by Daron Cam . Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary's College. wikiHow marks an article as reader-approved once it receives enough positive feedback. In this case, 84% of readers who voted found the article helpful, earning it our reader-approved status. This article has been viewed 557,594 times.

Although math problems may be solved in different ways, there is a general method of visualizing, approaching and solving math problems that may help you to solve even the most difficult problem. Using these strategies can also help you to improve your math skills overall. Keep reading to learn about some of these math problem solving strategies.

Understanding the Problem

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Developing a Plan

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Solving the Problem

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To solve a math problem, try rewriting the problem in your own words so it's easier to solve. You can also make a drawing of the problem to help you figure out what it's asking you to do. If you're still completely stuck, try solving a different problem that's similar but easier and then use the same steps to solve the harder problem. Even if you can't figure out how to solve it, try to make an educated guess instead of leaving the question blank. To learn how to come up with a solid plan to use to help you solve a math problem, scroll down! Did this summary help you? Yes No

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Maths Tricks

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Maths tricks are the ways to solve complex mathematical problems easily and quickly.  Mathematics is not only limited to learning from textbooks, there are different learning styles that make mathematics easier. Simple Maths magic tricks help us with fast calculations and improve our mathematical skills.  For example, the multiplication tricks will help students to learn maths tables and quick multiplication.

Maths is not easy for some students. The Maths tricks are not only helpful for school-going kids but also supports you to manage time in final exams as well as in the comp etitive exam and solve the Maths questions with accuracy. These tricks are very helpful for Class 5, 6, 7, 8, 9 and 10 students.

Mathematical tricks are the best way to make Maths a fun subject. Therefore, learning simple Maths tricks will help the students to gain their confidence and enhance problem-solving skills. With these learning skills, they can achieve a big success in the competitive exams and upcoming future.    

12 Maths Tricks (With Examples)

Imagine how mathematics would be easy and interesting when you have the ability to calculate the problems in a matter of seconds using some Maths tricks. There are different kinds of arithmetic operations  like addition, subtraction, division, multiplication, squaring, roots, powers, logarithms, divisions, etc. Here are some of the best tricks, which will help students to perform arithmetic calculations easily.

1. Maths Tricks for Addition

With the help of basic principles of tens and unit places, the addition of two-digit numbers is performed by

2. Maths Tricks for Subtraction

Here is an example that requires a lot of borrowing

 3.  Quick Multiplication Tricks by Breaking Down Numbers

4. Multiplied By 15

5. Multiplication of Two-Digit Numbers

If anyone of the given numbers is an even number, then follow the steps to solve

6. Maths Division Tricks

The numbers that can be evenly divided by certain numbers are:

7. Maths Trick to Find Percentage

Let us take; we have to find the percentage of the number 5% of 475, follow the steps.

8. Maths Magic tricks to Calculate Squares ending with digit 5

So, 75 = 7(7 + 1)25 = (7 x 8) 25  = 5625.

9. Tricks to Multiply by 2 and 4

When a number is multiplied by 2 or 4, then the last digit of the resulting value will be an even number always.

10. Multiplication by 5

When a number is multiplied by 5, then the resulting value will either end with 0 or 5.

11. Multiplication by 10

When a number is multiplied by 10, then the resulting value ends with 0 always.

12. Tricks to Memorise Table of 9

It is easy to remember the table of 9. Just we need to focus on the pattern.

09, 18, 27, 36, 45, 54, 63, 72, 81, 90

We can see the numbers at the ten’s place are increasing by 1, and the numbers at the unit place are decreasing by 1.

Maths is a fun subject. Adding tricks to this subject will make it more interesting. Students will be able to solve all the complex problems using these Maths magic tricks. These tricks also help students to improve their problem-solving skills and boost their confidence.

Maths Tricks Practice Questions

Find more maths tricks questions for practice here.

Maths Tricks Related Articles

Frequently asked questions on maths tricks, what is the use of maths tricks, what are multiplication tricks, how to add in a faster way, how to multiply quickly, how to find if a number is divisible by 9, how to find if a number is divisible by 13, how to multiply 5 with an even number.

Assume that, 5 should be multiplied by 48. Follow the below steps to find the product value. Step 1: Divide the given even number by 2. Hence, 48 divided by 2 is 24. Step 2: Add zero to the result, obtained in step 1 to get the product value. So, we get 240. Therefore, the product of 5 and 48 is 240.

How to multiply 5 with an odd number?

Let us consider an example, 5 × 25. Here, 25 is an odd number. Go through the below steps to find the product. Step 1: Subtract 1 from the odd number (i.e. the number that is being multiplied by 5). So, 25 – 1 = 24. Step 2: Half the number that is obtained in step 1. Hence, 24/2 = 12. Step 3: Keep the number 5 in unit digits and append the result obtained in step 2. Hence, we get 125. So, we get 5 × 25 is 125.

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What you need to know about the debt ceiling as the deadline looms

Kelsey Snell in 2018.

Kelsey Snell

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People pass the front of the New York Stock Exchange in New York, on March 22. Brinkmanship in Washington over raising the U.S. debt ceiling has begun to raise worries in parts of the financial markets. Peter Morgan/AP hide caption

People pass the front of the New York Stock Exchange in New York, on March 22. Brinkmanship in Washington over raising the U.S. debt ceiling has begun to raise worries in parts of the financial markets.

The federal government is perilously close to being unable to make payments on the country's debt. It is up to Congress to vote to increase the nation's borrowing cap, known as the debt limit. But House Speaker Kevin McCarthy, R-Calif., is in a standoff with President Biden over Republican demands to tie the debt limit to spending caps and other policy demands.

Treasury Secretary Janet Yellen has warned that the country could run out of borrowing authority by June 1, leaving negotiators little time to reach an agreement.

Biden recently met with McCarthy, House Democratic Leader Hakeem Jeffries, D-N.Y., Senate Majority Leader Chuck Schumer, D-N.Y., and Senate Minority Leader Mitch McConnell, R-Ky., to discuss a path forward. The group failed to reach a deal, but staff level talks are ongoing in an effort to avoid default.

Here are nine questions you may be asking about the debt ceiling and the fight over it.

What is the debt ceiling?

The "debt ceiling" or "debt limit" is a cap on how much debt the federal government is allowed to accumulate. Congress is constitutionally required to authorize the issuance of debt. Doing so then allows the government borrow to meet its existing legal obligations like Social Security and Medicare benefits, military salaries, interest on the national debt, tax refunds and other payments.

"It used to be that every time you did a Treasury auction where you borrowed, Congress would pass a new law just for that one auction," said Jason Furman, a top economic adviser to former President Barack Obama and an economics professor at Harvard.

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"In 1917, the United States needed to borrow a lot of money for World War I," he said. "So in order to simplify that process and make it easier, Congress shifted to a new system where they said, you can borrow up to this amount of money and then come back to us and we'll raise it."

Congress has increased or suspended the debt limit 78 times since 1960 , according to the Treasury Department.

How do experts know when the government has really run out of funds?

Economists look at how much the government is expected to bring in through tax payments, when those payments are expected to arrive in Treasury accounts and scheduled debt payments to determine a timeframe, known as an X-Date for when the debt authority might run out.

However, the Treasury Department has access to a few tools, known as extraordinary measures , to avoid default. Those measures include moving investments and deploying accounting tools to shift funds around.

The federal government technically hit the debt limit in January and extraordinary measures have kept payments flowing since then. Experts cannot pinpoint the exact date when funds will run out but they can identify a general range which is expected to fall sometime in early June or possibly as late as July or August.

What the debt ceiling standoff could mean for your retirement plans

What the debt ceiling standoff could mean for your retirement plans

Why is there a fight over it.

Debt has generally been an unpopular concept in American politics.

Every vote a lawmaker casts is part of that person's political record and many lawmakers do not want to be seen as signing off on more federal borrowing or spending.

Lawmakers also like to tack extraneous priorities onto bills that are seen as must-pass legislation. That makes the debt limit a prime target for political fights.

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Speaker of the House Kevin McCarthy of Calif., left, and Senate Majority Leader Chuck Schumer of N.Y., right, listen as President Biden before an Oval Office meeting on the debt limit on May 9. Senate Minority Leader Mitch McConnell of Kentucky and House Minority Leader Hakeem Jeffries of New York also attended. Evan Vucci/AP hide caption

Speaker of the House Kevin McCarthy of Calif., left, and Senate Majority Leader Chuck Schumer of N.Y., right, listen as President Biden before an Oval Office meeting on the debt limit on May 9. Senate Minority Leader Mitch McConnell of Kentucky and House Minority Leader Hakeem Jeffries of New York also attended.

"Everybody uses [bills to increase] the debt ceiling for their favorite policies," said Maya MacGuineas, the president of the Committee for a Responsible Federal Budget. "The real problem here is that you now have people actually talking about defaulting."

In the past, votes to increase the debt limit were relatively quiet, non-controversial affairs. That changed in 2011 when the country came dangerously close to default.

Mark Zandi, an analyst at Moody's Analytics, said there have been political battles over the debt before but none were as dangerous or consequential as the 2011 fight.

"It wasn't clear up until the very end that lawmakers were going to figure out a way to sign on the dotted line and increase the limit," Zandi said. "The stock market at one point I think was down intraday almost 20%. That's a pretty large market swoon."

At the time, Republican House Speaker John Boehner, R-Ohio, was in a standoff with Obama over spending. Republicans wanted deep spending cuts and caps on how much federal spending could grow after the cuts were enacted.

Obama insisted Congress raise the debt limit without any extraneous policies --known as a clean increase.

Congress eventually reached a deal to increase the debt limit along with caps on future spending but not before the credit rating agency Standard & Poor's downgraded the nation's debt for the first time ever.

Many economists say the situation today is strikingly similar to the political fight in 2011 and there are serious concerns that the country could default.

What could happen if it's not raised?

The Treasury Department would be unable to make payments when they are due. Missing a payment of any kind or size would be considered a default.

The fight over the debt ceiling could sink the economy. This is how we got here

The fight over the debt ceiling could sink the economy. This is how we got here

Some Republicans have suggested choosing which debts to pay, a system called payment prioritization . Congress would have to pass a law to make that possible, which is politically very unlikely. Most experts say it might also be impossible to execute from a practical standpoint and the idea is not being seriously considered as a solution at this time.

Has the U.S. ever failed to make these debt payments?

And that is part of why the federal government is able to easily sell share Treasury bonds to investors across the globe and why the U.S. dollar is one of the most trusted currencies.

"Treasuries are the debt vehicle that are most trusted in the entire world to the point where even if there is an economic crisis that originated in the U.S., people come and buy treasuries because they trust them," MacGuineas said. "They trust the U.S. they trust the fact that they will get paid if that is called into question, because we actually do start to default and we don't pay the interest that is due. We will never be able to regain that most trusted role in the same capacity we had before"

Would capping or cutting spending now resolve the problem?

No, the debt limit is related to money that has been spent as a result of laws Congress already passed.

"As a mathematical consequence of the laws Congress already passed, you have to borrow a certain amount," Furman said. "This borrowing isn't some unilateral thing that President Biden wants to do in order to do his favorite projects. It is in order to accomplish what Congress told him to accomplish."

In fact, some of the debt being accumulated is the result of laws passed under former presidents, including Donald Trump.

Spending caps and other changes included in a bill passed by House Republicans are separate policies intended to address future debt accumulation, not the current need to increase the debt limit.

What else could be affected by a default?

A U.S. default could cause a huge ripple of negative consequences throughout the global financial system. Any hit to the country's credit rating could do long-term harm to the value of U.S. treasuries and make the country a less appealing investment.

"I am truly concerned there is an actual chance of default and that is so dangerous and such a sign that the U.S. is not able to govern itself in a way that is functioning," MacGuineas said. "We should all be worried both about the debt ceiling itself, but also about what it says about our politics."

Zandi warned that the consequences could go beyond just investment and lending rates.

"Don't worry about your stock portfolio, worry about your job," he said. "Because a lot of jobs are going to be lost. Unemployment is going to be a lot higher. Is the economy struggling already trying to avoid recession because of high inflation, high interest rates? This will certainly push us and, you know, it's going to be about layoffs. Stock portfolios will be the least of people's worries."

Furman said it could be worse than the 2008 financial crisis when the fall of Lehman Brothers Bank triggered a global financial crisis.

"It could be worse than Lehman Brothers, where everyone basically demands their money back because they don't believe the collateral anymore," Furman said. "And you have the equivalent of a run on the global financial system."

Is default the same thing as a shutdown?

No. A government shutdown occurs when Congress fails to authorize annual spending bills before the end of the fiscal year on Sept. 30.

The U.S. could run out of cash to pay its bills by June 1, Yellen warns Congress

The U.S. could run out of cash to pay its bills by June 1, Yellen warns Congress

The two issues sometimes become linked because lawmakers have occasionally extended the debt limit to intentionally align with the end of the fiscal year in order to force broader spending discussions alongside the debt authorization.

Are there other ways this problem could be fixed, aside from just increasing the debt limit?

Most experts agree the current debt limit process isn't working. MacGuineas of the Committee for a Responsible Federal Budget said Congress should be reassessing debt and spending priorities but the debt limit mechanism does not actually force them to make choices.

"The debt ceiling is a terrible way to try to impose fiscal responsibility," she said. "It doesn't make sense. It says after you vote to borrow a lot of money then you will then vote whether to actually make good on those bills. That's a dumb approach."

Instead, she suggested a system where Congress agrees to increase the debt limit when they pass legislation.

Others economists have suggested abolishing the debt limit entirely.

Other less popular proposals include minting a $1 trillion platinum coin to cover the debt or raising it so high that the next debate will be stalled for years or decades.

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