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How to Solve a Problem

Last Updated: April 3, 2023 Fact Checked

This article was co-authored by Rachel Clissold . Rachel Clissold is a Life Coach and Consultant in Sydney, Australia. With over six years of coaching experience and over 17 years of corporate training, Rachel specializes in helping business leaders move through internal roadblocks, gain more freedom and clarity, and optimize their company’s efficiency and productivity. Rachel uses a wide range of techniques including coaching, intuitive guidance, neuro-linguistic programming, and holistic biohacking to help clients overcome fear, break through limitations, and bring their epic visions to life. Rachel is an acclaimed Reiki Master Practitioner, Qualified practitioner in NLP, EFT, Hypnosis & Past Life Regression. She has created events with up to 500 people around Australia, United Kingdom, Bali, and Costa Rica. There are 12 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 1,311,074 times.

How you deal with challenges will often determine your success and happiness. If you’re stuck on how to solve a problem, try defining it and breaking it into smaller pieces. Choose whether to approach the problem logically or whether you should think about how the outcome might make you feel. Find ways to creatively approach your problems by working with other people and approaching the problem from a different perspective.

Approaching the Problem

• For example, if your room is constantly messy, the problem might not be that you’re a messy person. It might be that you lack containers or places to put your items in an organized way.
• Try to be as clear and thorough as possible when defining the problem. If it is a personal issue, be honest with yourself as to the causes of the problem. If it is a logistics problem, determine exactly where and when the problem occurs.
• Determine whether the problem is real or self-created. Do you need to solve this problem or is this about something you want? Putting things in perspective can help you navigate the problem-solving process.

• For example, you might have several problems to solve and need to decide which ones to tackle first. Solving one problem may ease tension or take stress off of another problem.
• Once you make a decision, don’t doubt yourself. Be willing to look forward from that point on without wondering what would have happened had you chosen something else.

• For example, if you need to turn in many assignments to pass a class, focus on how many you have to do and approach them one by one.
• Try to combine and solve problems together whenever possible. For example, if you're running out of time to study, try listening to a recorded lecture while walking to class or flip through note cards as you're waiting for dinner.

• For example, if you’re trying to pass a cumulative test, figure out what you already know and what you need to study for. Review everything you already know, then start learning more information from your notes, textbook, or other resources that may help you.

• Pay attention to know these scenarios make you feel.

• For example, if you have a deadline, you may skip cooking dinner or going to the gym so that you can give that time to your project.
• Cut down on unnecessary tasks whenever possible. For example, you might get your groceries delivered to you to save on shopping time. You can spend that time instead on other tasks.

Taking a Creative Approach

• If you’re making a complex decision, write down your alternatives. This way, you won’t forget any options and will be able to cross off any that aren’t plausible.
• For example, you might be hungry and need something to eat. Think about whether you want to cook food, get fast food, order takeout, or sit down at a restaurant.

• Problems like accepting the job across the country that offers good pay but takes you away from your family may require different ways of approach. Consider the logical solution, but also consider your thoughts, feelings, and the way the decision affects others.

• For example, if you’re buying a home and not sure how to make your final decision, talk to other homeowners about their thoughts or regrets about buying a home.

• For example, if you’re having financial difficulties, notice how your efforts are affecting the money coming in and the money you’re spending. If keeping a budget helps, keep with it. If using cash exclusively is a headache, try something else.
• Keep a journal where you record your progress, successes, and challenges. You can look at this for motivation when you are feeling discouraged.

Managing Your Emotions While Confronting Difficulties

• The first step is often the scariest. Try doing something small to start. For example, if you're trying to become more active, start going for daily walks.

• For example, if you’re overwhelmed by having a long to-do list, maybe the problems isn’t the list, but not saying “no” to things you can’t do.
• If you're feeling stressed, angry, or overwhelmed, you may be burned out. Make a list of things that cause stress or frustration. Try to cut down on these in the future. If you start feeling overwhelmed again, it may be a sign that you need to cut back.

• Find a therapist by calling your local mental health clinic or your insurance provider. You can also get a recommendation from a physician or friend.

Expert Q&A

• If you start feeling overwhelmed or frustrated, take a breather. Realize that every problem has a solution, but sometimes you're so wrapped up in it that you can't see anything but the problem. Thanks Helpful 0 Not Helpful 0
• Don't turn away from your problems. It will come back sooner or later and it will be more difficult to solve. Common sense can help to reduce the size of the problem. Thanks Helpful 0 Not Helpful 0

You Might Also Like

• ↑ https://hbr.org/2017/06/how-you-define-the-problem-determines-whether-you-solve-it
• ↑ https://www.cuesta.edu/student/resources/ssc/study_guides/critical_thinking/106_think_decisions.html
• ↑ https://au.reachout.com/articles/a-step-by-step-guide-to-problem-solving
• ↑ Rachel Clissold. Certified Life Coach. Expert Interview. 26 August 2020.
• ↑ https://serc.carleton.edu/geoethics/Decision-Making
• ↑ https://www.psychologytoday.com/blog/positive-psychology-in-the-classroom/201303/visualize-the-good-and-the-bad
• ↑ https://www.britannica.com/topic/operations-research/Resource-allocation
• ↑ https://www.niu.edu/citl/resources/guides/instructional-guide/brainstorming.shtml
• ↑ https://www.healthywa.wa.gov.au/Articles/N_R/Problem-solving
• ↑ https://www.collegetransfer.net/Home/ChangeSwitchTransfer/I-want-to/Earn-My-College-Degree/Overcoming-Obstacles
• ↑ https://psychcentral.com/lib/5-ways-to-solve-all-your-problems/
• ↑ https://www.apa.org/topics/psychotherapy/understanding

About This Article

To solve a problem, start by brainstorming and writing down any solutions you can think of. Then, go through your list of solutions and cross off any that aren't plausible. Once you know what realistic options you have, choose one of them that makes the most sense for your situation. If the solution is long or complex, try breaking it up into smaller, more manageable steps so you don't get overwhelmed. Then, focus on one step at a time until you've solved your problem. To learn how to manage your emotions when you're solving a particularly difficult problem, scroll down. Did this summary help you? Yes No

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Article • 11 min read

Getting to the Root of a Problem Quickly

By the Mind Tools Content Team

5 Whys Root-Cause Analysis

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.

What Is a 5 Whys Template?

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

Figure 1: 5 Whys Example (Single Lane)

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)

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.

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.

Appreciation

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.

Tips for Using the 5 Whys Technique

• Try to move quickly from one question to the next. That way, you'll have the full picture before you jump to any conclusions.
• 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.
• Know when to stop! The important point is to stop asking "Why?" when you stop producing useful responses.

Frequently Asked Questions About 5 Whys

1. what is the 5 whys technique.

The 5 Whys Technique is a problem-solving method involving repeatedly asking "why?" It's a way of quickly getting to the root cause of a situation.

2. Who Invented 5 Whys?

The 5 Whys technique was invented in the 1930s by Sakichi Toyoda, the Japanese industrialist, inventor, and founder of Toyota Industries.

5 Whys Infographic

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

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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7 Problem-Solving Skills That Can Help You Be a More Successful Manager

Discover what problem-solving is, and why it's important for managers. Understand the steps of the process and learn about seven problem-solving skills.

1Managers oversee the day-to-day operations of a particular department, and sometimes a whole company, using their problem-solving skills regularly. Managers with good problem-solving skills can help ensure companies run smoothly and prosper.

If you're a current manager or are striving to become one, read this guide to discover what problem-solving skills are and why it's important for managers to have them. Learn the steps of the problem-solving process, and explore seven skills that can help make problem-solving easier and more effective.

What is problem-solving?

Problem-solving is both an ability and a process. As an ability, problem-solving can aid in resolving issues faced in different environments like home, school, abroad, and social situations, among others. As a process, problem-solving involves a series of steps for finding solutions to questions or concerns that arise throughout life.

The importance of problem-solving for managers

Managers deal with problems regularly, whether supervising a staff of two or 100. When people solve problems quickly and effectively, workplaces can benefit in a number of ways. These include:

Greater creativity

Higher productivity

Increased job fulfillment

Satisfied clients or customers

Better cooperation and cohesion

Improved environments for employees and customers

7 skills that make problem-solving easier

Companies depend on managers who can solve problems adeptly. Although problem-solving is a skill in its own right, a subset of seven skills can help make the process of problem-solving easier. These include analysis, communication, emotional intelligence, resilience, creativity, adaptability, and teamwork.

1. Analysis

As a manager , you'll solve each problem by assessing the situation first. Then, you’ll use analytical skills to distinguish between ineffective and effective solutions.

2. Communication

Effective communication plays a significant role in problem-solving, particularly when others are involved. Some skills that can help enhance communication at work include active listening, speaking with an even tone and volume, and supporting verbal information with written communication.

3. Emotional intelligence

Emotional intelligence is the ability to recognize and manage emotions in any situation. People with emotional intelligence usually solve problems calmly and systematically, which often yields better results.

4. Resilience

Emotional intelligence and resilience are closely related traits. Resiliency is the ability to cope with and bounce back quickly from difficult situations. Those who possess resilience are often capable of accurately interpreting people and situations, which can be incredibly advantageous when difficulties arise.

5. Creativity 

When brainstorming solutions to problems, creativity can help you to think outside the box. Problem-solving strategies can be enhanced with the application of creative techniques. You can use creativity to:

Approach problems from different angles

Improve your problem-solving process

Spark creativity in your employees and peers

6. Adaptability

Adaptability is the capacity to adjust to change. When a particular solution to an issue doesn't work, an adaptable person can revisit the concern to think up another one without getting frustrated.

7. Teamwork

Finding a solution to a problem regularly involves working in a team. Good teamwork requires being comfortable working with others and collaborating with them, which can result in better problem-solving overall.

Steps of the problem-solving process

Effective problem-solving involves five essential steps. One way to remember them is through the IDEAL model created in 1984 by psychology professors John D. Bransford and Barry S. Stein [ 1 ]. The steps to solving problems in this model include: identifying that there is a problem, defining the goals you hope to achieve, exploring potential solutions, choosing a solution and acting on it, and looking at (or evaluating) the outcome.

1. Identify that there is a problem and root out its cause.

To solve a problem, you must first admit that one exists to then find its root cause. Finding the cause of the problem may involve asking questions like:

Can the problem be solved?

How big of a problem is it?

Why do I think the problem is occurring?

What are some things I know about the situation?

What are some things I don't know about the situation?

Are there any people who contributed to the problem?

Are there materials or processes that contributed to the problem?

Are there any patterns I can identify?

2. Define the goals you hope to achieve.

Every problem is different. The goals you hope to achieve when problem-solving depend on the scope of the problem. Some examples of goals you might set include:

Gather as much factual information as possible.

Brainstorm many different strategies to come up with the best one.

Be flexible when considering other viewpoints.

Articulate clearly and encourage questions, so everyone involved is on the same page.

Be open to other strategies if the chosen strategy doesn't work.

Stay positive throughout the process.

3. Explore potential solutions.

Once you've defined the goals you hope to achieve when problem-solving , it's time to start the process. This involves steps that often include fact-finding, brainstorming, prioritizing solutions, and assessing the cost of top solutions in terms of time, labor, and money.

4. Choose a solution and act on it.

Evaluate the pros and cons of each potential solution, and choose the one most likely to solve the problem within your given budget, abilities, and resources. Once you choose a solution, it's important to make a commitment and see it through. Draw up a plan of action for implementation, and share it with all involved parties clearly and effectively, both verbally and in writing. Make sure everyone understands their role for a successful conclusion.

5. Look at (or evaluate) the outcome.

Evaluation offers insights into your current situation and future problem-solving. When evaluating the outcome, ask yourself questions like:

Did the solution work?

Will this solution work for other problems?

Were there any changes you would have made?

Would another solution have worked better?

As a current or future manager looking to build your problem-solving skills, it is often helpful to take a professional course. Consider Improving Communication Skills offered by the University of Pennsylvania on Coursera. You'll learn how to boost your ability to persuade, ask questions, negotiate, apologize, and more. 

You might also consider taking Emotional Intelligence: Cultivating Immensely Human Interactions , offered by the University of Michigan on Coursera. You'll explore the interpersonal and intrapersonal skills common to people with emotional intelligence, and you'll learn how emotional intelligence is connected to team success and leadership.

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Article sources

Tennessee Tech. “ The Ideal Problem Solver (2nd ed.) , https://www.tntech.edu/cat/pdf/useful_links/idealproblemsolver.pdf.” Accessed December 6, 2022.

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Reach a solution faster with these problem-solving techniques

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.

• Brainstorm as many ideas as you can. Don’t evaluate, critique, or prioritize them — just write them all down. The idea is to keep moving. The faster you go, the more you’ll get into your creative flow. If you’re not into brainstorming, a group mind map works just as well.
• Turn all your problems into questions. This encourages the group (or you) to address the situation more creatively and helps remove the burden of blame.
• Keep your language positive and affirmative. Avoid words like ‘no’ and ‘no but’ like the plague. Instead, ask ‘yes and’ to keep the conversation flowing and expand ideas.

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.

• Hurson’s Productive Thinking Model: In his 2007 book Think Better: An Innovator’s Guide to Productive Thinking , Tim Hurson defines six steps intended to give structure to solution planning while maintaining creativity. It involves working together to answer the following questions: 1) What’s going on? 2) What is success? 3) What is the question? 4) Generate answers 5) Create the solution 6) Align resources.
• Means-End Analysis (MEA): This approach is designed to reduce the difference between the problem and the goal. To narrow this gap, teams collect all the information they believe has led them to the problem, then systematically try to eliminate the issues one by one, starting with the biggest.
• Plan Do Check Act (PDCA): A favorite of developers, this iterative technique focuses on continually improving the process, one step at a time. Teams begin by setting out objectives, then implement the plan, compare it against previous results, then define the solution based on the knowledge gained. And then they repeat.

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:

• Confirmation bias: This is when you search for or interpret information that confirms your existing belief while disregarding data that doesn’t support it.
• Unnecessary constraints: This happens when people get overwhelmed with the drama of a problem and make the situation more confusing than it needs to be. The best way to avoid this is to have a plan in place and a clear schedule to help people work toward a solution.
• Fixedness: This is when people are inflexible and can’t accept different perspectives.
• Groupthink: This happens when people start agreeing with each other because it’s easier than risking the challenge of conflict.
• Rigidity: People naturally want to resist change . It’s important to have self-awareness, so you can spot when you (or your team) are avoiding learning or implementing something new just because it’s never been done before. One way to change perspective is through something called constructive controversy . Split people into two teams and ask one group to play devil’s advocate to refute a solution, while the other defends it. Forcing people to discuss the pros and cons objectively brings any unconscious bias to the surface and helps people think more flexibly.

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 Math Problems Faster: 15 Techniques to Show Students

Written by Marcus Guido

• Teaching Strategies

“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.

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:

• (393 + 7) + (89 – 7)

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:

• (567 – 67) – (153 – 67)

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

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.

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.

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

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

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:

• Subtract 1 from the integer: 81 – 1 = 80
• Square the integer, which is now an easier number: 80 x 80 = 6,400
• Add the integer with the resulting square twice: 6,400 + 80 + 80 = 6,560
• Add 1: 6,560 + 1 = 6,561

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

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:

• 14 hours – 10 hours = 4 hours
• 12 – 10 = 2
• 10 – 10 = 0
• 4 hours + 2 hours + 0 hours = 6 hours

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

• 10 hours – 6 hours = 4 hours

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

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

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

Each student should ask him or herself:

• What am I looking for?  — Students should read the question over and over, looking for buzzwords and identifying important details.
• What information do I need?  — Students should determine which facts, figures and variables they need to solve the question. For example, if they determine the question is rooted in subtraction, they need the minuend and subtrahend.
• What information do I have?  — Students should be able to create the core equation using the information in the word problem, after determining which details are important.

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.

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Problem-Solving Strategies and Obstacles

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

Sean is a fact-checker and researcher with experience in sociology, field research, and data analytics.

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• Application
• Improvement

From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.

What Is Problem-Solving?

In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.

A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.

Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.

The problem-solving process involves:

• Discovery of the problem
• Deciding to tackle the issue
• Seeking to understand the problem more fully
• Researching available options or solutions
• Taking action to resolve the issue

Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.

Problem-Solving Mental Processes

Several mental processes are at work during problem-solving. Among them are:

• Perceptually recognizing the problem
• Representing the problem in memory
• Considering relevant information that applies to the problem
• Identifying different aspects of the problem
• Labeling and describing the problem

Problem-Solving Strategies

There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.

An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.

In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.

One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.

There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.

Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.

If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.

While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.

Trial and Error

A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.

This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.

In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.

Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .

Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.

How to Apply Problem-Solving Strategies in Real Life

If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:

• Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
• Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
• Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
• Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.

Obstacles to Problem-Solving

Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:

• Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
• Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
• Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
• Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.

How to Improve Your Problem-Solving Skills

In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:

• Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
• Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
• Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
• Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
• Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
• Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.

You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.

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Stewart SL, Celebre A, Hirdes JP, Poss JW. Risk of suicide and self-harm in kids: The development of an algorithm to identify high-risk individuals within the children's mental health system . Child Psychiat Human Develop . 2020;51:913-924. doi:10.1007/s10578-020-00968-9

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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."

How to improve your problem solving skills and build effective problem solving strategies

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Effective problem solving is all about using the right process and following a plan tailored to the issue at hand. Recognizing your team or organization has an issue isn’t enough to come up with effective problem solving strategies. 

To truly understand a problem and develop appropriate solutions, you will want to follow a solid process, follow the necessary problem solving steps, and bring all of your problem solving skills to the table.  

We’ll first guide you through the seven step problem solving process you and your team can use to effectively solve complex business challenges. We’ll also look at what problem solving strategies you can employ with your team when looking for a way to approach the process. We’ll then discuss the problem solving skills you need to be more effective at solving problems, complete with an activity from the SessionLab library you can use to develop that skill in your team.

Let’s get to it! 

What is a problem solving process?

• What are the problem solving steps I need to follow?

Problem solving strategies

What skills do i need to be an effective problem solver, how can i improve my problem solving skills.

Solving problems is like baking a cake. You can go straight into the kitchen without a recipe or the right ingredients and do your best, but the end result is unlikely to be very tasty!

Using a process to bake a cake allows you to use the best ingredients without waste, collect the right tools, account for allergies, decide whether it is a birthday or wedding cake, and then bake efficiently and on time. The result is a better cake that is fit for purpose, tastes better and has created less mess in the kitchen. Also, it should have chocolate sprinkles. Having a step by step process to solve organizational problems allows you to go through each stage methodically and ensure you are trying to solve the right problems and select the most appropriate, effective solutions.

What are the problem solving steps I need to follow? 

All problem solving processes go through a number of steps in order to move from identifying a problem to resolving it.

Depending on your problem solving model and who you ask, there can be anything between four and nine problem solving steps you should follow in order to find the right solution. Whatever framework you and your group use, there are some key items that should be addressed in order to have an effective process.

We’ve looked at problem solving processes from sources such as the American Society for Quality and their four step approach , and Mediate ‘s six step process. By reflecting on those and our own problem solving processes, we’ve come up with a sequence of seven problem solving steps we feel best covers everything you need in order to effectively solve problems.

1. Problem identification 

The first stage of any problem solving process is to identify the problem or problems you might want to solve. Effective problem solving strategies always begin by allowing a group scope to articulate what they believe the problem to be and then coming to some consensus over which problem they approach first. Problem solving activities used at this stage often have a focus on creating frank, open discussion so that potential problems can be brought to the surface.

2. Problem analysis 

Though this step is not a million miles from problem identification, problem analysis deserves to be considered separately. It can often be an overlooked part of the process and is instrumental when it comes to developing effective solutions.

The process of problem analysis means ensuring that the problem you are seeking to solve is the right problem . As part of this stage, you may look deeper and try to find the root cause of a specific problem at a team or organizational level.

Remember that problem solving strategies should not only be focused on putting out fires in the short term but developing long term solutions that deal with the root cause of organizational challenges. 

Whatever your approach, analyzing a problem is crucial in being able to select an appropriate solution and the problem solving skills deployed in this stage are beneficial for the rest of the process and ensuring the solutions you create are fit for purpose.

3. Solution generation

Once your group has nailed down the particulars of the problem you wish to solve, you want to encourage a free flow of ideas connecting to solving that problem. This can take the form of problem solving games that encourage creative thinking or problem solving activities designed to produce working prototypes of possible solutions. 

The key to ensuring the success of this stage of the problem solving process is to encourage quick, creative thinking and create an open space where all ideas are considered. The best solutions can come from unlikely places and by using problem solving techniques that celebrate invention, you might come up with solution gold. 

4. Solution development

No solution is likely to be perfect right out of the gate. It’s important to discuss and develop the solutions your group has come up with over the course of following the previous problem solving steps in order to arrive at the best possible solution. Problem solving games used in this stage involve lots of critical thinking, measuring potential effort and impact, and looking at possible solutions analytically. 

During this stage, you will often ask your team to iterate and improve upon your frontrunning solutions and develop them further. Remember that problem solving strategies always benefit from a multitude of voices and opinions, and not to let ego get involved when it comes to choosing which solutions to develop and take further.

Finding the best solution is the goal of all problem solving workshops and here is the place to ensure that your solution is well thought out, sufficiently robust and fit for purpose. 

5. Decision making 

Nearly there! Once your group has reached consensus and selected a solution that applies to the problem at hand you have some decisions to make. You will want to work on allocating ownership of the project, figure out who will do what, how the success of the solution will be measured and decide the next course of action.

The decision making stage is a part of the problem solving process that can get missed or taken as for granted. Fail to properly allocate roles and plan out how a solution will actually be implemented and it less likely to be successful in solving the problem.

Have clear accountabilities, actions, timeframes, and follow-ups. Make these decisions and set clear next-steps in the problem solving workshop so that everyone is aligned and you can move forward effectively as a group. 

Ensuring that you plan for the roll-out of a solution is one of the most important problem solving steps. Without adequate planning or oversight, it can prove impossible to measure success or iterate further if the problem was not solved. 

6. Solution implementation 

This is what we were waiting for! All problem solving strategies have the end goal of implementing a solution and solving a problem in mind. 

Remember that in order for any solution to be successful, you need to help your group through all of the previous problem solving steps thoughtfully. Only then can you ensure that you are solving the right problem but also that you have developed the correct solution and can then successfully implement and measure the impact of that solution.

Project management and communication skills are key here – your solution may need to adjust when out in the wild or you might discover new challenges along the way.

7. Solution evaluation 

So you and your team developed a great solution to a problem and have a gut feeling its been solved. Work done, right? Wrong. All problem solving strategies benefit from evaluation, consideration, and feedback. You might find that the solution does not work for everyone, might create new problems, or is potentially so successful that you will want to roll it out to larger teams or as part of other initiatives. 

None of that is possible without taking the time to evaluate the success of the solution you developed in your problem solving model and adjust if necessary.

Remember that the problem solving process is often iterative and it can be common to not solve complex issues on the first try. Even when this is the case, you and your team will have generated learning that will be important for future problem solving workshops or in other parts of the organization. 

It’s worth underlining how important record keeping is throughout the problem solving process. If a solution didn’t work, you need to have the data and records to see why that was the case. If you go back to the drawing board, notes from the previous workshop can help save time. Data and insight is invaluable at every stage of the problem solving process and this one is no different.

Problem solving workshops made easy

Problem solving strategies are methods of approaching and facilitating the process of problem-solving with a set of techniques , actions, and processes. Different strategies are more effective if you are trying to solve broad problems such as achieving higher growth versus more focused problems like, how do we improve our customer onboarding process?

Broadly, the problem solving steps outlined above should be included in any problem solving strategy though choosing where to focus your time and what approaches should be taken is where they begin to differ. You might find that some strategies ask for the problem identification to be done prior to the session or that everything happens in the course of a one day workshop.

The key similarity is that all good problem solving strategies are structured and designed. Four hours of open discussion is never going to be as productive as a four-hour workshop designed to lead a group through a problem solving process.

Good problem solving strategies are tailored to the team, organization and problem you will be attempting to solve. Here are some example problem solving strategies you can learn from or use to get started.

Use a workshop to lead a team through a group process

Often, the first step to solving problems or organizational challenges is bringing a group together effectively. Most teams have the tools, knowledge, and expertise necessary to solve their challenges – they just need some guidance in how to use leverage those skills and a structure and format that allows people to focus their energies.

Facilitated workshops are one of the most effective ways of solving problems of any scale. By designing and planning your workshop carefully, you can tailor the approach and scope to best fit the needs of your team and organization. 

Problem solving workshop

• Creating a bespoke, tailored process
• Tackling problems of any size
• Building in-house workshop ability and encouraging their use

Workshops are an effective strategy for solving problems. By using tried and test facilitation techniques and methods, you can design and deliver a workshop that is perfectly suited to the unique variables of your organization. You may only have the capacity for a half-day workshop and so need a problem solving process to match. 

By using our session planner tool and importing methods from our library of 700+ facilitation techniques, you can create the right problem solving workshop for your team. It might be that you want to encourage creative thinking or look at things from a new angle to unblock your groups approach to problem solving. By tailoring your workshop design to the purpose, you can help ensure great results.

One of the main benefits of a workshop is the structured approach to problem solving. Not only does this mean that the workshop itself will be successful, but many of the methods and techniques will help your team improve their working processes outside of the workshop. 

We believe that workshops are one of the best tools you can use to improve the way your team works together. Start with a problem solving workshop and then see what team building, culture or design workshops can do for your organization!

Run a design sprint

Great for: 

• aligning large, multi-discipline teams
• quickly designing and testing solutions
• tackling large, complex organizational challenges and breaking them down into smaller tasks

By using design thinking principles and methods, a design sprint is a great way of identifying, prioritizing and prototyping solutions to long term challenges that can help solve major organizational problems with quick action and measurable results.

Some familiarity with design thinking is useful, though not integral, and this strategy can really help a team align if there is some discussion around which problems should be approached first. 

The stage-based structure of the design sprint is also very useful for teams new to design thinking.  The inspiration phase, where you look to competitors that have solved your problem, and the rapid prototyping and testing phases are great for introducing new concepts that will benefit a team in all their future work. 

It can be common for teams to look inward for solutions and so looking to the market for solutions you can iterate on can be very productive. Instilling an agile prototyping and testing mindset can also be great when helping teams move forwards – generating and testing solutions quickly can help save time in the long run and is also pretty exciting!

Break problems down into smaller issues

Organizational challenges and problems are often complicated and large scale in nature. Sometimes, trying to resolve such an issue in one swoop is simply unachievable or overwhelming. Try breaking down such problems into smaller issues that you can work on step by step. You may not be able to solve the problem of churning customers off the bat, but you can work with your team to identify smaller effort but high impact elements and work on those first.

This problem solving strategy can help a team generate momentum, prioritize and get some easy wins. It’s also a great strategy to employ with teams who are just beginning to learn how to approach the problem solving process. If you want some insight into a way to employ this strategy, we recommend looking at our design sprint template below!

Use guiding frameworks or try new methodologies

Some problems are best solved by introducing a major shift in perspective or by using new methodologies that encourage your team to think differently.

Props and tools such as Methodkit , which uses a card-based toolkit for facilitation, or Lego Serious Play can be great ways to engage your team and find an inclusive, democratic problem solving strategy. Remember that play and creativity are great tools for achieving change and whatever the challenge, engaging your participants can be very effective where other strategies may have failed.

LEGO Serious Play

• Improving core problem solving skills
• Thinking outside of the box
• Encouraging creative solutions

LEGO Serious Play is a problem solving methodology designed to get participants thinking differently by using 3D models and kinesthetic learning styles. By physically building LEGO models based on questions and exercises, participants are encouraged to think outside of the box and create their own responses. 

Collaborate LEGO Serious Play exercises are also used to encourage communication and build problem solving skills in a group. By using this problem solving process, you can often help different kinds of learners and personality types contribute and unblock organizational problems with creative thinking. 

Problem solving strategies like LEGO Serious Play are super effective at helping a team solve more skills-based problems such as communication between teams or a lack of creative thinking. Some problems are not suited to LEGO Serious Play and require a different problem solving strategy.

Card Decks and Method Kits

• New facilitators or non-facilitators 
• Approaching difficult subjects with a simple, creative framework
• Engaging those with varied learning styles

Card decks and method kids are great tools for those new to facilitation or for whom facilitation is not the primary role. Card decks such as the emotional culture deck can be used for complete workshops and in many cases, can be used right out of the box. Methodkit has a variety of kits designed for scenarios ranging from personal development through to personas and global challenges so you can find the right deck for your particular needs.

Having an easy to use framework that encourages creativity or a new approach can take some of the friction or planning difficulties out of the workshop process and energize a team in any setting. Simplicity is the key with these methods. By ensuring everyone on your team can get involved and engage with the process as quickly as possible can really contribute to the success of your problem solving strategy.

Source external advice

Looking to peers, experts and external facilitators can be a great way of approaching the problem solving process. Your team may not have the necessary expertise, insights of experience to tackle some issues, or you might simply benefit from a fresh perspective. Some problems may require bringing together an entire team, and coaching managers or team members individually might be the right approach. Remember that not all problems are best resolved in the same manner.

If you’re a solo entrepreneur, peer groups, coaches and mentors can also be invaluable at not only solving specific business problems, but in providing a support network for resolving future challenges. One great approach is to join a Mastermind Group and link up with like-minded individuals and all grow together. Remember that however you approach the sourcing of external advice, do so thoughtfully, respectfully and honestly. Reciprocate where you can and prepare to be surprised by just how kind and helpful your peers can be!

Mastermind Group

• Solo entrepreneurs or small teams with low capacity
• Peer learning and gaining outside expertise
• Getting multiple external points of view quickly

Problem solving in large organizations with lots of skilled team members is one thing, but how about if you work for yourself or in a very small team without the capacity to get the most from a design sprint or LEGO Serious Play session? 

A mastermind group – sometimes known as a peer advisory board – is where a group of people come together to support one another in their own goals, challenges, and businesses. Each participant comes to the group with their own purpose and the other members of the group will help them create solutions, brainstorm ideas, and support one another. 

Mastermind groups are very effective in creating an energized, supportive atmosphere that can deliver meaningful results. Learning from peers from outside of your organization or industry can really help unlock new ways of thinking and drive growth. Access to the experience and skills of your peers can be invaluable in helping fill the gaps in your own ability, particularly in young companies.

A mastermind group is a great solution for solo entrepreneurs, small teams, or for organizations that feel that external expertise or fresh perspectives will be beneficial for them. It is worth noting that Mastermind groups are often only as good as the participants and what they can bring to the group. Participants need to be committed, engaged and understand how to work in this context. 

Coaching and mentoring

• Focused learning and development
• Filling skills gaps
• Working on a range of challenges over time

Receiving advice from a business coach or building a mentor/mentee relationship can be an effective way of resolving certain challenges. The one-to-one format of most coaching and mentor relationships can really help solve the challenges those individuals are having and benefit the organization as a result.

A great mentor can be invaluable when it comes to spotting potential problems before they arise and coming to understand a mentee very well has a host of other business benefits. You might run an internal mentorship program to help develop your team’s problem solving skills and strategies or as part of a large learning and development program. External coaches can also be an important part of your problem solving strategy, filling skills gaps for your management team or helping with specific business issues. 

Now we’ve explored the problem solving process and the steps you will want to go through in order to have an effective session, let’s look at the skills you and your team need to be more effective problem solvers.

Problem solving skills are highly sought after, whatever industry or team you work in. Organizations are keen to employ people who are able to approach problems thoughtfully and find strong, realistic solutions. Whether you are a facilitator , a team leader or a developer, being an effective problem solver is a skill you’ll want to develop.

Problem solving skills form a whole suite of techniques and approaches that an individual uses to not only identify problems but to discuss them productively before then developing appropriate solutions.

Here are some of the most important problem solving skills everyone from executives to junior staff members should learn. We’ve also included an activity or exercise from the SessionLab library that can help you and your team develop that skill. 

If you’re running a workshop or training session to try and improve problem solving skills in your team, try using these methods to supercharge your process!

Active listening

Active listening is one of the most important skills anyone who works with people can possess. In short, active listening is a technique used to not only better understand what is being said by an individual, but also to be more aware of the underlying message the speaker is trying to convey. When it comes to problem solving, active listening is integral for understanding the position of every participant and to clarify the challenges, ideas and solutions they bring to the table.

Some active listening skills include:

• Paying complete attention to the speaker.
• Removing distractions.
• Avoid interruption.
• Taking the time to fully understand before preparing a rebuttal.
• Responding respectfully and appropriately.
• Demonstrate attentiveness and positivity with an open posture, making eye contact with the speaker, smiling and nodding if appropriate. Show that you are listening and encourage them to continue.
• Be aware of and respectful of feelings. Judge the situation and respond appropriately. You can disagree without being disrespectful.   
• Observe body language. 
• Paraphrase what was said in your own words, either mentally or verbally.
• Remain neutral. 
• Reflect and take a moment before responding.
• Ask deeper questions based on what is said and clarify points where necessary.   

Active Listening   #hyperisland   #skills   #active listening   #remote-friendly   This activity supports participants to reflect on a question and generate their own solutions using simple principles of active listening and peer coaching. It’s an excellent introduction to active listening but can also be used with groups that are already familiar with it. Participants work in groups of three and take turns being: “the subject”, the listener, and the observer.

Analytical skills

All problem solving models require strong analytical skills, particularly during the beginning of the process and when it comes to analyzing how solutions have performed.

Analytical skills are primarily focused on performing an effective analysis by collecting, studying and parsing data related to a problem or opportunity. 

It often involves spotting patterns, being able to see things from different perspectives and using observable facts and data to make suggestions or produce insight. 

Analytical skills are also important at every stage of the problem solving process and by having these skills, you can ensure that any ideas or solutions you create or backed up analytically and have been sufficiently thought out.

Nine Whys   #innovation   #issue analysis   #liberating structures   With breathtaking simplicity, you can rapidly clarify for individuals and a group what is essentially important in their work. You can quickly reveal when a compelling purpose is missing in a gathering and avoid moving forward without clarity. When a group discovers an unambiguous shared purpose, more freedom and more responsibility are unleashed. You have laid the foundation for spreading and scaling innovations with fidelity.

Collaboration

Trying to solve problems on your own is difficult. Being able to collaborate effectively, with a free exchange of ideas, to delegate and be a productive member of a team is hugely important to all problem solving strategies.

Remember that whatever your role, collaboration is integral, and in a problem solving process, you are all working together to find the best solution for everyone. 

Marshmallow challenge with debriefing   #teamwork   #team   #leadership   #collaboration   In eighteen minutes, teams must build the tallest free-standing structure out of 20 sticks of spaghetti, one yard of tape, one yard of string, and one marshmallow. The marshmallow needs to be on top. The Marshmallow Challenge was developed by Tom Wujec, who has done the activity with hundreds of groups around the world. Visit the Marshmallow Challenge website for more information. This version has an extra debriefing question added with sample questions focusing on roles within the team.

Communication  

Being an effective communicator means being empathetic, clear and succinct, asking the right questions, and demonstrating active listening skills throughout any discussion or meeting. 

In a problem solving setting, you need to communicate well in order to progress through each stage of the process effectively. As a team leader, it may also fall to you to facilitate communication between parties who may not see eye to eye. Effective communication also means helping others to express themselves and be heard in a group.

Bus Trip   #feedback   #communication   #appreciation   #closing   #thiagi   #team   This is one of my favourite feedback games. I use Bus Trip at the end of a training session or a meeting, and I use it all the time. The game creates a massive amount of energy with lots of smiles, laughs, and sometimes even a teardrop or two.

Creative problem solving skills can be some of the best tools in your arsenal. Thinking creatively, being able to generate lots of ideas and come up with out of the box solutions is useful at every step of the process. 

The kinds of problems you will likely discuss in a problem solving workshop are often difficult to solve, and by approaching things in a fresh, creative manner, you can often create more innovative solutions.

Having practical creative skills is also a boon when it comes to problem solving. If you can help create quality design sketches and prototypes in record time, it can help bring a team to alignment more quickly or provide a base for further iteration.

The paper clip method   #sharing   #creativity   #warm up   #idea generation   #brainstorming   The power of brainstorming. A training for project leaders, creativity training, and to catalyse getting new solutions.

Critical thinking

Critical thinking is one of the fundamental problem solving skills you’ll want to develop when working on developing solutions. Critical thinking is the ability to analyze, rationalize and evaluate while being aware of personal bias, outlying factors and remaining open-minded.

Defining and analyzing problems without deploying critical thinking skills can mean you and your team go down the wrong path. Developing solutions to complex issues requires critical thinking too – ensuring your team considers all possibilities and rationally evaluating them. 

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.

Data analysis 

Though it shares lots of space with general analytical skills, data analysis skills are something you want to cultivate in their own right in order to be an effective problem solver.

Being good at data analysis doesn’t just mean being able to find insights from data, but also selecting the appropriate data for a given issue, interpreting it effectively and knowing how to model and present that data. Depending on the problem at hand, it might also include a working knowledge of specific data analysis tools and procedures. 

Having a solid grasp of data analysis techniques is useful if you’re leading a problem solving workshop but if you’re not an expert, don’t worry. Bring people into the group who has this skill set and help your team be more effective as a result.

Decision making

All problems need a solution and all solutions require that someone make the decision to implement them. Without strong decision making skills, teams can become bogged down in discussion and less effective as a result. 

Making decisions is a key part of the problem solving process. It’s important to remember that decision making is not restricted to the leadership team. Every staff member makes decisions every day and developing these skills ensures that your team is able to solve problems at any scale. Remember that making decisions does not mean leaping to the first solution but weighing up the options and coming to an informed, well thought out solution to any given problem that works for the whole team.

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

Dependability

Most complex organizational problems require multiple people to be involved in delivering the solution. Ensuring that the team and organization can depend on you to take the necessary actions and communicate where necessary is key to ensuring problems are solved effectively.

Being dependable also means working to deadlines and to brief. It is often a matter of creating trust in a team so that everyone can depend on one another to complete the agreed actions in the agreed time frame so that the team can move forward together. Being undependable can create problems of friction and can limit the effectiveness of your solutions so be sure to bear this in mind throughout a project. 

Team Purpose & Culture   #team   #hyperisland   #culture   #remote-friendly   This is an essential process designed to help teams define their purpose (why they exist) and their culture (how they work together to achieve that purpose). Defining these two things will help any team to be more focused and aligned. With support of tangible examples from other companies, the team members work as individuals and a group to codify the way they work together. The goal is a visual manifestation of both the purpose and culture that can be put up in the team’s work space.

Emotional intelligence

Emotional intelligence is an important skill for any successful team member, whether communicating internally or with clients or users. In the problem solving process, emotional intelligence means being attuned to how people are feeling and thinking, communicating effectively and being self-aware of what you bring to a room. 

There are often differences of opinion when working through problem solving processes, and it can be easy to let things become impassioned or combative. Developing your emotional intelligence means being empathetic to your colleagues and managing your own emotions throughout the problem and solution process. Be kind, be thoughtful and put your points across care and attention. 

Being emotionally intelligent is a skill for life and by deploying it at work, you can not only work efficiently but empathetically. Check out the emotional culture workshop template for more!

Facilitation

As we’ve clarified in our facilitation skills post, facilitation is the art of leading people through processes towards agreed-upon objectives in a manner that encourages participation, ownership, and creativity by all those involved. While facilitation is a set of interrelated skills in itself, the broad definition of facilitation can be invaluable when it comes to problem solving. Leading a team through a problem solving process is made more effective if you improve and utilize facilitation skills – whether you’re a manager, team leader or external stakeholder.

The Six Thinking Hats   #creative thinking   #meeting facilitation   #problem solving   #issue resolution   #idea generation   #conflict resolution   The Six Thinking Hats are used by individuals and groups to separate out conflicting styles of thinking. They enable and encourage a group of people to think constructively together in exploring and implementing change, rather than using argument to fight over who is right and who is wrong.

Flexibility 

Being flexible is a vital skill when it comes to problem solving. This does not mean immediately bowing to pressure or changing your opinion quickly: instead, being flexible is all about seeing things from new perspectives, receiving new information and factoring it into your thought process.

Flexibility is also important when it comes to rolling out solutions. It might be that other organizational projects have greater priority or require the same resources as your chosen solution. Being flexible means understanding needs and challenges across the team and being open to shifting or arranging your own schedule as necessary. Again, this does not mean immediately making way for other projects. It’s about articulating your own needs, understanding the needs of others and being able to come to a meaningful compromise.

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.

Working in any group can lead to unconscious elements of groupthink or situations in which you may not wish to be entirely honest. Disagreeing with the opinions of the executive team or wishing to save the feelings of a coworker can be tricky to navigate, but being honest is absolutely vital when to comes to developing effective solutions and ensuring your voice is heard. 

Remember that being honest does not mean being brutally candid. You can deliver your honest feedback and opinions thoughtfully and without creating friction by using other skills such as emotional intelligence. 

Explore your Values   #hyperisland   #skills   #values   #remote-friendly   Your Values is an exercise for participants to explore what their most important values are. It’s done in an intuitive and rapid way to encourage participants to follow their intuitive feeling rather than over-thinking and finding the “correct” values. It is a good exercise to use to initiate reflection and dialogue around personal values.

Initiative 

The problem solving process is multi-faceted and requires different approaches at certain points of the process. Taking initiative to bring problems to the attention of the team, collect data or lead the solution creating process is always valuable. You might even roadtest your own small scale solutions or brainstorm before a session. Taking initiative is particularly effective if you have good deal of knowledge in that area or have ownership of a particular project and want to get things kickstarted.

That said, be sure to remember to honor the process and work in service of the team. If you are asked to own one part of the problem solving process and you don’t complete that task because your initiative leads you to work on something else, that’s not an effective method of solving business challenges.

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.

Impartiality

A particularly useful problem solving skill for product owners or managers is the ability to remain impartial throughout much of the process. In practice, this means treating all points of view and ideas brought forward in a meeting equally and ensuring that your own areas of interest or ownership are not favored over others. 

There may be a stage in the process where a decision maker has to weigh the cost and ROI of possible solutions against the company roadmap though even then, ensuring that the decision made is based on merit and not personal opinion. 

Empathy map   #frame insights   #create   #design   #issue analysis   An empathy map is a tool to help a design team to empathize with the people they are designing for. You can make an empathy map for a group of people or for a persona. To be used after doing personas when more insights are needed.

Being a good leader means getting a team aligned, energized and focused around a common goal. In the problem solving process, strong leadership helps ensure that the process is efficient, that any conflicts are resolved and that a team is managed in the direction of success.

It’s common for managers or executives to assume this role in a problem solving workshop, though it’s important that the leader maintains impartiality and does not bulldoze the group in a particular direction. Remember that good leadership means working in service of the purpose and team and ensuring the workshop is a safe space for employees of any level to contribute. Take a look at our leadership games and activities post for more exercises and methods to help improve leadership in your organization.

Leadership Pizza   #leadership   #team   #remote-friendly   This leadership development activity offers a self-assessment framework for people to first identify what skills, attributes and attitudes they find important for effective leadership, and then assess their own development and initiate goal setting.

In the context of problem solving, mediation is important in keeping a team engaged, happy and free of conflict. When leading or facilitating a problem solving workshop, you are likely to run into differences of opinion. Depending on the nature of the problem, certain issues may be brought up that are emotive in nature. 

Being an effective mediator means helping those people on either side of such a divide are heard, listen to one another and encouraged to find common ground and a resolution. Mediating skills are useful for leaders and managers in many situations and the problem solving process is no different.

Conflict Responses   #hyperisland   #team   #issue resolution   A workshop for a team to reflect on past conflicts, and use them to generate guidelines for effective conflict handling. The workshop uses the Thomas-Killman model of conflict responses to frame a reflective discussion. Use it to open up a discussion around conflict with a team.

Planning 

Solving organizational problems is much more effective when following a process or problem solving model. Planning skills are vital in order to structure, deliver and follow-through on a problem solving workshop and ensure your solutions are intelligently deployed.

Planning skills include the ability to organize tasks and a team, plan and design the process and take into account any potential challenges. Taking the time to plan carefully can save time and frustration later in the process and is valuable for ensuring a team is positioned for success.

3 Action Steps   #hyperisland   #action   #remote-friendly   This is a small-scale strategic planning session that helps groups and individuals to take action toward a desired change. It is often used at the end of a workshop or programme. The group discusses and agrees on a vision, then creates some action steps that will lead them towards that vision. The scope of the challenge is also defined, through discussion of the helpful and harmful factors influencing the group.

Prioritization

As organisations grow, the scale and variation of problems they face multiplies. Your team or is likely to face numerous challenges in different areas and so having the skills to analyze and prioritize becomes very important, particularly for those in leadership roles.

A thorough problem solving process is likely to deliver multiple solutions and you may have several different problems you wish to solve simultaneously. Prioritization is the ability to measure the importance, value, and effectiveness of those possible solutions and choose which to enact and in what order. The process of prioritization is integral in ensuring the biggest challenges are addressed with the most impactful solutions.

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.

Project management

Some problem solving skills are utilized in a workshop or ideation phases, while others come in useful when it comes to decision making. Overseeing an entire problem solving process and ensuring its success requires strong project management skills. 

While project management incorporates many of the other skills listed here, it is important to note the distinction of considering all of the factors of a project and managing them successfully. Being able to negotiate with stakeholders, manage tasks, time and people, consider costs and ROI, and tie everything together is massively helpful when going through the problem solving process. 

Record keeping

Working out meaningful solutions to organizational challenges is only one part of the process.  Thoughtfully documenting and keeping records of each problem solving step for future consultation is important in ensuring efficiency and meaningful change. 

For example, some problems may be lower priority than others but can be revisited in the future. If the team has ideated on solutions and found some are not up to the task, record those so you can rule them out and avoiding repeating work. Keeping records of the process also helps you improve and refine your problem solving model next time around!

Personal Kanban   #gamestorming   #action   #agile   #project planning   Personal Kanban is a tool for organizing your work to be more efficient and productive. It is based on agile methods and principles.

Research skills

Conducting research to support both the identification of problems and the development of appropriate solutions is important for an effective process. Knowing where to go to collect research, how to conduct research efficiently, and identifying pieces of research are relevant are all things a good researcher can do well. 

In larger groups, not everyone has to demonstrate this ability in order for a problem solving workshop to be effective. That said, having people with research skills involved in the process, particularly if they have existing area knowledge, can help ensure the solutions that are developed with data that supports their intention. Remember that being able to deliver the results of research efficiently and in a way the team can easily understand is also important. The best data in the world is only as effective as how it is delivered and interpreted.

Customer experience map   #ideation   #concepts   #research   #design   #issue analysis   #remote-friendly   Customer experience mapping is a method of documenting and visualizing the experience a customer has as they use the product or service. It also maps out their responses to their experiences. To be used when there is a solution (even in a conceptual stage) that can be analyzed.

Risk management

Managing risk is an often overlooked part of the problem solving process. Solutions are often developed with the intention of reducing exposure to risk or solving issues that create risk but sometimes, great solutions are more experimental in nature and as such, deploying them needs to be carefully considered. 

Managing risk means acknowledging that there may be risks associated with more out of the box solutions or trying new things, but that this must be measured against the possible benefits and other organizational factors. 

Be informed, get the right data and stakeholders in the room and you can appropriately factor risk into your decision making process. 

Decisions, Decisions…   #communication   #decision making   #thiagi   #action   #issue analysis   When it comes to decision-making, why are some of us more prone to take risks while others are risk-averse? One explanation might be the way the decision and options were presented.  This exercise, based on Kahneman and Tversky’s classic study , illustrates how the framing effect influences our judgement and our ability to make decisions . The participants are divided into two groups. Both groups are presented with the same problem and two alternative programs for solving them. The two programs both have the same consequences but are presented differently. The debriefing discussion examines how the framing of the program impacted the participant’s decision.

Team-building 

No single person is as good at problem solving as a team. Building an effective team and helping them come together around a common purpose is one of the most important problem solving skills, doubly so for leaders. By bringing a team together and helping them work efficiently, you pave the way for team ownership of a problem and the development of effective solutions. 

In a problem solving workshop, it can be tempting to jump right into the deep end, though taking the time to break the ice, energize the team and align them with a game or exercise will pay off over the course of the day.

Remember that you will likely go through the problem solving process multiple times over an organization’s lifespan and building a strong team culture will make future problem solving more effective. It’s also great to work with people you know, trust and have fun with. Working on team building in and out of the problem solving process is a hallmark of successful teams that can work together to solve business problems.

9 Dimensions Team Building Activity   #ice breaker   #teambuilding   #team   #remote-friendly   9 Dimensions is a powerful activity designed to build relationships and trust among team members. There are 2 variations of this icebreaker. The first version is for teams who want to get to know each other better. The second version is for teams who want to explore how they are working together as a team.

Time management 

The problem solving process is designed to lead a team from identifying a problem through to delivering a solution and evaluating its effectiveness. Without effective time management skills or timeboxing of tasks, it can be easy for a team to get bogged down or be inefficient.

By using a problem solving model and carefully designing your workshop, you can allocate time efficiently and trust that the process will deliver the results you need in a good timeframe.

Time management also comes into play when it comes to rolling out solutions, particularly those that are experimental in nature. Having a clear timeframe for implementing and evaluating solutions is vital for ensuring their success and being able to pivot if necessary.

Improving your skills at problem solving is often a career-long pursuit though there are methods you can use to make the learning process more efficient and to supercharge your problem solving skillset.

Remember that the skills you need to be a great problem solver have a large overlap with those skills you need to be effective in any role. Investing time and effort to develop your active listening or critical thinking skills is valuable in any context. Here are 7 ways to improve your problem solving skills.

Share best practices

Remember that your team is an excellent source of skills, wisdom, and techniques and that you should all take advantage of one another where possible. Best practices that one team has for solving problems, conducting research or making decisions should be shared across the organization. If you have in-house staff that have done active listening training or are data analysis pros, have them lead a training session. 

Your team is one of your best resources. Create space and internal processes for the sharing of skills so that you can all grow together. 

Ask for help and attend training

Once you’ve figured out you have a skills gap, the next step is to take action to fill that skills gap. That might be by asking your superior for training or coaching, or liaising with team members with that skill set. You might even attend specialized training for certain skills – active listening or critical thinking, for example, are business-critical skills that are regularly offered as part of a training scheme.

Whatever method you choose, remember that taking action of some description is necessary for growth. Whether that means practicing, getting help, attending training or doing some background reading, taking active steps to improve your skills is the way to go.

Learn a process 

Problem solving can be complicated, particularly when attempting to solve large problems for the first time. Using a problem solving process helps give structure to your problem solving efforts and focus on creating outcomes, rather than worrying about the format. 

Tools such as the seven-step problem solving process above are effective because not only do they feature steps that will help a team solve problems, they also develop skills along the way. Each step asks for people to engage with the process using different skills and in doing so, helps the team learn and grow together. Group processes of varying complexity and purpose can also be found in the SessionLab library of facilitation techniques . Using a tried and tested process and really help ease the learning curve for both those leading such a process, as well as those undergoing the purpose.

Effective teams make decisions about where they should and shouldn’t expend additional effort. By using a problem solving process, you can focus on the things that matter, rather than stumbling towards a solution haphazardly. 

Create a feedback loop

Some skills gaps are more obvious than others. It’s possible that your perception of your active listening skills differs from those of your colleagues. 

It’s valuable to create a system where team members can provide feedback in an ordered and friendly manner so they can all learn from one another. Only by identifying areas of improvement can you then work to improve them. 

Remember that feedback systems require oversight and consideration so that they don’t turn into a place to complain about colleagues. Design the system intelligently so that you encourage the creation of learning opportunities, rather than encouraging people to list their pet peeves.

While practice might not make perfect, it does make the problem solving process easier. If you are having trouble with critical thinking, don’t shy away from doing it. Get involved where you can and stretch those muscles as regularly as possible. 

Problem solving skills come more naturally to some than to others and that’s okay. Take opportunities to get involved and see where you can practice your skills in situations outside of a workshop context. Try collaborating in other circumstances at work or conduct data analysis on your own projects. You can often develop those skills you need for problem solving simply by doing them. Get involved!

Use expert exercises and methods

Learn from the best. Our library of 700+ facilitation techniques is full of activities and methods that help develop the skills you need to be an effective problem solver. Check out our templates to see how to approach problem solving and other organizational challenges in a structured and intelligent manner.

There is no single approach to improving problem solving skills, but by using the techniques employed by others you can learn from their example and develop processes that have seen proven results. 

Try new ways of thinking and change your mindset

Using tried and tested exercises that you know well can help deliver results, but you do run the risk of missing out on the learning opportunities offered by new approaches. As with the problem solving process, changing your mindset can remove blockages and be used to develop your problem solving skills.

Most teams have members with mixed skill sets and specialties. Mix people from different teams and share skills and different points of view. Teach your customer support team how to use design thinking methods or help your developers with conflict resolution techniques. Try switching perspectives with facilitation techniques like Flip It! or by using new problem solving methodologies or models. Give design thinking, liberating structures or lego serious play a try if you want to try a new approach. You will find that framing problems in new ways and using existing skills in new contexts can be hugely useful for personal development and improving your skillset. It’s also a lot of fun to try new things. Give it a go!

Encountering business challenges and needing to find appropriate solutions is not unique to your organization. Lots of very smart people have developed methods, theories and approaches to help develop problem solving skills and create effective solutions. Learn from them!

Books like The Art of Thinking Clearly , Think Smarter, or Thinking Fast, Thinking Slow are great places to start, though it’s also worth looking at blogs related to organizations facing similar problems to yours, or browsing for success stories. Seeing how Dropbox massively increased growth and working backward can help you see the skills or approach you might be lacking to solve that same problem. Learning from others by reading their stories or approaches can be time-consuming but ultimately rewarding.

A tired, distracted mind is not in the best position to learn new skills. It can be tempted to burn the candle at both ends and develop problem solving skills outside of work. Absolutely use your time effectively and take opportunities for self-improvement, though remember that rest is hugely important and that without letting your brain rest, you cannot be at your most effective. 

Creating distance between yourself and the problem you might be facing can also be useful. By letting an idea sit, you can find that a better one presents itself or you can develop it further. Take regular breaks when working and create a space for downtime. Remember that working smarter is preferable to working harder and that self-care is important for any effective learning or improvement process.

Want to design better group processes?

Over to you

Now we’ve explored some of the key problem solving skills and the problem solving steps necessary for an effective process, you’re ready to begin developing more effective solutions and leading problem solving workshops.

Need more inspiration? Check out our post on problem solving activities you can use when guiding a group towards a great solution in your next workshop or meeting. Have questions? Did you have a great problem solving technique you use with your team? Get in touch in the comments below. We’d love to chat!

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3 tricks for solving problems faster and better

Recent research by Evan Polman of NYU and Kyle J. Emich of Cornell may shed some light on why. In three sets of experiments , they found that when people solved problems on behalf of others, they produced faster and more creative solutions than they did when they solved the same problems for themselves.

In the first experiment, Polman and Emich asked participants either to draw an alien for a story they were going to write themselves or for someone else’s story. The aliens people sketched for others were more creative than the ones they drew for themselves.

In the second study, participants were asked to come up with gift ideas for themselves, for someone close to them, or for someone far away. The result: The more distant the recipient, the more creative the gift.

And in the third study, participants had to solve the following problem:

A prisoner was attempting to escape from a tower. He found a rope in his cell that was half as long enough to permit him to reach the ground safely. He divided the rope in half, tied the two parts together, and escaped. How could he have done this?

Subjects were more likely to come up with the answer on behalf of another person than for themselves; the farther away the other person was imagined to be, the more likely the participants were to come up with the correct answer.

Polman and Emich say the principle at work is something called “ construal-level theory ,” which in simple terms means that we think in more abstract terms about distant problems (or problems belonging to distant people) — and thinking at a more abstract level produces more creative solutions.

So given that we’re often more creative solving someone else’s problems, what can we do to more effectively solve our own? Here are three ideas:

1. Trade problems with someone. When you get stuck, stop hammering away at the problem and find a colleague to swap with.

2. Solve problems on behalf of someone else. Create some psychological distance from your project by pretending that you’re doing it on behalf of someone else. Use your imagination here: the “other person” could be the woman across the hall, a relative, or a stranger halfway across the world. The farther away, the better.

3. Put some distance between yourself and your project. Writers know something magical happens when you put your manuscript away in a drawer. When you come back to it a week or a month or six months later, you have a fresher, more creative perspective on the work. When you can, build some slack into your deadlines and try putting your work out of sight for as long as you can manage.

Have you tried this approach? Has anyone set up a website to allow people to swap problems? (Seems like a promising business.) And how the heck did the prisoner escape? If you’ve got answers, respond in the Comments section.

41 Responses to “3 tricks for solving problems faster and better”

Presumably he split the rope length-ways, by unravelling the strands, to produce two lengths each half as thick as the original rope. 🙂

The research is fascinating. It aligns a bit with the old saying, “A problem shared is a problem halved.”

This simplest solution is most often the best. Unfortunately, we are often too entwined in our own issues to see the big picture.

What an awesome post!

I love the idea of trading problems with someone else.

“I’ll solve your scheduling problem if you can tackle world peace. Thanks!”

I’m imagining that an emotional involvement in a situation prevents us from being totally objective and free-minded about a solution, as well.

Love the Pink Blog. Great content.

Yes, I agree that it was most likely split length wise. In my opinion, this is a much easier creative riddle than the Candle Problem.

Very interesting post. I think a more feasible application for some software would be for internal use at an organization.

I also have noticed that when people become so bogged down by their own stress, often not all related to the specific problem at hand, that they defend the problem and seem to lack a true desire to solve it quickly. Sincerely admitting that you do in fact want to solve it is the most important step, though it is often overlooked.

Great take on an interesting finding. Would you say your hints are the equivalent of asking “what would N.N (insert prefered role model) do to solve a problem like this?”

Dan, great post. I think this is one of those “I kinda knew that” but now “I know that” actually works scenarios. I think this confirms.

a. Why consultants can play an integral role in problem solving. b. How executive roundtables can provide such broad insight to a problem quickly and efficiently. c. Why coaches and mentors can help frame a problem in a way where an emotional detachment is able to take place.

Last point – the rope scenario problem seems appropriate. Too often ropes are used to hand ourselves rather than being used creatively for escape or rescue.

Similarly, I’ve always found explaining the problem to someone else helps. Not because they come up with a solution (though they may), but because the very act of laying something out so that someone else understands it renders it amenable to a more objective analysis. I’ve often solved the ‘impossible’ problem half way through explaining it to a third party.

I coach a lot of coaches … and find a very helpful question can be, “What would you tell a client if they were in your situation?”

Can see the challenge when the research indicates that the best solutions tend to come from abstract thinking – and when we go to problem solve in our own business and life, we often switch on our linear thinking mode.

Fascinating and practical read. Thanks.

Nate, I agree it’s easy to get caught up in the problem and not see the big picture. It’s as if your in a maze, and you can only see what is immediately around you. However, someone else with a better view from above the maze can see the whole thing. It is much easier for them to solve the maze or the problem.

Aga, I like your thoughts too. It’s hard to make a decision when emotions are involved.

Interesting post!

As a designer, I often follow Rule 3. I have what I call my “24 hour rule.” Often I’ll have what I think is a fantastic idea but if it still seems fantastic after a day then I pursue it. (I’m always shocked at how often I’ve changed my mind after those 24 hours. “How could I have thought that one up?!”)

I don’t have problems buying gifts for those close to me. A few years back I even wrote a post on how to become a good gift-giver: http://ow.ly/4sHXI . I think it’s easier to buy a gift for someone close to you as there’s greater access to their likes and dislikes. Oh, and I know *exactly* what gift I want! -g

Another way to look at this solution is with an idiom. By dividing the rope he created two halves. We all know that “two halves make a ‘hole'” so once he divided the rope he was able to walk right out of his cell scott free.

The idea of solving problems on behalf of someone else, even if it’s re-framing the problem you have as belonging to someone else, is a fascinating idea, and really struck a chord with me.

As an improv-comedian \ actor, I’m never at a loss for what to do – there are plenty of “offers” from my fellow players on stage (their posture, what they said, how they said it, etc). We often use the phrase “mistakes are gifts” because they give you something to build on.

Conversely, writing at times seems much more difficult. When writing on a deadline for someone else, I almost never get writers block, and I don’t get distracted easily. But if I’m writing something on my own, it’s a whole different story.

I’m going to experiment with defining the completion of personal writing projects as solving a problem for someone else, and see what results I get. But even thinking about it, I have a different feeling about completing them. -Ken-

This is very interesting. I have a colleague I call my “thinking partner”. When I am stuck, I call him, when he is stuck he calls me. We find it so much easier to solve each other’s problems. I guess we’re not alone in this. Perhaps more organizations should talk about and encourage employees to find their “thinking partner”. Sometimes just the way we talk about problems makes them seem more manageable. For example, I’ll say, “I’ve been carrying this situation around in my mind and it’s getting heavy…will you hold it for a while?” We laugh, but knowing someone else is “carrying” it for me, clears my mind and allows me to be more creative about it.

A great message on sharing the burden and sharing the rewards.

As for the puzzle, the two halves of the rope made a “hole.” The prisoner put a hole in the floor (or door) and crawled out to freedom.

I think Rod raises some good points in that these data seem to support the work of consultants. I would extend the usefulness to most (if not all?) collaboration. The adage goes that two heads are better than one. While that may be true, I prefer those two heads to be from different fields to allow different ways of thinking to enter the conversation.

With Love and Gratitude,

This is 100% the case and I see this consistently. my blog stillmansays.com documents my adventures sitting out in Union Square in New York City with two folding chairs and a table with a sign that reads “Creative Approaches To What You Have Been Thinking About” and a smaller sign that reads “Pay What You Like or Take What You Need”.

Yes I am creative and capable but that distance allows the space to go in some remarkable directions.

So, how do you solve a problem like Maria? Trade her with Mother Superior for a problem named Marta?

Great post, Daniel.

I am both a writer and a teacher. I regularly collaborate with other teachers on class projects and assignments. One such example is my collaboration with another teacher on English assignments. She gives them, I correct them and she follows up. The collaboration works well.

As for the rope problem, why has no one suggested a Mobius Strip cut repeatly into thirds? The tower can be as tall as the jailer wants and the prisoner can still escape (ignoring that new pesky prisoner weight to rope tensile strength problem 😉 ).

yes i also thought that the tensile strength might not be sufficient enough. But that is already been said in the question itself. It says you divide rope in half and escape that means the prisoner did escaped. But by what? divinding the rope in half.How? not lateraly but verticallyy!!

As a golf instructor and business person… seems I’m always entrenched with problems… actually solving them is kind of what I do for a living. Solving a slice, solving a hook, solving why a person’s golf game goes south after the 14th hole.

As a businessman… I also have to solve the problem of marketing, sales, budgeting, etc… I think the golf professional part in me has assisted me in solving some of the business aspects of my profession. Simply because no two golf swings are alike… so creativity is essential. YET… at the same time… looking for common keys to one’s success… in golf or business.

Thanks for another great article!

The photo of the guy in the jar is quite appropriate. One of the ways I have heard this process described is that when you are in the problem you are inside the jar and it’s difficult to comprehend what’s going on and what to do about it, but anyone on the outside of the problem can easily read the label on the jar and suggest ways to handle the situation that wouldn’t easily occur to you.

I do something similar pretty often–when I have a problem, I pretend I’m someone else (someone who’s courage/intelligence/creativity/boldness I admire) and think of how that person would handle it. I usually come up with a better solution than if “I” handled it.

I wonder if many of us tend to be more self-conscious and unconsciously self-editing when the outcome directly reflects on us. The abstract distance of working on someone problem may act as the equivalent of a psychological disguise, liberating us from this self-consciousness and self-editing.

Being too close to the problem can hinder problem solving, absolutely. It is so easy to raise objections to possible solutions when you are intimately acquainted with the problem. “That won’t work because of [name complexity here].”

This is true when working with a client to solve a problem. They can be very quick to point out why a proposed creative solution will fail, and can hinder real progress. Remove that party, and solutions can be proposed, tested, and implemented in very short time spans.

Thank you for the post. The study findings are very interesting and enlightening.

I have noticed that for more complex problems (and for finding good gifts), distancing yourself from the problem, or asking someone else to solve it, is indeed helpful. However, in this “prisoner attempting to escape from a tower” problem, I decided to try to find an answer putting myself in the place of the prisoner, just to see what would happen. It took me just a few seconds to come to the solution already mentioned by various people, cut the rope in half lengthwise.

Dan, I think the prisoner split the rope in two, tied a large knot just below one of the severed ends, and pulled the strands apart (so that, when laid on his pillow, it would resemble human hair).

Later, after the prisoner was unresponsive to the prison guard’s bed check, the guard entered the cell, walked over to the bedside and asked, “Are you feeling okay?”

Just then, the crafty prisoner emerged from a darkened corner of the cell, slipped through the open door, and as he pulled the cell door closed behind him answered, “I’m afraid not.”

Just a theory… Steve Curtin

Not strictly for the purpose of swapping problems, but Lissn.com pairs you up with a random stranger for chatting. It strikes me that the problem swapping idea would just be an extension of a system like that. Find me someone I don’t know, who is willing to swap problems. If you need creative solutions, you may not even care about filtering who you are paired with, since creatives solutions may come from expertise you did not expect. The only challenge is overcoming Metcalfe’s law to build a network large enough that you can easily find a counterpart.

This raises one (of many 🙂 problems with education. The insular nature of the teaching profession prevents exactly this kind of interaction.

Some proactive districts have hired coaches to help stimulate the kind of conversations that would build the kind of perspective you write about, but that’s a major culture shift and so has encountered a lot of resistance.

Ideally, we would build more collaboration into the structure of a teacher’s (and any professional’s) work day. A short-term loss that should lead to long-term gains.

I wonder whether our need for purpose, quenched in this case by helping someone else solve a problem, is at work here.

I say it this way: It’s always easier doing somebody else’s homework.

This approach clearly works. I recently visited with some regional folks at work who were meeting with various managers, looking for some ideas to solve a problem. I thought the solution I suggested was obvious, that five other people would have already mentioned it by that point in time. But when I mentioned my idea, their faces lit up – it had never, ever dawned on them to look for a solution in that particular direction! And yes, when I’m stuck on a painting, comic, etc, I do put the piece away for a while to think it over.

Someone else can still be you in the mirror. I use to speak and teach someone in the mirror and this results have been splendid to my educational progress. wow

It is amazing to know that there are articles like this on web.Thanks for helping me out…

See, I guess I didn’t understand the rope problem correctly. In my solution, the ends of the rope are tied together to make a loop, the loop is slung over the tower, and the guy escapes by shimmying down, like the telephone linemen of old.

They obvious answer didn’t occur to me.

From this tiny post, you learn so much about my mind and my life 🙂

Great post as always.

In our work with positive deviants, they rarely encounter these limitations. In fact, as we wrote about in “Positive Deviants Rule!”, they are often the best source of innovation in an organization.

Positive deviants appear to be less limited than others because they have an exceptionally strong sense of “purpose” (as used in DRIVE). This drive to achieving a purpose is so strong, and so proactive, that their starting point of all problem solving and work is “how do we do this the right way.” As such, they are rarely constrained by their own or organizational limitations.

The implications for the rest of us to transcend our typical constraints is to go back to “purpose” and get refocused on the big picture of what you are trying to do and why you are trying to do it. The stronger you hold on to your purpose, the more likely you are to let go of constraints and come up with better “out-of-the-box” solutions.

I like Andrew’s rope answer better, but maybe he looped the rope around the tower (like a belt) and climbed down that way.

I believe that a natural creative wisdom exists deep within every one of us and the blocks to that wisdom, particularly when it comes to ones self, are rooted in disempowering subconscious beliefs. As an example, subconscious beliefs of unworthiness or being undeserving (Which are more common in the workplace than you’d ever imagine) would result in that shut down for yourself while the problem would be more easily solved for someone else.

I think he folded the rope in half, made a lasso and threw it over a nearby treetop. Then he pulled it closer, hopped onto the tree and climbed down that way…

I think this is quite interesting and taps into something I first witnessed when I started teaching music, and then was just thinking over again last night.

I had been studying the flute for years, but then as a college undergrad took some work teaching 9-12 year olds. I heard myself saying the same things to these kids as my teacher said to me, even despite our huge skill gap. It was so much easier to find the energy to see it in others and problem solve about how to best address the problem each student might be facing. I realized I needed to harness that objectivity in my own practice, but sometimes easier said than done, especially when the thing you are trying to solve connects to hopes, dreams and fears – as our biggest problems do.

Fast forward many years to last night, where I no longer play the flute, and I was thinking about the same thing again. When a problem swirls around in my head, as it was last night, it very rarely goes anywhere useful. If I articulate it to someone else, that can help, but there’s not always someone I know immediately who’s interested in hearing it or helping to solve it. It occurred to me that it always helps me to actually write down my problem, something like what Gretchen Rubin describes as ‘identifying the problem’. Some problems need many small ‘sub-problems’ articulated in this way, and it takes some investment of energy upfront, but I find doing this definitely helps to give me objectivity to solve my own problem.

Thanks, I have recently been seeking for details about this subject for ages and yours is the best I have found so far.

Divide vertically, not horizontally.

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Trauma-informed practices in schools, teacher well-being, cultivating diversity, equity, & inclusion, integrating technology in the classroom, social-emotional development, covid-19 resources, invest in resilience: summer toolkit, civics & resilience, all toolkits, degree programs, trauma-informed professional development, teacher licensure & certification, how to become - career information, classroom management, instructional design, lifestyle & self-care, online higher ed teaching, current events, 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

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 =

• Step 1: Take the number being multiplied by 5 and cut it in half, this makes the number 4 become the number 2.
• Step 2: Add a zero to the number to find the answer. In this case, the answer is 20.

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

For instance, consider 5 x 3.

• Step 1: Subtract one from the number being multiplied by 5, in this instance the number 3 becomes the number 2.
• Step 2: Now halve the number 2, which makes it the number 1. Make 5 the last digit. The number produced is 15, which is the answer.

4. Division tricks

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

• 10 if the number ends in 0
• 9 when the digits are added together and the total is evenly divisible by 9
• 8 if the last three digits are evenly divisible by 8 or are 000
• 6 if it is an even number and when the digits are added together the answer is evenly divisible by 3
• 5 if it ends in a 0 or 5
• 4 if it ends in 00 or a two digit number that is evenly divisible by 4
• 3 when the digits are added together and the result is evenly divisible by the number 3
• 2 if it ends in 0, 2, 4, 6, or 8

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:

• Step 1: Move the decimal point over by one place, 235 becomes 23.5.
• Step 2: Divide 23.5 by the number 2, the answer is 11.75. That is also the answer to the original equation.

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

Let’s use the number 35 as an example.

• Step 1: Multiply the first digit by itself plus 1.
• Step 2: Put a 25 at the end.

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.

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Math Hacks: How to Think Faster and Solve Problems Quicker

Do you ever wish you could solve math problems faster and more efficiently? If so, you’re not alone. Many students struggle with math and would like to have a better understanding of the subject. Fortunately, there are some proven techniques that can help you think faster, work more accurately, and solve math problems more quickly. This guide will provide you with some basic tips on how to maximize your performance in mathematics.

Using Technology

Source: businessinsider.com

The use of technology can be especially useful when working through math problems. From scientific calculators and apps to computer programs, there are many resources that can help you think faster and solve problems quicker.

Scientific calculators are great for doing calculations on the fly, while a graphing calculator helps identify patterns in data. Apps like CameraMath and programs provide step-by-step tutorials and allow you to explore concepts quickly. They often have interactive features that require you to type in your own expressions, allowing you to quickly explore several different options and arrive at a satisfactory solution.

Computer software may be the best resource for solving complex equations or visualizing data sets in two or three dimensions. With the help of software like this, it is possible to automate much of the work that goes into solving tough math problems, from performing tedious calculations to categorizing related topics into helpful visual graphs. Allowing technology to do some of the heavy liftings can help free up your own mental energy so you can focus on finding patterns within data sets and developing creative solutions for more challenging mathematics tasks.

Problem-Solving Strategies

Source: oneeducation.org.uk

First, it is important to identify the problem and break it down into its component parts. Analyze the data available on the subject and ask relevant questions about them in order to gain a more thorough understanding of the elements comprising it. This may help by leading a person towards recognizing relevant information that can be used in solving the problem or by enabling them to create hypotheses as potential solutions.

Guessing and checking, looking at concrete examples and identifying counter-examples, or generating new possibilities are all helpful methods when formulating hypotheses or answering questions relating to the data set.

When evaluating a hypothesis or considering alternatives, numerical estimation techniques may be of use. This involves using existing numbers that one is familiar with in order to process information faster or simulates an answer in light of restricted time constraints. Comparing possible outcomes alongside relative directions is also beneficial when trying to make an accurate guess.

Along these lines, charts and diagrams are great visual tools for simplifying complex ideas quickly for improved comprehension as well as aiding one’s memory recall in faster identification of problems; this could be especially useful when dealing with multi-step equations or trying breaking large cohesive units into manageable bits.

Finally, if complex calculations are required during lengthy exercise tests one’s mental capacities then expressions such as mnemonics (anagrams) can help greatly by providing easier recall while attempting various problems at once under time pressure so corrections may be implemented without too much ado if achieving accuracy is important.

Math Shortcuts

Source: dkfindout.com

Studying math shortcuts can result in dramatic increases in speed and precision when working with problem-solving. Here are some examples of common shortcuts used throughout mathematics:

• Estimation: Estimation is a way of using educated guessing to quickly determine an accurate answer without one hundred percent precision. In many cases, it can be used as a substitute for precise calculation, allowing for faster problem-solving.
• Memorization: Memorizing certain formulas or equations can assist in solving problems quickly by eliminating guessing or long calculations and by helping you focus on applying them appropriately. Besides reducing overall time, memorization also helps increase general understanding because fundamental principles must be kept in mind even as shortcuts are employed.
• Algorithm: An algorithm functions as a formula — it offers steps that methodically provide results like complex equations, but for different types of problems; this combines logic and math to save processing time and reduce guesswork when approaching logical issues.
• Graphical Calculation: Graphical calculation is making use of graphs instead of algebraic operations to solve problems; its advantage lies in quick visual processing instead of employing computations when answering set questions.

Whether you’re a student struggling with calculus or a professional seeking to improve your math skills, resources like plainmath.net can provide you with helpful tips and tricks to help you think faster and solve problems quicker.

Memory Techniques

Source: meer.com

Memory techniques are methods for improving the recall of information and skills. Having a good memory is essential for mastering math and problem-solving tasks, and developing strong memory skills across all areas of your life. Memory techniques can help boost your memory power and you may even find that using memorization tricks can enhance your understanding of mathematical concepts in general.

For example, the Method of Loci is a technique that can help encode information in a way that helps with its recall. This technique involves creating mental images or “loci” to link items to a familiar environment such as your house or office. Through this method, you create vivid images around specific items which makes it easier to remember where you placed them later on by visualizing the associated scenario.

The Mnemonic Linking Method is another useful memorization tool that presents the material as a story or series of events so it becomes easier to remember later on. This mental image approach uses linking words and phrases from numerous topics to connect one idea to other memories already stored in our brain, making it much easier for us to capture and retain information over time quickly.

Finally, The Peg System works by associating specific topics with everyday items or numbers so they become easier to recall shortly thereafter. The rhymes used are also known as pegs because they deposit data into our memory container like pegs on a clothesline would hang clothes onto poles. All these memorization systems work well when used repeatedly over time helping you improve the speed with unfamiliar math problems faster than before without having to rely solely on the brute force approach.

In summary, the key to thinking faster and solving problems more quickly is to stay organized, use diagrams, stick to the question at hand, keep track of your definitions and ideas, and practice as much as you can.

With these valuable tips in mind, you’ll be able to confidently approach any math problem that comes your way. Don’t be discouraged by challenging problems; instead, break them down into component parts and work through it in a step-by-step manner.

And remember – with enough practice and patience anyone can become proficient in mathematics.

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Do You Understand the Problem You’re Trying to Solve?

To solve tough problems at work, first ask these questions.

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Problem solving skills are invaluable in any job. But all too often, we jump to find solutions to a problem without taking time to really understand the dilemma we face, according to Thomas Wedell-Wedellsborg , an expert in innovation and the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

In this episode, you’ll learn how to reframe tough problems by asking questions that reveal all the factors and assumptions that contribute to the situation. You’ll also learn why searching for just one root cause can be misleading.

Key episode topics include: leadership, decision making and problem solving, power and influence, business management.

HBR On Leadership curates the best case studies and conversations with the world’s top business and management experts, to help you unlock the best in those around you. New episodes every week.

• Listen to the original HBR IdeaCast episode: The Secret to Better Problem Solving (2016)
• Find more episodes of HBR IdeaCast
• Discover 100 years of Harvard Business Review articles, case studies, podcasts, and more at HBR.org .

HANNAH BATES: Welcome to HBR on Leadership , case studies and conversations with the world’s top business and management experts, hand-selected to help you unlock the best in those around you.

Problem solving skills are invaluable in any job. But even the most experienced among us can fall into the trap of solving the wrong problem.

Thomas Wedell-Wedellsborg says that all too often, we jump to find solutions to a problem – without taking time to really understand what we’re facing.

He’s an expert in innovation, and he’s the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

  In this episode, you’ll learn how to reframe tough problems, by asking questions that reveal all the factors and assumptions that contribute to the situation. You’ll also learn why searching for one root cause can be misleading. And you’ll learn how to use experimentation and rapid prototyping as problem-solving tools.

This episode originally aired on HBR IdeaCast in December 2016. Here it is.

SARAH GREEN CARMICHAEL: Welcome to the HBR IdeaCast from Harvard Business Review. I’m Sarah Green Carmichael.

Problem solving is popular. People put it on their resumes. Managers believe they excel at it. Companies count it as a key proficiency. We solve customers’ problems.

The problem is we often solve the wrong problems. Albert Einstein and Peter Drucker alike have discussed the difficulty of effective diagnosis. There are great frameworks for getting teams to attack true problems, but they’re often hard to do daily and on the fly. That’s where our guest comes in.

Thomas Wedell-Wedellsborg is a consultant who helps companies and managers reframe their problems so they can come up with an effective solution faster. He asks the question “Are You Solving The Right Problems?” in the January-February 2017 issue of Harvard Business Review. Thomas, thank you so much for coming on the HBR IdeaCast .

THOMAS WEDELL-WEDELLSBORG: Thanks for inviting me.

SARAH GREEN CARMICHAEL: So, I thought maybe we could start by talking about the problem of talking about problem reframing. What is that exactly?

THOMAS WEDELL-WEDELLSBORG: Basically, when people face a problem, they tend to jump into solution mode to rapidly, and very often that means that they don’t really understand, necessarily, the problem they’re trying to solve. And so, reframing is really a– at heart, it’s a method that helps you avoid that by taking a second to go in and ask two questions, basically saying, first of all, wait. What is the problem we’re trying to solve? And then crucially asking, is there a different way to think about what the problem actually is?

SARAH GREEN CARMICHAEL: So, I feel like so often when this comes up in meetings, you know, someone says that, and maybe they throw out the Einstein quote about you spend an hour of problem solving, you spend 55 minutes to find the problem. And then everyone else in the room kind of gets irritated. So, maybe just give us an example of maybe how this would work in practice in a way that would not, sort of, set people’s teeth on edge, like oh, here Sarah goes again, reframing the whole problem instead of just solving it.

THOMAS WEDELL-WEDELLSBORG: I mean, you’re bringing up something that’s, I think is crucial, which is to create legitimacy for the method. So, one of the reasons why I put out the article is to give people a tool to say actually, this thing is still important, and we need to do it. But I think the really critical thing in order to make this work in a meeting is actually to learn how to do it fast, because if you have the idea that you need to spend 30 minutes in a meeting delving deeply into the problem, I mean, that’s going to be uphill for most problems. So, the critical thing here is really to try to make it a practice you can implement very, very rapidly.

There’s an example that I would suggest memorizing. This is the example that I use to explain very rapidly what it is. And it’s basically, I call it the slow elevator problem. You imagine that you are the owner of an office building, and that your tenants are complaining that the elevator’s slow.

Now, if you take that problem framing for granted, you’re going to start thinking creatively around how do we make the elevator faster. Do we install a new motor? Do we have to buy a new lift somewhere?

The thing is, though, if you ask people who actually work with facilities management, well, they’re going to have a different solution for you, which is put up a mirror next to the elevator. That’s what happens is, of course, that people go oh, I’m busy. I’m busy. I’m– oh, a mirror. Oh, that’s beautiful.

And then they forget time. What’s interesting about that example is that the idea with a mirror is actually a solution to a different problem than the one you first proposed. And so, the whole idea here is once you get good at using reframing, you can quickly identify other aspects of the problem that might be much better to try to solve than the original one you found. It’s not necessarily that the first one is wrong. It’s just that there might be better problems out there to attack that we can, means we can do things much faster, cheaper, or better.

SARAH GREEN CARMICHAEL: So, in that example, I can understand how A, it’s probably expensive to make the elevator faster, so it’s much cheaper just to put up a mirror. And B, maybe the real problem people are actually feeling, even though they’re not articulating it right, is like, I hate waiting for the elevator. But if you let them sort of fix their hair or check their teeth, they’re suddenly distracted and don’t notice.

But if you have, this is sort of a pedestrian example, but say you have a roommate or a spouse who doesn’t clean up the kitchen. Facing that problem and not having your elegant solution already there to highlight the contrast between the perceived problem and the real problem, how would you take a problem like that and attack it using this method so that you can see what some of the other options might be?

THOMAS WEDELL-WEDELLSBORG: Right. So, I mean, let’s say it’s you who have that problem. I would go in and say, first of all, what would you say the problem is? Like, if you were to describe your view of the problem, what would that be?

SARAH GREEN CARMICHAEL: I hate cleaning the kitchen, and I want someone else to clean it up.

THOMAS WEDELL-WEDELLSBORG: OK. So, my first observation, you know, that somebody else might not necessarily be your spouse. So, already there, there’s an inbuilt assumption in your question around oh, it has to be my husband who does the cleaning. So, it might actually be worth, already there to say, is that really the only problem you have? That you hate cleaning the kitchen, and you want to avoid it? Or might there be something around, as well, getting a better relationship in terms of how you solve problems in general or establishing a better way to handle small problems when dealing with your spouse?

SARAH GREEN CARMICHAEL: Or maybe, now that I’m thinking that, maybe the problem is that you just can’t find the stuff in the kitchen when you need to find it.

THOMAS WEDELL-WEDELLSBORG: Right, and so that’s an example of a reframing, that actually why is it a problem that the kitchen is not clean? Is it only because you hate the act of cleaning, or does it actually mean that it just takes you a lot longer and gets a lot messier to actually use the kitchen, which is a different problem. The way you describe this problem now, is there anything that’s missing from that description?

SARAH GREEN CARMICHAEL: That is a really good question.

THOMAS WEDELL-WEDELLSBORG: Other, basically asking other factors that we are not talking about right now, and I say those because people tend to, when given a problem, they tend to delve deeper into the detail. What often is missing is actually an element outside of the initial description of the problem that might be really relevant to what’s going on. Like, why does the kitchen get messy in the first place? Is it something about the way you use it or your cooking habits? Is it because the neighbor’s kids, kind of, use it all the time?

There might, very often, there might be issues that you’re not really thinking about when you first describe the problem that actually has a big effect on it.

SARAH GREEN CARMICHAEL: I think at this point it would be helpful to maybe get another business example, and I’m wondering if you could tell us the story of the dog adoption problem.

THOMAS WEDELL-WEDELLSBORG: Yeah. This is a big problem in the US. If you work in the shelter industry, basically because dogs are so popular, more than 3 million dogs every year enter a shelter, and currently only about half of those actually find a new home and get adopted. And so, this is a problem that has persisted. It’s been, like, a structural problem for decades in this space. In the last three years, where people found new ways to address it.

So a woman called Lori Weise who runs a rescue organization in South LA, and she actually went in and challenged the very idea of what we were trying to do. She said, no, no. The problem we’re trying to solve is not about how to get more people to adopt dogs. It is about keeping the dogs with their first family so they never enter the shelter system in the first place.

In 2013, she started what’s called a Shelter Intervention Program that basically works like this. If a family comes and wants to hand over their dog, these are called owner surrenders. It’s about 30% of all dogs that come into a shelter. All they would do is go up and ask, if you could, would you like to keep your animal? And if they said yes, they would try to fix whatever helped them fix the problem, but that made them turn over this.

And sometimes that might be that they moved into a new building. The landlord required a deposit, and they simply didn’t have the money to put down a deposit. Or the dog might need a $10 rabies shot, but they didn’t know how to get access to a vet.

And so, by instigating that program, just in the first year, she took her, basically the amount of dollars they spent per animal they helped went from something like $85 down to around $60. Just an immediate impact, and her program now is being rolled out, is being supported by the ASPCA, which is one of the big animal welfare stations, and it’s being rolled out to various other places.

And I think what really struck me with that example was this was not dependent on having the internet. This was not, oh, we needed to have everybody mobile before we could come up with this. This, conceivably, we could have done 20 years ago. Only, it only happened when somebody, like in this case Lori, went in and actually rethought what the problem they were trying to solve was in the first place.

SARAH GREEN CARMICHAEL: So, what I also think is so interesting about that example is that when you talk about it, it doesn’t sound like the kind of thing that would have been thought of through other kinds of problem solving methods. There wasn’t necessarily an After Action Review or a 5 Whys exercise or a Six Sigma type intervention. I don’t want to throw those other methods under the bus, but how can you get such powerful results with such a very simple way of thinking about something?

THOMAS WEDELL-WEDELLSBORG: That was something that struck me as well. This, in a way, reframing and the idea of the problem diagnosis is important is something we’ve known for a long, long time. And we’ve actually have built some tools to help out. If you worked with us professionally, you are familiar with, like, Six Sigma, TRIZ, and so on. You mentioned 5 Whys. A root cause analysis is another one that a lot of people are familiar with.

Those are our good tools, and they’re definitely better than nothing. But what I notice when I work with the companies applying those was those tools tend to make you dig deeper into the first understanding of the problem we have. If it’s the elevator example, people start asking, well, is that the cable strength, or is the capacity of the elevator? That they kind of get caught by the details.

That, in a way, is a bad way to work on problems because it really assumes that there’s like a, you can almost hear it, a root cause. That you have to dig down and find the one true problem, and everything else was just symptoms. That’s a bad way to think about problems because problems tend to be multicausal.

There tend to be lots of causes or levers you can potentially press to address a problem. And if you think there’s only one, if that’s the right problem, that’s actually a dangerous way. And so I think that’s why, that this is a method I’ve worked with over the last five years, trying to basically refine how to make people better at this, and the key tends to be this thing about shifting out and saying, is there a totally different way of thinking about the problem versus getting too caught up in the mechanistic details of what happens.

SARAH GREEN CARMICHAEL: What about experimentation? Because that’s another method that’s become really popular with the rise of Lean Startup and lots of other innovation methodologies. Why wouldn’t it have worked to, say, experiment with many different types of fixing the dog adoption problem, and then just pick the one that works the best?

THOMAS WEDELL-WEDELLSBORG: You could say in the dog space, that’s what’s been going on. I mean, there is, in this industry and a lot of, it’s largely volunteer driven. People have experimented, and they found different ways of trying to cope. And that has definitely made the problem better. So, I wouldn’t say that experimentation is bad, quite the contrary. Rapid prototyping, quickly putting something out into the world and learning from it, that’s a fantastic way to learn more and to move forward.

My point is, though, that I feel we’ve come to rely too much on that. There’s like, if you look at the start up space, the wisdom is now just to put something quickly into the market, and then if it doesn’t work, pivot and just do more stuff. What reframing really is, I think of it as the cognitive counterpoint to prototyping. So, this is really a way of seeing very quickly, like not just working on the solution, but also working on our understanding of the problem and trying to see is there a different way to think about that.

If you only stick with experimentation, again, you tend to sometimes stay too much in the same space trying minute variations of something instead of taking a step back and saying, wait a minute. What is this telling us about what the real issue is?

SARAH GREEN CARMICHAEL: So, to go back to something that we touched on earlier, when we were talking about the completely hypothetical example of a spouse who does not clean the kitchen–

THOMAS WEDELL-WEDELLSBORG: Completely, completely hypothetical.

SARAH GREEN CARMICHAEL: Yes. For the record, my husband is a great kitchen cleaner.

You started asking me some questions that I could see immediately were helping me rethink that problem. Is that kind of the key, just having a checklist of questions to ask yourself? How do you really start to put this into practice?

THOMAS WEDELL-WEDELLSBORG: I think there are two steps in that. The first one is just to make yourself better at the method. Yes, you should kind of work with a checklist. In the article, I kind of outlined seven practices that you can use to do this.

But importantly, I would say you have to consider that as, basically, a set of training wheels. I think there’s a big, big danger in getting caught in a checklist. This is something I work with.

My co-author Paddy Miller, it’s one of his insights. That if you start giving people a checklist for things like this, they start following it. And that’s actually a problem, because what you really want them to do is start challenging their thinking.

So the way to handle this is to get some practice using it. Do use the checklist initially, but then try to step away from it and try to see if you can organically make– it’s almost a habit of mind. When you run into a colleague in the hallway and she has a problem and you have five minutes, like, delving in and just starting asking some of those questions and using your intuition to say, wait, how is she talking about this problem? And is there a question or two I can ask her about the problem that can help her rethink it?

SARAH GREEN CARMICHAEL: Well, that is also just a very different approach, because I think in that situation, most of us can’t go 30 seconds without jumping in and offering solutions.

THOMAS WEDELL-WEDELLSBORG: Very true. The drive toward solutions is very strong. And to be clear, I mean, there’s nothing wrong with that if the solutions work. So, many problems are just solved by oh, you know, oh, here’s the way to do that. Great.

But this is really a powerful method for those problems where either it’s something we’ve been banging our heads against tons of times without making progress, or when you need to come up with a really creative solution. When you’re facing a competitor with a much bigger budget, and you know, if you solve the same problem later, you’re not going to win. So, that basic idea of taking that approach to problems can often help you move forward in a different way than just like, oh, I have a solution.

I would say there’s also, there’s some interesting psychological stuff going on, right? Where you may have tried this, but if somebody tries to serve up a solution to a problem I have, I’m often resistant towards them. Kind if like, no, no, no, no, no, no. That solution is not going to work in my world. Whereas if you get them to discuss and analyze what the problem really is, you might actually dig something up.

Let’s go back to the kitchen example. One powerful question is just to say, what’s your own part in creating this problem? It’s very often, like, people, they describe problems as if it’s something that’s inflicted upon them from the external world, and they are innocent bystanders in that.

SARAH GREEN CARMICHAEL: Right, or crazy customers with unreasonable demands.

THOMAS WEDELL-WEDELLSBORG: Exactly, right. I don’t think I’ve ever met an agency or consultancy that didn’t, like, gossip about their customers. Oh, my god, they’re horrible. That, you know, classic thing, why don’t they want to take more risk? Well, risk is bad.

It’s their business that’s on the line, not the consultancy’s, right? So, absolutely, that’s one of the things when you step into a different mindset and kind of, wait. Oh yeah, maybe I actually am part of creating this problem in a sense, as well. That tends to open some new doors for you to move forward, in a way, with stuff that you may have been struggling with for years.

SARAH GREEN CARMICHAEL: So, we’ve surfaced a couple of questions that are useful. I’m curious to know, what are some of the other questions that you find yourself asking in these situations, given that you have made this sort of mental habit that you do? What are the questions that people seem to find really useful?

THOMAS WEDELL-WEDELLSBORG: One easy one is just to ask if there are any positive exceptions to the problem. So, was there day where your kitchen was actually spotlessly clean? And then asking, what was different about that day? Like, what happened there that didn’t happen the other days? That can very often point people towards a factor that they hadn’t considered previously.

SARAH GREEN CARMICHAEL: We got take-out.

THOMAS WEDELL-WEDELLSBORG: S,o that is your solution. Take-out from [INAUDIBLE]. That might have other problems.

Another good question, and this is a little bit more high level. It’s actually more making an observation about labeling how that person thinks about the problem. And what I mean with that is, we have problem categories in our head. So, if I say, let’s say that you describe a problem to me and say, well, we have a really great product and are, it’s much better than our previous product, but people aren’t buying it. I think we need to put more marketing dollars into this.

Now you can go in and say, that’s interesting. This sounds like you’re thinking of this as a communications problem. Is there a different way of thinking about that? Because you can almost tell how, when the second you say communications, there are some ideas about how do you solve a communications problem. Typically with more communication.

And what you might do is go in and suggest, well, have you considered that it might be, say, an incentive problem? Are there incentives on behalf of the purchasing manager at your clients that are obstructing you? Might there be incentive issues with your own sales force that makes them want to sell the old product instead of the new one?

So literally, just identifying what type of problem does this person think about, and is there different potential way of thinking about it? Might it be an emotional problem, a timing problem, an expectations management problem? Thinking about what label of what type of problem that person is kind of thinking as it of.

SARAH GREEN CARMICHAEL: That’s really interesting, too, because I think so many of us get requests for advice that we’re really not qualified to give. So, maybe the next time that happens, instead of muddying my way through, I will just ask some of those questions that we talked about instead.

THOMAS WEDELL-WEDELLSBORG: That sounds like a good idea.

SARAH GREEN CARMICHAEL: So, Thomas, this has really helped me reframe the way I think about a couple of problems in my own life, and I’m just wondering. I know you do this professionally, but is there a problem in your life that thinking this way has helped you solve?

THOMAS WEDELL-WEDELLSBORG: I’ve, of course, I’ve been swallowing my own medicine on this, too, and I think I have, well, maybe two different examples, and in one case somebody else did the reframing for me. But in one case, when I was younger, I often kind of struggled a little bit. I mean, this is my teenage years, kind of hanging out with my parents. I thought they were pretty annoying people. That’s not really fair, because they’re quite wonderful, but that’s what life is when you’re a teenager.

And one of the things that struck me, suddenly, and this was kind of the positive exception was, there was actually an evening where we really had a good time, and there wasn’t a conflict. And the core thing was, I wasn’t just seeing them in their old house where I grew up. It was, actually, we were at a restaurant. And it suddenly struck me that so much of the sometimes, kind of, a little bit, you love them but they’re annoying kind of dynamic, is tied to the place, is tied to the setting you are in.

And of course, if– you know, I live abroad now, if I visit my parents and I stay in my old bedroom, you know, my mother comes in and wants to wake me up in the morning. Stuff like that, right? And it just struck me so, so clearly that it’s– when I change this setting, if I go out and have dinner with them at a different place, that the dynamic, just that dynamic disappears.

SARAH GREEN CARMICHAEL: Well, Thomas, this has been really, really helpful. Thank you for talking with me today.

THOMAS WEDELL-WEDELLSBORG: Thank you, Sarah.  

HANNAH BATES: That was Thomas Wedell-Wedellsborg in conversation with Sarah Green Carmichael on the HBR IdeaCast. He’s an expert in problem solving and innovation, and he’s the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

We’ll be back next Wednesday with another hand-picked conversation about leadership from the Harvard Business Review. If you found this episode helpful, share it with your friends and colleagues, and follow our show on Apple Podcasts, Spotify, or wherever you get your podcasts. While you’re there, be sure to leave us a review.

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This episode was produced by Anne Saini, and me, Hannah Bates. Ian Fox is our editor. Music by Coma Media. Special thanks to Maureen Hoch, Adi Ignatius, Karen Player, Ramsey Khabbaz, Nicole Smith, Anne Bartholomew, and you – our listener.

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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

Satisficing

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.

Psychology, like other disciplines, uses the scientific method to acquire knowledge and uncover truths—but we still ask experts for information and rely on intuition. Here's why.

We all experience these 3 cognitive blind spots at work, frequently unaware of their costs in terms of productivity and misunderstanding. Try these strategies to work around them.

Have you ever fallen for fake news? This toolkit can help you easily evaluate whether a claim is real or phony.

An insidious form of prejudice occurs when a more powerful group ignores groups with less power and keeps them out of the minds of society.

Chatbot designers engage in dishonest anthropomorphism by designing features to exploit our heuristic processing and dupe us into overtrusting and assigning moral responsibility.

How do social media influencers convert a scroll into a like, follow, and sale? Here are the psychological principles used by digital influencers.

Sometimes, we submit to the oppressive aspects of life voluntarily, by accepting them as fixed and immutable even when they are not. We fall into a mental trap. Why?

Despite the bombardment of societal messages to never quit, sometimes changing course is exactly what you should do.

Many have experienced the "Mandela Effect." Some believe that the past has been subtly changed or that we live in a divergent reality. Here's what psychology has to say.

Rain is forecast? Bring an umbrella. New film got rave reviews? Check it out. New finding links a lifestyle factor to disease? Ask questions.

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Netflix's hit sci-fi series '3 Body Problem' is based on a real math problem that is so complex it's impossible to solve

• The three-body problem is a centuries-old physics question that puzzled Isaac Newton .
• It describes the orbits of three bodies, like planets or stars, trapped in each other's gravity.
• The problem is unsolvable and led to the development of chaos theory.

While Netflix's "3 Body Problem" is a science-fiction show, its name comes from a real math problem that's puzzled scientists since the late 1600s.

In physics, the three-body problem refers to the motion of three bodies trapped in each other's gravitational grip — like a three-star system.

It might sound simple enough, but once you dig into the mathematics, the orbital paths of each object get complicated very quickly.

Two-body vs. three- and multi-body systems

A simpler version is a two-body system like binary stars. Two-body systems have periodic orbits, meaning they are mathematically predictable because they follow the same trajectory over and over. So, if you have the stars' initial positions and velocities, you can calculate where they've been or will be in space far into the past and future.

However, "throwing in a third body that's close enough to interact leads to chaos," Shane Ross, an aerospace and ocean engineering professor at Virginia Tech, told Business Insider. In fact, it's nearly impossible to precisely predict the orbital paths of any system with three bodies or more.

While two orbiting planets might look like a ven diagram with ovular paths overlapping, the paths of three bodies interacting often resemble tangled spaghetti. Their trajectories usually aren't as stable as systems with only two bodies.

All that uncertainty makes what's known as the three-body problem largely unsolvable, Ross said. But there are certain exceptions.

The three-body problem is over 300 years old

The three-body problem dates back to Isaac Newton , who published his "Principia" in 1687.

In the book, the mathematician noted that the planets move in elliptical orbits around the sun. Yet the gravitational pull from Jupiter seemed to affect Saturn's orbital path.

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The three-body problem didn't just affect distant planets. Trying to understand the variations in the moon's movements caused Newton literal headaches, he complained.

But Newton never fully figured out the three-body problem. And it remained a mathematical mystery for nearly 200 years.

In 1889, a Swedish journal awarded mathematician Henri Poincaré a gold medal and 2,500 Swedish crowns, roughly half a year's salary for a professor at the time, for his essay about the three-body problem that outlined the basis for an entirely new mathematical theory called chaos theory .

According to chaos theory, when there is uncertainty about a system's initial conditions, like an object's mass or velocity, that uncertainty ripples out, making the future more and more unpredictable.

Think of it like taking a wrong turn on a trip. If you make a left instead of a right at the end of your journey, you're probably closer to your destination than if you made the mistake at the very beginning.

Can you solve the three-body problem?

Cracking the three-body problem would help scientists chart the movements of meteors and planets, including Earth, into the extremely far future. Even comparatively small movements of our planet could have large impacts on our climate, Ross said.

Though the three-body problem is considered mathematically unsolvable, there are solutions to specific scenarios. In fact, there are a few that mathematicians have found.

For example, three bodies could stably orbit in a figure eight or equally spaced around a ring. Both are possible depending on the initial positions and velocities of the bodies.

One way researchers look for solutions is with " restricted " three-body problems, where two main bodies (like the sun and Earth) interact and a third object with much smaller mass (like the moon) offers less gravitational interference. In this case, the three-body problem looks a lot like a two-body problem since the sun and Earth comprise the majority of mass in the system.

However, if you're looking at a three-star system, like the one in Netflix's show "3 Body Problem," that's a lot more complicated.

Computers can also run simulations far more efficiently than humans, though due to the inherent uncertainties, the results are typically approximate orbits instead of exact.

Finding solutions to three-body problems is also essential to space travel, Ross said. For his work, he inputs data about the Earth, moon, and spacecraft into a computer. "We can build up a whole library of possible trajectories," he said, "and that gives us an idea of the types of motion that are possible."

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