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Overview of the Problem-Solving Mental Process

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

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

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You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

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

What is Problem Solving? (Steps, Techniques, Examples)

By Status.net Editorial Team on May 7, 2023 — 5 minutes to read

What Is Problem Solving?

Definition and importance.

Problem solving is the process of finding solutions to obstacles or challenges you encounter in your life or work. It is a crucial skill that allows you to tackle complex situations, adapt to changes, and overcome difficulties with ease. Mastering this ability will contribute to both your personal and professional growth, leading to more successful outcomes and better decision-making.

Problem-Solving Steps

The problem-solving process typically includes the following steps:

• Identify the issue : Recognize the problem that needs to be solved.
• Analyze the situation : Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present.
• Generate potential solutions : Brainstorm a list of possible solutions to the issue, without immediately judging or evaluating them.
• Evaluate options : Weigh the pros and cons of each potential solution, considering factors such as feasibility, effectiveness, and potential risks.
• Select the best solution : Choose the option that best addresses the problem and aligns with your objectives.
• Implement the solution : Put the selected solution into action and monitor the results to ensure it resolves the issue.
• Review and learn : Reflect on the problem-solving process, identify any improvements or adjustments that can be made, and apply these learnings to future situations.

Defining the Problem

To start tackling a problem, first, identify and understand it. Analyzing the issue thoroughly helps to clarify its scope and nature. Ask questions to gather information and consider the problem from various angles. Some strategies to define the problem include:

• Brainstorming with others
• Asking the 5 Ws and 1 H (Who, What, When, Where, Why, and How)
• Analyzing cause and effect
• Creating a problem statement

Generating Solutions

Once the problem is clearly understood, brainstorm possible solutions. Think creatively and keep an open mind, as well as considering lessons from past experiences. Consider:

• Creating a list of potential ideas to solve the problem
• Grouping and categorizing similar solutions
• Prioritizing potential solutions based on feasibility, cost, and resources required
• Involving others to share diverse opinions and inputs

Evaluating and Selecting Solutions

Evaluate each potential solution, weighing its pros and cons. To facilitate decision-making, use techniques such as:

• SWOT analysis (Strengths, Weaknesses, Opportunities, Threats)
• Decision-making matrices
• Pros and cons lists
• Risk assessments

After evaluating, choose the most suitable solution based on effectiveness, cost, and time constraints.

Implementing and Monitoring the Solution

Implement the chosen solution and monitor its progress. Key actions include:

• Communicating the solution to relevant parties
• Setting timelines and milestones
• Assigning tasks and responsibilities
• Monitoring the solution and making adjustments as necessary
• Evaluating the effectiveness of the solution after implementation

Utilize feedback from stakeholders and consider potential improvements. Remember that problem-solving is an ongoing process that can always be refined and enhanced.

Problem-Solving Techniques

During each step, you may find it helpful to utilize various problem-solving techniques, such as:

• Brainstorming : A free-flowing, open-minded session where ideas are generated and listed without judgment, to encourage creativity and innovative thinking.
• Root cause analysis : A method that explores the underlying causes of a problem to find the most effective solution rather than addressing superficial symptoms.
• SWOT analysis : A tool used to evaluate the strengths, weaknesses, opportunities, and threats related to a problem or decision, providing a comprehensive view of the situation.
• Mind mapping : A visual technique that uses diagrams to organize and connect ideas, helping to identify patterns, relationships, and possible solutions.

Brainstorming

When facing a problem, start by conducting a brainstorming session. Gather your team and encourage an open discussion where everyone contributes ideas, no matter how outlandish they may seem. This helps you:

• Generate a diverse range of solutions
• Encourage all team members to participate
• Foster creative thinking

When brainstorming, remember to:

• Reserve judgment until the session is over
• Encourage wild ideas
• Combine and improve upon ideas

Root Cause Analysis

For effective problem-solving, identifying the root cause of the issue at hand is crucial. Try these methods:

• 5 Whys : Ask “why” five times to get to the underlying cause.
• Fishbone Diagram : Create a diagram representing the problem and break it down into categories of potential causes.
• Pareto Analysis : Determine the few most significant causes underlying the majority of problems.

SWOT Analysis

SWOT analysis helps you examine the Strengths, Weaknesses, Opportunities, and Threats related to your problem. To perform a SWOT analysis:

• List your problem’s strengths, such as relevant resources or strong partnerships.
• Identify its weaknesses, such as knowledge gaps or limited resources.
• Explore opportunities, like trends or new technologies, that could help solve the problem.
• Recognize potential threats, like competition or regulatory barriers.

SWOT analysis aids in understanding the internal and external factors affecting the problem, which can help guide your solution.

Mind Mapping

A mind map is a visual representation of your problem and potential solutions. It enables you to organize information in a structured and intuitive manner. To create a mind map:

• Write the problem in the center of a blank page.
• Draw branches from the central problem to related sub-problems or contributing factors.
• Add more branches to represent potential solutions or further ideas.

Mind mapping allows you to visually see connections between ideas and promotes creativity in problem-solving.

Examples of Problem Solving in Various Contexts

In the business world, you might encounter problems related to finances, operations, or communication. Applying problem-solving skills in these situations could look like:

• Identifying areas of improvement in your company’s financial performance and implementing cost-saving measures
• Resolving internal conflicts among team members by listening and understanding different perspectives, then proposing and negotiating solutions
• Streamlining a process for better productivity by removing redundancies, automating tasks, or re-allocating resources

In educational contexts, problem-solving can be seen in various aspects, such as:

• Addressing a gap in students’ understanding by employing diverse teaching methods to cater to different learning styles
• Developing a strategy for successful time management to balance academic responsibilities and extracurricular activities
• Seeking resources and support to provide equal opportunities for learners with special needs or disabilities

Everyday life is full of challenges that require problem-solving skills. Some examples include:

• Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
• Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
• Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
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A guide to problem-solving techniques, steps, and skills

You might associate problem-solving with the math exercises that a seven-year-old would do at school. But problem-solving isn’t just about math — it’s a crucial skill that helps everyone make better decisions in everyday life or work.

Problem-solving involves finding effective solutions to address complex challenges, in any context they may arise.

Unfortunately, structured and systematic problem-solving methods aren’t commonly taught. Instead, when solving a problem, PMs tend to rely heavily on intuition. While for simple issues this might work well, solving a complex problem with a straightforward solution is often ineffective and can even create more problems.

In this article, you’ll learn a framework for approaching problem-solving, alongside how you can improve your problem-solving skills.

The 7 steps to problem-solving

When it comes to problem-solving there are seven key steps that you should follow: define the problem, disaggregate, prioritize problem branches, create an analysis plan, conduct analysis, synthesis, and communication.

1. Define the problem

Problem-solving begins with a clear understanding of the issue at hand. Without a well-defined problem statement, confusion and misunderstandings can hinder progress. It’s crucial to ensure that the problem statement is outcome-focused, specific, measurable whenever possible, and time-bound.

Additionally, aligning the problem definition with relevant stakeholders and decision-makers is essential to ensure efforts are directed towards addressing the actual problem rather than side issues.

2. Disaggregate

Complex issues often require deeper analysis. Instead of tackling the entire problem at once, the next step is to break it down into smaller, more manageable components.

Various types of logic trees (also known as issue trees or decision trees) can be used to break down the problem. At each stage where new branches are created, it’s important for them to be “MECE” – mutually exclusive and collectively exhaustive. This process of breaking down continues until manageable components are identified, allowing for individual examination.

The decomposition of the problem demands looking at the problem from various perspectives. That is why collaboration within a team often yields more valuable results, as diverse viewpoints lead to a richer pool of ideas and solutions.

3. Prioritize problem branches

The next step involves prioritization. Not all branches of the problem tree have the same impact, so it’s important to understand the significance of each and focus attention on the most impactful areas. Prioritizing helps streamline efforts and minimize the time required to solve the problem.

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4. Create an analysis plan

For prioritized components, you may need to conduct in-depth analysis. Before proceeding, a work plan is created for data gathering and analysis. If work is conducted within a team, having a plan provides guidance on what needs to be achieved, who is responsible for which tasks, and the timelines involved.

5. Conduct analysis

Data gathering and analysis are central to the problem-solving process. It’s a good practice to set time limits for this phase to prevent excessive time spent on perfecting details. You can employ heuristics and rule-of-thumb reasoning to improve efficiency and direct efforts towards the most impactful work.

6. Synthesis

After each individual branch component has been researched, the problem isn’t solved yet. The next step is synthesizing the data logically to address the initial question. The synthesis process and the logical relationship between the individual branch results depend on the logic tree used.

7. Communication

The last step is communicating the story and the solution of the problem to the stakeholders and decision-makers. Clear effective communication is necessary to build trust in the solution and facilitates understanding among all parties involved. It ensures that stakeholders grasp the intricacies of the problem and the proposed solution, leading to informed decision-making.

Exploring problem-solving in various contexts

While problem-solving has traditionally been associated with fields like engineering and science, today it has become a fundamental skill for individuals across all professions. In fact, problem-solving consistently ranks as one of the top skills required by employers.

Problem-solving techniques can be applied in diverse contexts:

• Individuals — What career path should I choose? Where should I live? These are examples of simple and common personal challenges that require effective problem-solving skills
• Organizations — Businesses also face many decisions that are not trivial to answer. Should we expand into new markets this year? How can we enhance the quality of our product development? Will our office accommodate the upcoming year’s growth in terms of capacity?
• Societal issues — The biggest world challenges are also complex problems that can be addressed with the same technique. How can we minimize the impact of climate change? How do we fight cancer?

Despite the variation in domains and contexts, the fundamental approach to solving these questions remains the same. It starts with gaining a clear understanding of the problem, followed by decomposition, conducting analysis of the decomposed branches, and synthesizing it into a result that answers the initial problem.

Real-world examples of problem-solving

Let’s now explore some examples where we can apply the problem solving framework.

Problem: In the production of electronic devices, you observe an increasing number of defects. How can you reduce the error rate and improve the quality?

Before delving into analysis, you can deprioritize branches that you already have information for or ones you deem less important. For instance, while transportation delays may occur, the resulting material degradation is likely negligible. For other branches, additional research and data gathering may be necessary.

Once results are obtained, synthesis is crucial to address the core question: How can you decrease the defect rate?

While all factors listed may play a role, their significance varies. Your task is to prioritize effectively. Through data analysis, you may discover that altering the equipment would bring the most substantial positive outcome. However, executing a solution isn’t always straightforward. In prioritizing, you should consider both the potential impact and the level of effort needed for implementation.

By evaluating impact and effort, you can systematically prioritize areas for improvement, focusing on those with high impact and requiring minimal effort to address. This approach ensures efficient allocation of resources towards improvements that offer the greatest return on investment.

Problem : What should be my next job role?

When breaking down this problem, you need to consider various factors that are important for your future happiness in the role. This includes aspects like the company culture, our interest in the work itself, and the lifestyle that you can afford with the role.

However, not all factors carry the same weight for us. To make sense of the results, we can assign a weight factor to each branch. For instance, passion for the job role may have a weight factor of 1, while interest in the industry may have a weight factor of 0.5, because that is less important for you.

By applying these weights to a specific role and summing the values, you can have an estimate of how suitable that role is for you. Moreover, you can compare two roles and make an informed decision based on these weighted indicators.

Key problem-solving skills

This framework provides the foundation and guidance needed to effectively solve problems. However, successfully applying this framework requires the following:

• Creativity — During the decomposition phase, it’s essential to approach the problem from various perspectives and think outside the box to generate innovative ideas for breaking down the problem tree
• Decision-making — Throughout the process, decisions must be made, even when full confidence is lacking. Employing rules of thumb to simplify analysis or selecting one tree cut over another requires decisiveness and comfort with choices made
• Analytical skills — Analytical and research skills are necessary for the phase following decomposition, involving data gathering and analysis on selected tree branches
• Teamwork — Collaboration and teamwork are crucial when working within a team setting. Solving problems effectively often requires collective effort and shared responsibility
• Communication — Clear and structured communication is essential to convey the problem solution to stakeholders and decision-makers and build trust

How to enhance your problem-solving skills

Problem-solving requires practice and a certain mindset. The more you practice, the easier it becomes. Here are some strategies to enhance your skills:

• Practice structured thinking in your daily life — Break down problems or questions into manageable parts. You don’t need to go through the entire problem-solving process and conduct detailed analysis. When conveying a message, simplify the conversation by breaking the message into smaller, more understandable segments
• Regularly challenging yourself with games and puzzles — Solving puzzles, riddles, or strategy games can boost your problem-solving skills and cognitive agility.
• Engage with individuals from diverse backgrounds and viewpoints — Conversing with people who offer different perspectives provides fresh insights and alternative solutions to problems. This boosts creativity and helps in approaching challenges from new angles

Final thoughts

Problem-solving extends far beyond mathematics or scientific fields; it’s a critical skill for making informed decisions in every area of life and work. The seven-step framework presented here provides a systematic approach to problem-solving, relevant across various domains.

Now, consider this: What’s one question currently on your mind? Grab a piece of paper and try to apply the problem-solving framework. You might uncover fresh insights you hadn’t considered before.

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How to Solve Problems

• Laura Amico

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

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

• Laura Amico is a former senior editor at Harvard Business Review.

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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 1,313,803 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 2 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 1 Not Helpful 0

Tips from our Readers

• Just take it day by day and write down your plans to form a routine that works best for you. Even if you don't get everything done, just doing what you can for the day is enough.
• Turn the above steps into questions, then answer them. Make your goal actionable by detailing exactly how you'll attempt to achieve it.
• Talk to people you trust and who you believe can help. Be open and just tell them the truth about what's going on.

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 • 7 min read

What Is Problem Solving?

Find a solution to any problem you face..

By the Mind Tools Content Team

We all spend a lot of our time solving problems, both at work and in our personal lives.

Some problems are small, and we can quickly sort them out ourselves. But others are complex challenges that take collaboration, creativity, and a considerable amount of effort to solve.

At work, the types of problems we face depend largely on the organizations we're in and the jobs we do. A manager in a cleaning company, for example, might spend their day untangling staffing issues, resolving client complaints, and sorting out problems with equipment and supplies. An aircraft designer, on the other hand, might be grappling with a problem about aerodynamics, or trying to work out why a new safety feature isn't working. Meanwhile, a politician might be exploring solutions to racial injustice or climate change.

But whatever issues we face, there are some common ways to tackle them effectively. And we can all boost our confidence and ability to succeed by building a strong set of problem-solving skills.

Mind Tools offers a large collection of resources to help you do just that!

How Well Do You Solve Problems?

Start by taking an honest look at your existing skills. What's your current approach to solving problems, and how well is it working? Our quiz, How Good Is Your Problem Solving? lets you analyze your abilities, and signposts ways to address any areas of weakness.

Define Every Problem

The first step in solving a problem is understanding what that problem actually is. You need to be sure that you're dealing with the real problem – not its symptoms. For example, if performance in your department is substandard, you might think that the problem lies with the individuals submitting work. However, if you look a bit deeper, the real issue might be a general lack of training, or an unreasonable workload across the team.

Tools like 5 Whys , Appreciation and Root Cause Analysis get you asking the right questions, and help you to work through the layers of a problem to uncover what's really going on.

However, defining a problem doesn't mean deciding how to solve it straightaway. It's important to look at the issue from a variety of perspectives. If you commit yourself too early, you can end up with a short-sighted solution. The CATWOE checklist provides a powerful reminder to look at many elements that may contribute to the problem, keeping you open to a variety of possible solutions.

Understanding Complexity

As you define your problem, you'll often discover just how complicated it is. There are likely several interrelated issues involved. That's why it's important to have ways to visualize, simplify and make sense of this tangled mess!

Affinity Diagrams are great for organizing many different pieces of information into common themes, and for understanding the relationships between them.

Another popular tool is the Cause-and-Effect Diagram . To generate viable solutions, you need a solid understanding of what's causing the problem.

When your problem occurs within a business process, creating a Flow Chart , Swim Lane Diagram or a Systems Diagram will help you to see how various activities and inputs fit together. This may well highlight a missing element or bottleneck that's causing your problem.

Quite often, what seems to be a single problem turns out to be a whole series of problems. The Drill Down technique prompts you to split your problem into smaller, more manageable parts.

General Problem-Solving Tools

When you understand the problem in front of you, you’re ready to start solving it. With your definition to guide you, you can generate several possible solutions, choose the best one, then put it into action. That's the four-step approach at the heart of good problem solving.

There are various problem-solving styles to use. For example:

• Constructive Controversy is a way of widening perspectives and energizing discussions.
• Inductive Reasoning makes the most of people’s experiences and know-how, and can speed up solution finding.
• Means-End Analysis can bring extra clarity to your thinking, and kick-start the process of implementing solutions.

Specific Problem-Solving Systems

Some particularly complicated or important problems call for a more comprehensive process. Again, Mind Tools has a range of approaches to try, including:

• Simplex , which involves an eight-stage process: problem finding, fact finding, defining the problem, idea finding, selecting and evaluating, planning, selling the idea, and acting. These steps build upon the basic, four-step process described above, and they create a cycle of problem finding and solving that will continually improve your organization.
• Appreciative Inquiry , which is a uniquely positive way of solving problems by examining what's working well in the areas surrounding them.
• Soft Systems Methodology , which takes you through four stages to uncover more details about what's creating your problem, and then define actions that will improve the situation.

Further Problem-Solving Strategies

Good problem solving requires a number of other skills – all of which are covered by Mind Tools.

For example, we have a large section of resources to improve your Creativity , so that you come up with a range of possible solutions.

By strengthening your Decision Making , you'll be better at evaluating the options, selecting the best ones, then choosing how to implement them.

And our Project Management collection has valuable advice for strengthening the whole problem-solving process. The resources there will help you to make effective changes – and then keep them working long term.

Problems are an inescapable part of life, both in and out of work. So we can all benefit from having strong problem-solving skills.

It's important to understand your current approach to problem solving, and to know where and how to improve.

Define every problem you encounter – and understand its complexity, rather than trying to solve it too soon.

There's a range of general problem-solving approaches, helping you to generate possible answers, choose the best ones, and then implement your solution.

Some complicated or serious problems require more specific problem-solving systems, especially when they relate to business processes.

By boosting your creativity, decision-making and project-management skills, you’ll become even better at solving all the problems you face.

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Member Podcast

How to master the seven-step problem-solving process

In this episode of the McKinsey Podcast , Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.

Podcast transcript

Simon London: Hello, and welcome to this episode of the McKinsey Podcast , with me, Simon London. What’s the number-one skill you need to succeed professionally? Salesmanship, perhaps? Or a facility with statistics? Or maybe the ability to communicate crisply and clearly? Many would argue that at the very top of the list comes problem solving: that is, the ability to think through and come up with an optimal course of action to address any complex challenge—in business, in public policy, or indeed in life.

Looked at this way, it’s no surprise that McKinsey takes problem solving very seriously, testing for it during the recruiting process and then honing it, in McKinsey consultants, through immersion in a structured seven-step method. To discuss the art of problem solving, I sat down in California with McKinsey senior partner Hugo Sarrazin and also with Charles Conn. Charles is a former McKinsey partner, entrepreneur, executive, and coauthor of the book Bulletproof Problem Solving: The One Skill That Changes Everything [John Wiley & Sons, 2018].

Charles and Hugo, welcome to the podcast. Thank you for being here.

Hugo Sarrazin: Our pleasure.

Charles Conn: It’s terrific to be here.

Simon London: Problem solving is a really interesting piece of terminology. It could mean so many different things. I have a son who’s a teenage climber. They talk about solving problems. Climbing is problem solving. Charles, when you talk about problem solving, what are you talking about?

Charles Conn: For me, problem solving is the answer to the question “What should I do?” It’s interesting when there’s uncertainty and complexity, and when it’s meaningful because there are consequences. Your son’s climbing is a perfect example. There are consequences, and it’s complicated, and there’s uncertainty—can he make that grab? I think we can apply that same frame almost at any level. You can think about questions like “What town would I like to live in?” or “Should I put solar panels on my roof?”

You might think that’s a funny thing to apply problem solving to, but in my mind it’s not fundamentally different from business problem solving, which answers the question “What should my strategy be?” Or problem solving at the policy level: “How do we combat climate change?” “Should I support the local school bond?” I think these are all part and parcel of the same type of question, “What should I do?”

I’m a big fan of structured problem solving. By following steps, we can more clearly understand what problem it is we’re solving, what are the components of the problem that we’re solving, which components are the most important ones for us to pay attention to, which analytic techniques we should apply to those, and how we can synthesize what we’ve learned back into a compelling story. That’s all it is, at its heart.

I think sometimes when people think about seven steps, they assume that there’s a rigidity to this. That’s not it at all. It’s actually to give you the scope for creativity, which often doesn’t exist when your problem solving is muddled.

Simon London: You were just talking about the seven-step process. That’s what’s written down in the book, but it’s a very McKinsey process as well. Without getting too deep into the weeds, let’s go through the steps, one by one. You were just talking about problem definition as being a particularly important thing to get right first. That’s the first step. Hugo, tell us about that.

Hugo Sarrazin: It is surprising how often people jump past this step and make a bunch of assumptions. The most powerful thing is to step back and ask the basic questions—“What are we trying to solve? What are the constraints that exist? What are the dependencies?” Let’s make those explicit and really push the thinking and defining. At McKinsey, we spend an enormous amount of time in writing that little statement, and the statement, if you’re a logic purist, is great. You debate. “Is it an ‘or’? Is it an ‘and’? What’s the action verb?” Because all these specific words help you get to the heart of what matters.

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Simon London: So this is a concise problem statement.

Hugo Sarrazin: Yeah. It’s not like “Can we grow in Japan?” That’s interesting, but it is “What, specifically, are we trying to uncover in the growth of a product in Japan? Or a segment in Japan? Or a channel in Japan?” When you spend an enormous amount of time, in the first meeting of the different stakeholders, debating this and having different people put forward what they think the problem definition is, you realize that people have completely different views of why they’re here. That, to me, is the most important step.

Charles Conn: I would agree with that. For me, the problem context is critical. When we understand “What are the forces acting upon your decision maker? How quickly is the answer needed? With what precision is the answer needed? Are there areas that are off limits or areas where we would particularly like to find our solution? Is the decision maker open to exploring other areas?” then you not only become more efficient, and move toward what we call the critical path in problem solving, but you also make it so much more likely that you’re not going to waste your time or your decision maker’s time.

How often do especially bright young people run off with half of the idea about what the problem is and start collecting data and start building models—only to discover that they’ve really gone off half-cocked.

Hugo Sarrazin: Yeah.

Charles Conn: And in the wrong direction.

Simon London: OK. So step one—and there is a real art and a structure to it—is define the problem. Step two, Charles?

Charles Conn: My favorite step is step two, which is to use logic trees to disaggregate the problem. Every problem we’re solving has some complexity and some uncertainty in it. The only way that we can really get our team working on the problem is to take the problem apart into logical pieces.

What we find, of course, is that the way to disaggregate the problem often gives you an insight into the answer to the problem quite quickly. I love to do two or three different cuts at it, each one giving a bit of a different insight into what might be going wrong. By doing sensible disaggregations, using logic trees, we can figure out which parts of the problem we should be looking at, and we can assign those different parts to team members.

Simon London: What’s a good example of a logic tree on a sort of ratable problem?

Charles Conn: Maybe the easiest one is the classic profit tree. Almost in every business that I would take a look at, I would start with a profit or return-on-assets tree. In its simplest form, you have the components of revenue, which are price and quantity, and the components of cost, which are cost and quantity. Each of those can be broken out. Cost can be broken into variable cost and fixed cost. The components of price can be broken into what your pricing scheme is. That simple tree often provides insight into what’s going on in a business or what the difference is between that business and the competitors.

If we add the leg, which is “What’s the asset base or investment element?”—so profit divided by assets—then we can ask the question “Is the business using its investments sensibly?” whether that’s in stores or in manufacturing or in transportation assets. I hope we can see just how simple this is, even though we’re describing it in words.

When I went to work with Gordon Moore at the Moore Foundation, the problem that he asked us to look at was “How can we save Pacific salmon?” Now, that sounds like an impossible question, but it was amenable to precisely the same type of disaggregation and allowed us to organize what became a 15-year effort to improve the likelihood of good outcomes for Pacific salmon.

Simon London: Now, is there a danger that your logic tree can be impossibly large? This, I think, brings us onto the third step in the process, which is that you have to prioritize.

Charles Conn: Absolutely. The third step, which we also emphasize, along with good problem definition, is rigorous prioritization—we ask the questions “How important is this lever or this branch of the tree in the overall outcome that we seek to achieve? How much can I move that lever?” Obviously, we try and focus our efforts on ones that have a big impact on the problem and the ones that we have the ability to change. With salmon, ocean conditions turned out to be a big lever, but not one that we could adjust. We focused our attention on fish habitats and fish-harvesting practices, which were big levers that we could affect.

People spend a lot of time arguing about branches that are either not important or that none of us can change. We see it in the public square. When we deal with questions at the policy level—“Should you support the death penalty?” “How do we affect climate change?” “How can we uncover the causes and address homelessness?”—it’s even more important that we’re focusing on levers that are big and movable.

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Simon London: Let’s move swiftly on to step four. You’ve defined your problem, you disaggregate it, you prioritize where you want to analyze—what you want to really look at hard. Then you got to the work plan. Now, what does that mean in practice?

Hugo Sarrazin: Depending on what you’ve prioritized, there are many things you could do. It could be breaking the work among the team members so that people have a clear piece of the work to do. It could be defining the specific analyses that need to get done and executed, and being clear on time lines. There’s always a level-one answer, there’s a level-two answer, there’s a level-three answer. Without being too flippant, I can solve any problem during a good dinner with wine. It won’t have a whole lot of backing.

Simon London: Not going to have a lot of depth to it.

Hugo Sarrazin: No, but it may be useful as a starting point. If the stakes are not that high, that could be OK. If it’s really high stakes, you may need level three and have the whole model validated in three different ways. You need to find a work plan that reflects the level of precision, the time frame you have, and the stakeholders you need to bring along in the exercise.

Charles Conn: I love the way you’ve described that, because, again, some people think of problem solving as a linear thing, but of course what’s critical is that it’s iterative. As you say, you can solve the problem in one day or even one hour.

Charles Conn: We encourage our teams everywhere to do that. We call it the one-day answer or the one-hour answer. In work planning, we’re always iterating. Every time you see a 50-page work plan that stretches out to three months, you know it’s wrong. It will be outmoded very quickly by that learning process that you described. Iterative problem solving is a critical part of this. Sometimes, people think work planning sounds dull, but it isn’t. It’s how we know what’s expected of us and when we need to deliver it and how we’re progressing toward the answer. It’s also the place where we can deal with biases. Bias is a feature of every human decision-making process. If we design our team interactions intelligently, we can avoid the worst sort of biases.

Simon London: Here we’re talking about cognitive biases primarily, right? It’s not that I’m biased against you because of your accent or something. These are the cognitive biases that behavioral sciences have shown we all carry around, things like anchoring, overoptimism—these kinds of things.

Both: Yeah.

Charles Conn: Availability bias is the one that I’m always alert to. You think you’ve seen the problem before, and therefore what’s available is your previous conception of it—and we have to be most careful about that. In any human setting, we also have to be careful about biases that are based on hierarchies, sometimes called sunflower bias. I’m sure, Hugo, with your teams, you make sure that the youngest team members speak first. Not the oldest team members, because it’s easy for people to look at who’s senior and alter their own creative approaches.

Hugo Sarrazin: It’s helpful, at that moment—if someone is asserting a point of view—to ask the question “This was true in what context?” You’re trying to apply something that worked in one context to a different one. That can be deadly if the context has changed, and that’s why organizations struggle to change. You promote all these people because they did something that worked well in the past, and then there’s a disruption in the industry, and they keep doing what got them promoted even though the context has changed.

Simon London: Right. Right.

Hugo Sarrazin: So it’s the same thing in problem solving.

Charles Conn: And it’s why diversity in our teams is so important. It’s one of the best things about the world that we’re in now. We’re likely to have people from different socioeconomic, ethnic, and national backgrounds, each of whom sees problems from a slightly different perspective. It is therefore much more likely that the team will uncover a truly creative and clever approach to problem solving.

Simon London: Let’s move on to step five. You’ve done your work plan. Now you’ve actually got to do the analysis. The thing that strikes me here is that the range of tools that we have at our disposal now, of course, is just huge, particularly with advances in computation, advanced analytics. There’s so many things that you can apply here. Just talk about the analysis stage. How do you pick the right tools?

Charles Conn: For me, the most important thing is that we start with simple heuristics and explanatory statistics before we go off and use the big-gun tools. We need to understand the shape and scope of our problem before we start applying these massive and complex analytical approaches.

Simon London: Would you agree with that?

Hugo Sarrazin: I agree. I think there are so many wonderful heuristics. You need to start there before you go deep into the modeling exercise. There’s an interesting dynamic that’s happening, though. In some cases, for some types of problems, it is even better to set yourself up to maximize your learning. Your problem-solving methodology is test and learn, test and learn, test and learn, and iterate. That is a heuristic in itself, the A/B testing that is used in many parts of the world. So that’s a problem-solving methodology. It’s nothing different. It just uses technology and feedback loops in a fast way. The other one is exploratory data analysis. When you’re dealing with a large-scale problem, and there’s so much data, I can get to the heuristics that Charles was talking about through very clever visualization of data.

You test with your data. You need to set up an environment to do so, but don’t get caught up in neural-network modeling immediately. You’re testing, you’re checking—“Is the data right? Is it sound? Does it make sense?”—before you launch too far.

Simon London: You do hear these ideas—that if you have a big enough data set and enough algorithms, they’re going to find things that you just wouldn’t have spotted, find solutions that maybe you wouldn’t have thought of. Does machine learning sort of revolutionize the problem-solving process? Or are these actually just other tools in the toolbox for structured problem solving?

Charles Conn: It can be revolutionary. There are some areas in which the pattern recognition of large data sets and good algorithms can help us see things that we otherwise couldn’t see. But I do think it’s terribly important we don’t think that this particular technique is a substitute for superb problem solving, starting with good problem definition. Many people use machine learning without understanding algorithms that themselves can have biases built into them. Just as 20 years ago, when we were doing statistical analysis, we knew that we needed good model definition, we still need a good understanding of our algorithms and really good problem definition before we launch off into big data sets and unknown algorithms.

Simon London: Step six. You’ve done your analysis.

Charles Conn: I take six and seven together, and this is the place where young problem solvers often make a mistake. They’ve got their analysis, and they assume that’s the answer, and of course it isn’t the answer. The ability to synthesize the pieces that came out of the analysis and begin to weave those into a story that helps people answer the question “What should I do?” This is back to where we started. If we can’t synthesize, and we can’t tell a story, then our decision maker can’t find the answer to “What should I do?”

Simon London: But, again, these final steps are about motivating people to action, right?

Charles Conn: Yeah.

Simon London: I am slightly torn about the nomenclature of problem solving because it’s on paper, right? Until you motivate people to action, you actually haven’t solved anything.

Charles Conn: I love this question because I think decision-making theory, without a bias to action, is a waste of time. Everything in how I approach this is to help people take action that makes the world better.

Simon London: Hence, these are absolutely critical steps. If you don’t do this well, you’ve just got a bunch of analysis.

Charles Conn: We end up in exactly the same place where we started, which is people speaking across each other, past each other in the public square, rather than actually working together, shoulder to shoulder, to crack these important problems.

Simon London: In the real world, we have a lot of uncertainty—arguably, increasing uncertainty. How do good problem solvers deal with that?

Hugo Sarrazin: At every step of the process. In the problem definition, when you’re defining the context, you need to understand those sources of uncertainty and whether they’re important or not important. It becomes important in the definition of the tree.

You need to think carefully about the branches of the tree that are more certain and less certain as you define them. They don’t have equal weight just because they’ve got equal space on the page. Then, when you’re prioritizing, your prioritization approach may put more emphasis on things that have low probability but huge impact—or, vice versa, may put a lot of priority on things that are very likely and, hopefully, have a reasonable impact. You can introduce that along the way. When you come back to the synthesis, you just need to be nuanced about what you’re understanding, the likelihood.

Often, people lack humility in the way they make their recommendations: “This is the answer.” They’re very precise, and I think we would all be well-served to say, “This is a likely answer under the following sets of conditions” and then make the level of uncertainty clearer, if that is appropriate. It doesn’t mean you’re always in the gray zone; it doesn’t mean you don’t have a point of view. It just means that you can be explicit about the certainty of your answer when you make that recommendation.

Simon London: So it sounds like there is an underlying principle: “Acknowledge and embrace the uncertainty. Don’t pretend that it isn’t there. Be very clear about what the uncertainties are up front, and then build that into every step of the process.”

Hugo Sarrazin: Every step of the process.

Simon London: Yeah. We have just walked through a particular structured methodology for problem solving. But, of course, this is not the only structured methodology for problem solving. One that is also very well-known is design thinking, which comes at things very differently. So, Hugo, I know you have worked with a lot of designers. Just give us a very quick summary. Design thinking—what is it, and how does it relate?

Hugo Sarrazin: It starts with an incredible amount of empathy for the user and uses that to define the problem. It does pause and go out in the wild and spend an enormous amount of time seeing how people interact with objects, seeing the experience they’re getting, seeing the pain points or joy—and uses that to infer and define the problem.

Simon London: Problem definition, but out in the world.

Hugo Sarrazin: With an enormous amount of empathy. There’s a huge emphasis on empathy. Traditional, more classic problem solving is you define the problem based on an understanding of the situation. This one almost presupposes that we don’t know the problem until we go see it. The second thing is you need to come up with multiple scenarios or answers or ideas or concepts, and there’s a lot of divergent thinking initially. That’s slightly different, versus the prioritization, but not for long. Eventually, you need to kind of say, “OK, I’m going to converge again.” Then you go and you bring things back to the customer and get feedback and iterate. Then you rinse and repeat, rinse and repeat. There’s a lot of tactile building, along the way, of prototypes and things like that. It’s very iterative.

Simon London: So, Charles, are these complements or are these alternatives?

Charles Conn: I think they’re entirely complementary, and I think Hugo’s description is perfect. When we do problem definition well in classic problem solving, we are demonstrating the kind of empathy, at the very beginning of our problem, that design thinking asks us to approach. When we ideate—and that’s very similar to the disaggregation, prioritization, and work-planning steps—we do precisely the same thing, and often we use contrasting teams, so that we do have divergent thinking. The best teams allow divergent thinking to bump them off whatever their initial biases in problem solving are. For me, design thinking gives us a constant reminder of creativity, empathy, and the tactile nature of problem solving, but it’s absolutely complementary, not alternative.

Simon London: I think, in a world of cross-functional teams, an interesting question is do people with design-thinking backgrounds really work well together with classical problem solvers? How do you make that chemistry happen?

Hugo Sarrazin: Yeah, it is not easy when people have spent an enormous amount of time seeped in design thinking or user-centric design, whichever word you want to use. If the person who’s applying classic problem-solving methodology is very rigid and mechanical in the way they’re doing it, there could be an enormous amount of tension. If there’s not clarity in the role and not clarity in the process, I think having the two together can be, sometimes, problematic.

The second thing that happens often is that the artifacts the two methodologies try to gravitate toward can be different. Classic problem solving often gravitates toward a model; design thinking migrates toward a prototype. Rather than writing a big deck with all my supporting evidence, they’ll bring an example, a thing, and that feels different. Then you spend your time differently to achieve those two end products, so that’s another source of friction.

Now, I still think it can be an incredibly powerful thing to have the two—if there are the right people with the right mind-set, if there is a team that is explicit about the roles, if we’re clear about the kind of outcomes we are attempting to bring forward. There’s an enormous amount of collaborativeness and respect.

Simon London: But they have to respect each other’s methodology and be prepared to flex, maybe, a little bit, in how this process is going to work.

Hugo Sarrazin: Absolutely.

Simon London: The other area where, it strikes me, there could be a little bit of a different sort of friction is this whole concept of the day-one answer, which is what we were just talking about in classical problem solving. Now, you know that this is probably not going to be your final answer, but that’s how you begin to structure the problem. Whereas I would imagine your design thinkers—no, they’re going off to do their ethnographic research and get out into the field, potentially for a long time, before they come back with at least an initial hypothesis.

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Hugo Sarrazin: That is a great callout, and that’s another difference. Designers typically will like to soak into the situation and avoid converging too quickly. There’s optionality and exploring different options. There’s a strong belief that keeps the solution space wide enough that you can come up with more radical ideas. If there’s a large design team or many designers on the team, and you come on Friday and say, “What’s our week-one answer?” they’re going to struggle. They’re not going to be comfortable, naturally, to give that answer. It doesn’t mean they don’t have an answer; it’s just not where they are in their thinking process.

Simon London: I think we are, sadly, out of time for today. But Charles and Hugo, thank you so much.

Charles Conn: It was a pleasure to be here, Simon.

Hugo Sarrazin: It was a pleasure. Thank you.

Simon London: And thanks, as always, to you, our listeners, for tuning into this episode of the McKinsey Podcast . If you want to learn more about problem solving, you can find the book, Bulletproof Problem Solving: The One Skill That Changes Everything , online or order it through your local bookstore. To learn more about McKinsey, you can of course find us at McKinsey.com.

Charles Conn is CEO of Oxford Sciences Innovation and an alumnus of McKinsey’s Sydney office. Hugo Sarrazin is a senior partner in the Silicon Valley office, where Simon London, a member of McKinsey Publishing, is also based.

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Problem solving techniques: Steps and methods

Posted on May 29, 2019

Constant disruption has become a hallmark of the modern workforce and organisations want problem solving skills to combat this. Employers need people who can respond to change – be that evolving technology, new competitors, different models for doing business, or any of the other transformations that have taken place in recent years.

In addition, problem solving techniques encompass many of the other top skills employers seek . For example, LinkedIn’s list of the most in-demand soft skills of 2019 includes creativity, collaboration and adaptability, all of which fall under the problem-solving umbrella.

Despite its importance, many employees misunderstand what the problem solving method really involves.

What constitutes effective problem solving?

Effective problem solving doesn’t mean going away and coming up with an answer immediately. In fact, this isn’t good problem solving at all, because you’ll be running with the first solution that comes into your mind, which often isn’t the best.

Instead, you should look at problem solving more as a process with several steps involved that will help you reach the best outcome. Those steps are:

• Define the problem
• List all the possible solutions
• Evaluate the options
• Select the best solution
• Create an implementation plan
• Communicate your solution

Let’s look at each step in a little more detail.

1. Define the problem

The first step to solving a problem is defining what the problem actually is – sounds simple, right? Well no. An effective problem solver will take the thoughts of everyone involved into account, but different people might have different ideas on what the root cause of the issue really is. It’s up to you to actively listen to everyone without bringing any of your own preconceived notions to the conversation. Learning to differentiate facts from opinion is an essential part of this process.

An effective problem solver will take the opinions of everyone involved into account

The same can be said of data. Depending on what the problem is, there will be varying amounts of information available that will help you work out what’s gone wrong. There should be at least some data involved in any problem, and it’s up to you to gather as much as possible and analyse it objectively.

2. List all the possible solutions

Once you’ve identified what the real issue is, it’s time to think of solutions. Brainstorming as many solutions as possible will help you arrive at the best answer because you’ll be considering all potential options and scenarios. You should take everyone’s thoughts into account when you’re brainstorming these ideas, as well as all the insights you’ve gleaned from your data analysis. It also helps to seek input from others at this stage, as they may come up with solutions you haven’t thought of.

Depending on the type of problem, it can be useful to think of both short-term and long-term solutions, as some of your options may take a while to implement.

3. Evaluate the options

Each option will have pros and cons, and it’s important you list all of these, as well as how each solution could impact key stakeholders. Once you’ve narrowed down your options to three or four, it’s often a good idea to go to other employees for feedback just in case you’ve missed something. You should also work out how each option ties in with the broader goals of the business.

There may be a way to merge two options together in order to satisfy more people.

4. Select an option

Only now should you choose which solution you’re going to go with. What you decide should be whatever solves the problem most effectively while also taking the interests of everyone involved into account. There may be a way to merge two options together in order to satisfy more people.

5. Create an implementation plan

At this point you might be thinking it’s time to sit back and relax – problem solved, right? There are actually two more steps involved if you want your problem solving method to be truly effective. The first is to create an implementation plan. After all, if you don’t carry out your solution effectively, you’re not really solving the problem at all. 

Create an implementation plan on how you will put your solution into practice. One problem solving technique that many use here is to introduce a testing and feedback phase just to make sure the option you’ve selected really is the most viable. You’ll also want to include any changes to your solution that may occur in your implementation plan, as well as how you’ll monitor compliance and success.

6. Communicate your solution

There’s one last step to consider as part of the problem solving methodology, and that’s communicating your solution . Without this crucial part of the process, how is anyone going to know what you’ve decided? Make sure you communicate your decision to all the people who might be impacted by it. Not everyone is going to be 100 per cent happy with it, so when you communicate you must give them context. Explain exactly why you’ve made that decision and how the pros mean it’s better than any of the other options you came up with.

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Problem management: 8 steps to better problem solving

Problem management is an 8 step framework most commonly used by IT teams. You can use problem management to solve for repeating major incidents. By organizing and structuring your problem solving, you can more effectively get to the root cause of high-impact problems—and devise a solution. Solving the root cause prevents recurrence and creates a repeatable solution to use on similar errors in the future.

In an IT department, errors and mishaps are part of the job. You can't always control these problems, but you can control how you respond to them with problem management. Problem management helps you solve larger problems and reduce the risk that they’ll happen again by identifying all connected problems, solving them, and planning for the future.

What is problem management?

Problem management is an 8 step framework most commonly used by IT teams. Your team can use problem management to solve for repeating major incidents. By organizing and structuring your problem solving, you can more effectively get to the root cause of high-impact problems—and devise a solution. Problem management is a process—used mostly by IT teams—to identify, react, and respond to issues. It’s not for every problem, but it’s a useful response when multiple major incidents occur that cause large work interruptions. Unlike problem solving, problem management goes beyond the initial incident to discover and dissect the root causes, preventing future incidents with permanent solutions.

The goals of problem management are to:

Prevent problems before they start.

Solve for repetitive errors.

Lessen each incident’s impact. 

Problem management vs. incident management 

Example: Someone leaves their unprotected laptop in a coffee shop, causing a security breach. The security team can use incident management to solve for this one, isolated event. In this case, the team could manually shut down the accounts connected to that laptop. If this continues to happen, IT would use problem management to solve the root of this issue—perhaps installing more security features on each company laptop so that if employees lose them, no one else can access the information.

Problem management vs. problem solving

While similar in name, problem management differs slightly from problem-solving. Problem management focuses on every aspect of the incident—identifying the root cause of the problem, solving it, and prevention. Problem solving is, as the name implies, focused solely on the solution step. 

Example: You’re launching a new password management system when it crashes—again. You don’t know if anything leaked, but you know it could contain confidential information. Plus, it’s happened before. You start the problem management process to ensure it doesn’t happen again. In that process, you’ll use problem solving as a step to fix the issue. In this case, perhaps securing confidential information before you try to launch a new software.

Problem management vs. change management 

Change management targets large transitions within your workplace, good and bad. These inevitable changes aren’t always negative, so you can’t always apply problem management as a solution. That’s where change management comes in—a framework that helps you adjust to any new scenario.

Example: Your company is transitioning to a new cloud platform. The transition happens incident-free—meaning you won’t need problem management—but you can ease the transition by implementing some change management best practices. Preparing and training team members in the new software is a good place to start.

Problem management vs. project management

Project management is the framework for larger collections of work. It’s the overarching method for how you work on any project, hit goals, and get results. You can use project management to help you with problem management, but they are not the same thing. Problem management and project management work together to solve issues as part of your problem management process.

Example: During problem management, you uncover a backend security issue that needs to be addressed—employees are using storage software with outdated security measures. To solve this, you create a project and outline the tasks from start to finish. In this case, you might need to alert senior executives, get approval to remove the software, and alert employees. You create a project schedule with a defined timeline and assign the tasks to relevant teams. In this process, you identified a desired outcome—remove the unsafe software—and solved it. That’s project management.

The 8 steps of problem management

It’s easy to get upset when problems occur. In fact, it’s totally normal. But an emotional response is not always the best response when faced with new incidents. Having a reliable system—such as problem management—removes the temptation to respond emotionally. Proactive project management gives your team a framework for problem solving. It’s an iterative process —the more you use it, the more likely you are to have fewer problems, faster response times, and better outputs. 

1. Identify the problem

During problem identification, you’re looking at the present—what’s happening right now? Here, you’ll define what the incident is and its scale. Is this a small, quick-fix, or a full overhaul? Consider using problem framing to define, prioritize, and understand the obstacles involved with these more complex problems. 

2. Diagnose the cause

Use problem analysis or root cause analysis to strategically look at the cause of a problem. Follow the trail of issues all the way back to its beginnings.

To diagnose the underlying cause, you’ll want to answer:

What factors or conditions led to the incident?

Do you see related incidents? Could those be coming from the same source?

Did someone miss a step? Are processes responsible for this problem?

3. Organize and prioritize

Now it’s time to build out your framework. Use an IT project plan to organize information in a space where everyone can make and see updates in real time. The easiest way to do this is with a project management tool where you can input ‌tasks, assign deadlines, and add dependencies to ensure nothing gets missed. To better organize your process, define:

What needs to be done? 

Who’s responsible for each aspect? If no one is, can we assign someone? 

When does each piece need to be completed?

What is the final number of incidents related to this problem?

Are any of these tasks dependent on another one? Do you need to set up dependencies ?

What are your highest priorities? How do they affect our larger business goals ? 

How should you plan for this in the future?

4. Create a workaround

If the incident has stopped work or altered it, you might need to create a workaround. This is not always necessary, but temporary workarounds can keep work on track and avoid backlog while you go through the problem management steps. When these workarounds are especially effective, you can make them permanent processes.

5. Update your known error database

Every time an incident occurs, create a known error record and add it to your known error database (KEDB). Recording incidents helps you catch recurrences and logs the solution, so you know how to solve similar errors in the future. 

6. Pause for change management (if necessary)

Larger, high-impact problems might require change management. For example, if you realize the problem’s root cause is a lack of staff, you might dedicate team members to help. You can use change management to help them transition their responsibilities, see how these new roles fit in with the entire team, and determine how they will collaborate moving forward.

7. Solve the problem

This is the fun part—you get to resolve problems. At this stage, you should know exactly what you’re dealing with and the steps you need to take. But remember—with problem management, it’s not enough to solve the current problem. You’ll want to take any steps to prevent this from happening again in the future. That could mean hiring a new role to cover gaps in workflows , investing in new softwares and tools, or training staff on best practices to prevent these types of incidents.

Read: Turn your team into skilled problem solvers with these problem-solving strategies

8. Reflect on the process

The problem management process has the added benefit of recording the process in its entirety, so you can review it in the future. Once you’ve solved the problem, take the time to review each step and reflect on the lessons learned during this process. Make note of who was involved, what you needed, and any opportunities to improve your response to the next incident. After you go through the problem management process a few times and understand the basic steps, stakeholders, workload, and resources you need, create a template to make the kickoff process easier in the future.

5 benefits of problem management

Problem management helps you discover every piece of the problem—from the current scenario down to its root cause. Not only does this have an immediate positive impact on the current issue at hand, it also promotes collaboration and helps to build a better product overall. 

Here are five other ways ‌problem management can benefit your team:

Avoids repeat incidents. When you manage the entire incident from start to finish, you will address the foundational problems that caused it. This leads to fewer repeat incidents.

Boosts cross-functional collaboration. Problem management is a collaborative process. One incident might require collaboration from IT, the security team, and legal. Depending on the level of the problem, it might trickle all the way back down to the product or service team, where core changes need to be made.

Creates a better user experience. It’s simple—the fewer incidents you have, the better your customer’s experience will be. Reducing incidents means fewer delays, downtime, and frustrations for your users, and a higher rate of customer satisfaction.

Improves response time. As you develop a flow and framework with a project management process, you’ll be better equipped to handle future incidents—even if they’re different scenarios.

Organizes problem solving. Problem management provides a structured, thoughtful approach to solving problems. This reduces impulsive responses and helps you keep a better problem record of incidents and solutions.

Problem management leads to better, faster solutions

IT teams will always have to deal with incidents, but they don’t have to be bogged down by them. That’s because problem management works. Whether you employ a full problem management team or choose to apply these practices to your current IT infrastructure, problem management—especially when combined with a project management tool—saves you time and effort down the road.

With IT project plans, we’ve made it easier than ever to track your problem management work in a shared tool. Try our free IT project template to see your work come together, effortlessly.

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10 Step Process for Effective Business Problem Solving

Posted august 3, 2021 by harriet genever.

When you start a small business or launch a startup, the one thing you can count on is the unexpected. No matter how thoroughly you plan, forecast , and test, problems are bound to arise. This is why as an entrepreneur, you need to know how to solve business problems effectively.

What is problem solving in business?

Problem solving in business relates to establishing processes that mitigate or remove obstacles currently preventing you from reaching strategic goals . These are typically complex issues that create a gap between actual results and your desired outcome. They may be present in a single team, operational process, or throughout your entire organization, typically without an immediate or obvious solution. 

To approach problem solving successfully, you need to establish consistent processes that help you evaluate, explore solutions, prioritize execution, and measure success. In many ways, it should be similar to how you review business performance through a monthly plan review . You work through the same documentation, look for gaps, dig deeper to identify the root cause, and hash out options. Without this process, you simply cannot expect to solve problems efficiently or effectively. 

Why problem solving is important for your business

While some would say problem-solving comes naturally, it’s actually a skill you can grow and refine over time. Problem solving skills will help you and your team tackle critical issues and conflicts as they arise. It starts from the top. You as the business owner or CEO needing to display the type of level-headed problem solving that you expect to see from your employees.

Doing so will help you and your staff quickly deal with issues, establish and refine a problem solving process, turn challenges into opportunities, and generally keep a level head. Now, the best business leaders didn’t just find a magic solution to solve their problems, they built processes and leveraged tools to find success. And you can do the same.

By following this 10-step process, you can develop your problem-solving skills and approach any issue that arises with confidence. 

1. Define the problem

When a problem arises, it can be very easy to jump right into creating a solution. However, if you don’t thoroughly examine what led to the problem in the first place, you may create a strategy that doesn’t actually solve it. You may just be treating the symptoms.

For instance, if you realize that your sales from new customers are dropping, your first inclination might be to rush into putting together a marketing plan to increase exposure. But what if decreasing sales are just a symptom of the real problem? 

When you define the problem, you want to be sure you’re not missing the forest for the trees. If you have a large issue on your hands, you’ll want to look at it from several different angles:

Competition 

Is a competitor’s promotion or pricing affecting your sales? Are there new entrants in your market? How are they marketing their product or business?

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Business model 

Is your business model sustainable? Is it realistic for how fast you want to grow? Should you explore different pricing or cost strategies?

Market factors

How are world events and the nation’s economy affecting your customers and your sales?

Are there any issues affecting your team? Do they have the tools and resources they need to succeed? 

Goal alignment 

Is everyone on your team working toward the same goal ? Have you communicated your short-term and long-term business goals clearly and often?

There are a lot of ways to approach the issue when you’re facing a serious business problem. The key is to make sure you’re getting a full snapshot of what’s going on so you don’t waste money and resources on band-aid solutions. 

Going back to our example, by looking at every facet of your business, you may discover that you’re spending more on advertising than your competitors already. And instead, there’s a communication gap within your team that’s leading to the mishandling of new customers and therefore lost sales. 

If you jumped into fixing the exposure of your brand, you would have been dumping more money into an area you’re already winning. Potentially leading to greater losses as more and more new customers are dropped due to poor internal communication.

This is why it’s so vital that you explore your blind spots and track the problem to its source.

2. Conduct a SWOT analysis

All good businesses solve some sort of problem for customers. What if your particular business problem is actually an opportunity, or even a strength if considered from a different angle? This is when you’d want to conduct a SWOT analysis to determine if that is in fact the case.

SWOT is a great tool for strategic planning and bringing multiple viewpoints to the table when you’re looking at investing resources to solve a problem. This may even be incorporated in your attempts to identify the source of your problem, as it can quickly outline specific strengths and weaknesses of your business. And then by identifying any potential opportunities or threats, you can utilize your findings to kickstart a solution. 

3. Identify multiple solutions with design thinking

As you approach solving your problem, you may want to consider using the design thinking approach . It’s often used by organizations looking to solve big, community-based problems. One of its strengths is that it requires involving a wide range of people in the problem-solving process. Which leads to multiple perspectives and solutions arising.

This approach—applying your company’s skills and expertise to a problem in the market—is the basis for design thinking.

It’s not about finding the most complex problems to solve, but about finding common needs within the organization and in the real world and coming up with solutions that fit those needs. When you’re solving business problems, this applies in the sense that you’re looking for solutions that address underlying issues—you’re looking at the big picture.

4. Conduct market research and customer outreach

Market research and customer outreach aren’t the sorts of things small business owners and startups can do once and then cross off the list. When you’re facing a roadblock, think back to the last time you did some solid market research or took a deep dive into understanding the competitive landscape .

Market research and the insights you get from customer outreach aren’t a silver bullet. Many companies struggle with what they should do with conflicting data points. But it’s worth struggling through and gathering information that can help you better understand your target market . Plus, your customers can be one of the best sources of criticism. It’s actually a gift if you can avoid taking the negatives personally .

The worst thing you can do when you’re facing challenges is isolating yourself from your customers and ignore your competition. So survey your customers. Put together a competitive matrix . 

5. Seek input from your team and your mentors

Don’t do your SWOT analysis or design thinking work by yourself. The freedom to express concerns, opinions, and ideas will allow people in an organization to speak up. Their feedback is going to help you move faster and more efficiently. If you have a team in place, bring them into the discussion. You hired them to be experts in their area; use their expertise to navigate and dig deeper into underlying causes of problems and potential solutions.

If you’re running your business solo, at least bring in a trusted mentor. SCORE offers a free business mentorship program if you don’t already have one. It can also be helpful to connect with a strategic business advisor , especially if business financials aren’t your strongest suit.

Quoting Stephen Covey, who said that “strength lies in differences, not in similarities,” speaking to the importance of diversity when it comes to problem-solving in business. The more diverse a team is , the more often innovative solutions to the problems faced by the organization appear.

In fact, it has been found that groups that show greater diversity were better at solving problems than groups made up specifically of highly skilled problem solvers. So whoever you bring in to help you problem-solve, resist the urge to surround yourself with people who already agree with you about everything.

6. Apply lean planning for nimble execution

So you do your SWOT analysis and your design thinking exercise. You come up with a set of strong, data-driven ideas. But implementing them requires you to adjust your budget, or your strategic plan, or even your understanding of your target market.

Are you willing to change course? Can you quickly make adjustments? Well in order to grow, you can’t be afraid to be nimble . 

By adopting the lean business planning method —the process of revising your business strategy regularly—you’ll be able to shift your strategies more fluidly. You don’t want to change course every week, and you don’t want to fall victim to shiny object thinking. But you can strike a balance that allows you to reduce your business’s risk while keeping your team heading in the right direction.

Along the way, you’ll make strategic decisions that don’t pan out the way you hoped. The best thing you can do is test your ideas and iterate often so you’re not wasting money and resources on things that don’t work. That’s Lean Planning .

7. Model different financial scenarios

When you’re trying to solve a serious business problem, one of the best things you can do is build a few different financial forecasts so you can model different scenarios. You might find that the idea that seemed the strongest will take longer than you thought to reverse a negative financial trend. At the very least you’ll have better insight into the financial impact of moving in a different direction.

The real benefit here is looking at different tactical approaches to the same problem. Maybe instead of increasing sales right now, you’re better off in the long run if you adopt a strategy to reduce churn and retain your best customers. You won’t know unless you model a few different scenarios. You can do this by using spreadsheets, and a tool like LivePlan can make it easier and quicker.

8. Watch your cash flow

While you’re working to solve a challenging business problem, pay particular attention to your cash flow and your cash flow forecast . Understanding when your company is at risk of running out of cash in the bank can help you be proactive. It’s a lot easier to get a line of credit while your financials still look good and healthy, than when you’re one pay period away from ruin.

If you’re dealing with a serious issue, it’s easy to start to get tunnel vision. You’ll benefit from maintaining a little breathing room for your business as you figure out what to do next.

9. Use a decision-making framework

Once you’ve gathered all the information you need, generated a number of ideas, and done some financial modeling, you might still feel uncertain. It’s natural—you’re not a fortune-teller. You’re trying to make the best decision you can with the information you have.

This article offers a really useful approach to making decisions. It starts with putting your options into a matrix like this one:

Use this sort of framework to put everything you’ve learned out on the table. If you’re working with a bigger team, this sort of exercise can also bring the rest of your team to the table so they feel some ownership over the outcome.

10. Identify key metrics to track

How will you know your problem is solved? And not just the symptom—how will you know when you’ve addressed the underlying issues? Before you dive into enacting the solution, make sure you know what success looks like.

Decide on a few key performance indicators . Take a baseline measurement, and set a goal and a timeframe. You’re essentially translating your solution into a plan, complete with milestones and goals. Without these, you’ve simply made a blind decision with no way to track success. You need those goals and milestones to make your plan real .

Problem solving skills to improve

As you and your team work through this process, it’s worth keeping in mind specific problem solving skills you should continue to develop. Bolstering your ability, as well as your team, to solve problems effectively will only make this process more useful and efficient. Here are a few key skills to work on.

Emotional intelligence

It can be very easy to make quick, emotional responses in a time of crisis or when discussing something you’re passionate about. To avoid making assumptions and letting your emotions get the best of you, you need to focus on empathizing with others. This involves understanding your own emotional state, reactions and listening carefully to the responses of your team. The more you’re able to listen carefully, the better you’ll be at asking for and taking advice that actually leads to effective problem solving.

Jumping right into a solution can immediately kill the possibility of solving your problem. Just like when you start a business , you need to do the research into what the problem you’re solving actually is. Luckily, you can embed research into your problem solving by holding active reviews of financial performance and team processes. Simply asking “What? Where? When? How?” can lead to more in-depth explorations of potential issues.

The best thing you can do to grow your research abilities is to encourage and practice curiosity. Look at every problem as an opportunity. Something that may be trouble now, but is worth exploring and finding the right solution. You’ll pick up best practices, useful tools and fine-tune your own research process the more you’re willing to explore.

Brainstorming

Creatively brainstorming with your team is somewhat of an art form. There needs to be a willingness to throw everything at the wall and act as if nothing is a bad idea at the start. This style of collaboration encourages participation without fear of rejection. It also helps outline potential solutions outside of your current scope, that you can refine and turn into realistic action.

Work on breaking down problems and try to give everyone in the room a voice. The more input you allow, the greater potential you have for finding the best solution.

Decisiveness

One thing that can drag out acting upon a potential solution, is being indecisive. If you aren’t willing to state when the final cutoff for deliberation is, you simply won’t take steps quickly enough. This is when having a process for problem solving comes in handy, as it purposefully outlines when you should start taking action.

Work on choosing decision-makers, identify necessary results and be prepared to analyze and adjust if necessary. You don’t have to get it right every time, but taking action at the right time, even if it fails, is almost more vital than never taking a step.  

Stemming off failure, you need to learn to be resilient. Again, no one gets it perfect every single time. There are so many factors in play to consider and sometimes even the most well-thought-out solution doesn’t stick. Instead of being down on yourself or your team, look to separate yourself from the problem and continue to think of it as a puzzle worth solving. Every failure is a learning opportunity and it only helps you further refine and eliminate issues in your strategy.

Problem solving is a process

The key to effective problem-solving in business is the ability to adapt. You can waste a lot of resources on staying the wrong course for too long. So make a plan to reduce your risk now. Think about what you’d do if you were faced with a problem large enough to sink your business. Be as proactive as you can.

Editor’s note: This article was originally published in 2016. It was updated in 2021.

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Harriet Genever

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The 7 Best AI Tools to Help Solve Math Problems

How do you make seven even? Use these tools to solve the big math problems in life.

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The test questions, wolframalpha, microsoft mathsolver.

While OpenAI's ChatGPT is one of the most widely known AI tools, there are numerous other platforms that students can use to improve their math skills.

I tested seven AI tools on two common math problems so you know what to expect from each platform and how to use each of them.

I used two math problems to test each tool and standardize the inputs.

• Solve for b: (2 / (b - 3)) - (6 / (2b + 1)) = 4
• Simplify the expression: (4 / 12) + (9 / 8) x (15 / 3) - (26 / 10)

These two problems give each AI tool a chance to show reasoning, problem-solving, accuracy, and how it can guide a learner through the process.

Thetawise provides more than simple answers; you can also opt to have the AI model tutor you by sharing a detailed step-by-step breakdown of the solution. Using the platform is fairly straightforward, given that all you need to do is navigate to the platform and key in the math problem at hand. Alternatively, you can even upload a photo of the math problem onto the platform, and the AI will analyze the image and provide you with an answer.

The AI platform gave us a step-by-step breakdown of the problem:

It resulted in the answer:

While the answer is correct, the tool also provides further options for students to generate a more detailed breakdown of the steps or ask more specific questions.

WolframAlpha is an AI tool capable of solving advanced arithmetic, calculus, and algebra equations. While WolframAlpha's free version provides you with a direct answer, the paid version of the tool generates step-by-step solutions. If you want to make the best use of WolframAlpha's capabilities, you can sign up for the Pro version, which costs $5 per month for the annual plan if you're a student.

As expected, Wolfram Alpha solved both problems, showcasing its ability to handle different problems and provide precise answers quickly.

Julius works pretty similarly to the other AI tools on this list. That said, the highlight of this platform is that it has a built-in community forum, which users can use to discuss their prompts, results, or even issues they might be facing with the platform. Its active user base helps you quickly exchange ideas and receive feedback or advice. The platform's default version uses a combination of GPT-4 and Calude-3, based on whichever model best suits the prompt you input.

We tested the platform's accuracy by submitting the same problems that we did with the other AI tools. When submitting your prompt, you have the option of typing your question or uploading an image or a Google Sheet.

Julius provided correct solutions and offered options to help users verify the solution.

One of the oldest AI platforms, Microsoft's MathSolver is a great option if you want a tool capable of providing free step-by-step solutions to calculus, algebra, and other math problems. Here's how it fared when we submitted our math problems.

Microsoft's MathSolver provided the correct answers, and you can view the steps to the solution, take a quiz, solve similar problems, and more. This can be a great way to practice and perfect your understanding of different concepts.

Symbolab allows you to practice your math skills via quizzes, track your progress, and provide solutions to mathematical problems of different types, including calculus, fractions, trigonometry, and more. You can also use the Digital Notebook feature to keep track of any math problems you solve and share them with your friends. Another highlight of this platform is that educators can use the tool to create a virtual classroom, generate assessments, and share feedback, among other things.

The platform not only displays the answer but also lets you view a breakdown of the steps involved in solving the problem. You can also share the answers and steps via email or social media or print them for reference.

Anthropic launched its Claude 3 AI models in March 2024. Anthropic stated that Claude Opus, the most advanced Claude 3 model, outperforms comparable AI tools on most benchmarks for AI systems, including basic mathematics, undergraduate-level expert knowledge, and graduate-level expert reasoning. To test the platform's accuracy and ease of use, we submitted our two math problems. Here's how the platform performed:

While Claude initially got the answer wrong, probing it and requesting further clarification led to a correct solution.

Remember that we used the free version of Claude to solve this problem; subscribing to Opus (its more advanced model) is recommended if you want to take advantage of Claude's more advanced problem-solving capabilities.

Given that Claude got the previous problem wrong, our second, more basic fraction-based problem will indicate if the AI's performance was an anomaly or part of a consistent pattern.

As you can see, Claude correctly solved this problem and provided a detailed step-by-step breakdown of how it arrived at the answer.

GPT-4 can solve problems with far greater accuracy than its predecessor, GPT-3.5. If you're using the free version of ChatGPT, you'll likely only have access to GPT 3.5 and GPT-4o . However, for $20 per month, you can subscribe to the Plus model, which gives you access to GPT-4 and allows you to input five times the number of messages per day compared to the free version. That said, let's check how it performs with math problems.

In both cases, GPT-4o provided the correct answer with a detailed breakdown of the steps. While the platform is free, unlike other models, it does not have a quiz feature or a community forum.

These AI tools offer unique features and capabilities that make them a good option for math problems. Ultimately, the best way to pick a tool is by testing different models to determine which platform best fits your preferences and learning needs.

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