define problem solving cycle

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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• Miles Anthony Smith
• Sep 12, 2022
• 12 min read

The Ultimate Problem-Solving Process Guide: 31 Steps and Resources

Updated: Jan 24, 2023

GOT CHALLENGES WITH YOUR PROBLEM-SOLVING PROCESS? ARE YOU FRUSTRATED?

prob·lem-solv·ing noun -the process of finding solutions to difficult or complex issues. It sounds so simple, doesn’t it? But in reality problem-solving is hard. It's almost always more complex than it seems. That's why problem-solving can be so frustrating sometimes. You can feel like you’re spinning your wheels, arguing in circles, or just failing to find answers that actually work. And when you've got a group working on a problem, it can get even muddier …differences of opinions, viewpoints colored by different backgrounds, history, life experiences, you name it. We’re all looking at life and work from different angles, and that often means disagreement. Sometimes sharp disagreement. That human element, figuring out how to take ourselves out of the equation and make solid, fact-based decisions , is precisely why there’s been so much written on problem-solving. Which creates its own set of problems. Whose method is best? How can you possibly sift through them all? Are we to have one person complete the entire problem-solving process by themselves or rely on a larger team to find answers to our most vexing challenges in the workplace ? Today, we’re going to make sense of it all. We’ll take a close look at nine top problem-solving methods. Then we’ll grab the best elements of all of them to give you a process that will have your team solving problems faster, with better results , and maybe with less sharp disagreement. Ready to dive in? Let’s go!

9 PROFITABLE PROBLEM-SOLVING TECHNIQUES AND METHODS

While there are loads of methods to choose from, we are going to focus on nine of the more common ones. You can use some of these problem-solving techniques reactively to solve a known issue or proactively to find more efficient or effective ways of performing tasks. If you want to explore other methods, check out this resource here . A helpful bit of advice here is to reassure people that you aren’t here to identify the person that caused the problem . You’re working to surface the issue, solve it and make sure it doesn’t happen again, regardless of the person working on the process. It can’t be understated how important it is to continually reassure people of this so that you get unfiltered access to information. Without this, people will often hide things to protect themselves . After all, nobody wants to look bad, do they? With that said, let’s get started...

1. CREATIVE PROBLEM SOLVING (CPS)

Alex Osborn coined the term “Creative Problem Solving” in the 1940s with this simple four-step process:

Clarify : Explore the vision, gather data, and formulate questions.

Ideate : This stage should use brainstorming to generate divergent thinking and ideas rather than the random ideas normally associated with brainstorming.

Develop : Formulate solutions as part of an overall plan.

Implement : Put the plan into practice and communicate it to all parties.

2. APPRECIATIVE INQUIRY

Source: http://www.davidcooperrider.com/ai-process/ This method seeks, first and foremost, to identify the strengths in people and organizations and play to that “positive core” rather than focus our energies on improving weaknesses . It starts with an “affirmative topic,” followed by the “positive core (strengths).” Then this method delves into the following stages:

Discovery (fact-finding)

Dream (visioning the future)

Design (strategic purpose)

Destiny (continuous improvement)

3. “FIVE WHYS” METHOD

This method simply suggests that we ask “Why” at least five times during our review of the problem and in search of a fix. This helps us dig deeper to find the the true reason for the problem, or the root cause. Now, this doesn’t mean we just keeping asking the same question five times. Once we get an answer to our first “why”, we ask why to that answer until we get to five “whys”.

Using the “five whys” is part of the “Analyze” phase of Six Sigma but can be used with or without the full Six Sigma process.

Review this simple Wikipedia example of the 5 Whys in action:

The vehicle will not start. (the problem)

Why? - The battery is dead. (First why)

Why? - The alternator is not functioning. (Second why)

Why? - The alternator belt has broken. (Third why)

Why? - The alternator belt was well beyond its useful service life and not replaced. (Fourth why)

Why? - The vehicle was not maintained according to the recommended service schedule. (Fifth why, a root cause)

4. LEAN SIX SIGMA (DMAIC METHOD)

While many people have at least heard of Lean or Six Sigma, do we know what it is? Like many problem-solving processes, it has five main steps to follow.

Define : Clearly laying out the problem and soliciting feedback from those who are customers of the process is necessary to starting off on the right foot.

Measure : Quantifying the current state of the problem is a key to measuring how well the fix performed once it was implemented.

Analyze : Finding out the root cause of the problem (see number 5 “Root Cause Analysis” below) is one of the hardest and least explored steps of Six Sigma.

Improve : Crafting, executing, and testing the solution for measureable improvement is key. What doesn’t get implemented and measured really won’t make a difference.

Control : Sustaining the fix through a monitoring plan will ensure things continue to stay on track rather than being a short-lived solution.

5. ROOT CAUSE ANALYSIS

Compared to other methods, you’ll more often find this technique in a reactive problem-solving mode, but it is helpful nonetheless. Put simply, it requires a persistent approach to finding the highest-level cause, since most reasons you’ll uncover for a problem don’t tell the whole story.

Most of the time, there are many factors that contributed to an issue. The main reason is often shrouded in either intentional or unintentional secrecy. Taking the time to drill down to the root of the issue is key to truly solving the problem.

6. DEMING-SHEWHART CYCLE: PLAN-DO-CHECK-ACT (PDCA)

Named for W. Edwards Deming and Walter A. Shewhart, this model follows a four-step process:

Plan: Establish goals and objectives at the outset to gain agreement. It’s best to start on a small scale in order to test results and get a quick win.

Do: This step is all about the implementation and execution of the solution.

Check: Study and compare actual to expected results. Chart this data to identify trends.

Act/Adjust: If the check phase showed different results, then adjust accordingly. If worse than expected, then try another fix. If the same or better than expected, then use that as the new baseline for future improvements.

7. 8D PROBLEM-SOLVING

While this is named “8D” for eight disciplines, there are actually nine , because the first is listed as step zero. Each of the disciplines represents a phase of this process. Its aim is to implement a quick fix in the short term while working on a more permanent solution with no recurring issues.

Prepare and Plan : Collecting initial information from the team and preparing your approach to the process is a necessary first step.

Form a Team : Select a cross-functional team of people, one leader to run meetings and the process, and one champion/sponsor who will be the final decision-maker.

Describe the Problem : Using inductive and deductive reasoning approaches, lay out the precise issue to be corrected.

Interim Containment Action : Determine if an interim solution needs to be implemented or if it can wait until the final fix is firmed up. If necessary, the interim action is usually removed once the permanent solution is ready for implementation.

Root Cause Analysis and Escape Point : Finding the root of the issue and where in the process it could’ve been found but was not will help identify where and why the issue happened.

Permanent Corrective Action : Incorporating key criteria into the solution, including requirements and wants, will help ensure buy-in from the team and your champion.

Implement and Validate the Permanent Corrective Action : Measuring results from the fix implemented validates it or sends the team back to the drawing board to identity a more robust solution.

Prevent Recurrence : Updating work procedure documents and regular communication about the changes are important to keep old habits in check.

Closure and Team Celebration : Taking time to praise the team for their efforts in resolving the problem acknowledges the part each person played and offers a way to move forward.

8. ARMY PROBLEM SOLVING PROCESS

The US Army has been solving problems for more than a couple of centuries , so why not take a look at the problem-solving process they’ve refined over many years? They recommend this five step process:

Identify the Problem : Take time to understand the situation and define a scope and limitations before moving forward.

Gather Information : Uncover facts, assumptions, and opinions about the problem, and challenge them to get to the truth.

Develop Screening and Evaluation Criteria :

Five screening items should be questioned. Is it feasible, acceptable, distinguishable, and complete?

Evaluation criteria should have these 5 elements: short title, definition, unit of measure, benchmark, and formula.

Generate, Analyze, and Compare Possible Solutions : Most fixes are analyzed, but do you compare yours to one another as a final vetting method?

Choose a Solution and Implement : Put the fix into practice and follow up to ensure it is being followed consistently and having the desired effect.

9. HURSON'S PRODUCTIVE THINKING MODEL

Tim Hurson introduced this model in 2007 with his book, Think Better. It consists of the following six actions.

Ask "What is going on?" : Define the impact of the problem and the aim of its solution.

Ask "What is success?" : Spell out the expected outcome, what should not be in fix, values to be considered, and how things will be evaluated.

Ask "What is the question?" : Tailor questions to the problem type. Valuable resources can be wasted asking questions that aren’t truly relevant to the issue.

Generate answers : Prioritize answers that are the most relevant to solutions, without excluding any suggestion to present to the decision-makers.

Forge the solution : Refine the raw list of prioritized fixes, looking for ways to combine them for a more powerful solution or eliminate fixes that don’t fit the evaluation criteria.

Align resources: Identify resources, team, and stakeholders needed to implement and maintain the solution.

STEAL THIS THOROUGH 8-STEP PROBLEM-SOLVING PROCESS

Now that we’ve reviewed a number of problem-solving methods, we’ve compiled the various steps into a straightforward, yet in-depth, s tep-by-step process to use the best of all methods.

1. DIG DEEP: IDENTIFY, DEFINE, AND CLARIFY THE ISSUE

“Elementary, my dear Watson,” you might say.

This is true, but we often forget the fundamentals before trying to solve a problem. So take some time to gain understanding of critical stakeholder’s viewpoints to clarify the problem and cement consensus behind what the issue really is.

Sometimes it feels like you’re on the same page, but minor misunderstandings mean you’re not really in full agreement.. It’s better to take the time to drill down on an issue before you get too far into solving a problem that may not be the exact problem . Which leads us to…

2. DIG DEEPER: ROOT CAUSE ANALYSIS

This part of the process involves identifying these three items :

What happened?

Why did it happen?

What process do we need to employ to significantly reduce the chances of it happening again ?

You’ll usually need to sort through a series of situations to find the primary cause. So be careful not to stop at the first cause you uncover . Dig further into the situation to expose the root of the issue. We don’t want to install a solution that only fixes a surface-level issue and not the root. T here are typically three types of causes :

Physical: Perhaps a part failed due to poor design or manufacturing.

Human error: A person either did something wrong or didn’t do what needed to be done.

Organizational: This one is mostly about a system, process, or policy that contributed to the error .

When searching for the root cause, it is important to ensure people that you aren’t there to assign blame to a person but rather identify the problem so a fix can prevent future issues.

3. PRODUCE A VARIETY OF SOLUTION OPTIONS

So far, you’ve approached the problem as a data scientist, searching for clues to the real issue. Now, it’s important to keep your eyes and ears open, in case you run across a fix suggested by one of those involved in the process failure. Because they are closest to the problem, they will often have an idea of how to fix things. In other cases, they may be too close, and unable to see how the process could change.

The bottom line is to solicit solution ideas from a variety of sources , both close to and far away from the process you’re trying to improve.

You just never know where the top fix might come from!

4. FULLY EVALUATE AND SELECT PLANNED FIX(ES)

Evaluating solutions to a defined problem can be tricky since each one will have cost, political, or other factors associated with it. Running each fix through a filter of cost and impact is a vital step toward identifying a solid solution and hopefully settling on the one with the highest impact and low or acceptable cost.

Categorizing each solution in one of these four categoriescan help teams sift through them:

High Cost/Low Impact: Implement these last, if at all, since t hey are expensive and won’t move the needle much .

Low Cost/Low Impact: These are cheap, but you won’t get much impact.

High Cost/High Impact: These can be used but should be second to the next category.

Low Cost/High Impact: Getting a solid “bang for your buck” is what these fixes are all about. Start with these first .

5. DOCUMENT THE FINAL SOLUTION AND WHAT SUCCESS LOOKS LIKE

Formalize a document that all interested parties (front-line staff, supervisors, leadership, etc.) agree to follow. This will go a long way towards making sure everyone fully understands what the new process looks like, as well as what success will look like .

While it might seem tedious, try to be overly descriptive in the explanation of the solution and how success will be achieved. This is usually necessary to gain full buy-in and commitment to continually following the solution. We often assume certain things that others may not know unless we are more explicit with our communications.

6. SUCCESSFULLY SELL AND EXECUTE THE FIX

Arriving at this stage in the process only to forget to consistently apply the solution would be a waste of time, yet many organizations fall down in the execution phase . Part of making sure that doesn’t happen is to communicate the fix and ask for questions multiple times until all parties have a solid grasp on what is now required of them.

One often-overlooked element of this is the politics involved in gaining approval for your solution. Knowing and anticipating objections of those in senior or key leadership positions is central to gaining buy-in before fix implementation.

7. RINSE AND REPEAT: EVALUATE, MONITOR, AND FOLLOW UP

Next, doing check-ins with the new process will ensure that the solution is working (or identity if further reforms are necessary) . You’ll also see if the measure of predefined success has been attained (or is making progress in that regard).

Without regularly monitoring the fix, you can only gauge the success or failure of the solution by speculation and hearsay. And without hard data to review, most people will tell their own version of the story.

8. COLLABORATIVE CONTINGENCIES, ITERATION, AND COURSE CORRECTION

Going into any problem-solving process, we should take note that we will not be done once the solution is implemented (or even if it seems to be working better at the moment). Any part of any process will always be subject to the need for future iterations and course corrections . To think otherwise would be either foolish or naive.

There might need to be slight, moderate, or wholesale changes to the solution previously implemented as new information is gained, new technologies are discovered, etc.

14 FRUITFUL RESOURCES AND EXERCISES FOR YOUR PROBLEM-SOLVING JOURNEY

Want to test your problem-solving skills?

Take a look at these twenty case study scenario exercises to see how well you can come up with solutions to these problems.

Still have a desire to discover more about solving problems?

Check out these 14 articles and books...

1. THE LEAN SIX SIGMA POCKET TOOLBOOK: A QUICK REFERENCE GUIDE TO NEARLY 100 TOOLS FOR IMPROVING QUALITY AND SPEED

This book is like a Bible for Lean Six Sigma , all in a pocket-sized package.

2. SOME SAGE PROBLEM SOLVING ADVICE

The American Society for Quality has a short article on how it’s important to focus on the problem before searching for a solution.

3. THE SECRET TO BETTER PROBLEM SOLVING: HARVARD BUSINESS REVIEW

Wondering if you are solving the right problems? Check out this Harvard Business Review article.

4. PROBLEM SOLVING 101 : A SIMPLE BOOK FOR SMART PEOPLE

Looking for a fun and easy problem-solving book that was written by a McKinsey consultant? Take a look!

5. THE BASICS OF CREATIVE PROBLEM SOLVING – CPS

If you want a deeper dive into the seven steps of Creative Problem Solving , see this article.

6. APPRECIATIVE INQUIRY : A POSITIVE REVOLUTION IN CHANGE

Appreciative Inquiry has been proven effective in organizations ranging from Roadway Express and British Airways to the United Nations and the United States Navy. Review this book to join the positive revolution.

7. PROBLEM SOLVING: NINE CASE STUDIES AND LESSONS LEARNED

The Seattle Police Department has put together nine case studies that you can practice solving . While they are about police work, they have practical application in the sleuthing of work-related problems.

8. ROOT CAUSE ANALYSIS : THE CORE OF PROBLEM SOLVING AND CORRECTIVE ACTION

Need a resource to delve further into Root Cause Analysis? Look no further than this book for answers to your most vexing questions .

9. SOLVING BUSINESS PROBLEMS : THE CASE OF POOR FRANK

This solid case study illustrates the complexities of solving problems in business.

10. THE 8-DISCIPLINES PROBLEM SOLVING METHODOLOGY

Learn all about the “8Ds” with this concise primer.

11. THE PROBLEM-SOLVING PROCESS THAT PREVENTS GROUPTHINK HBR

Need to reduce groupthink in your organization’s problem-solving process ? Check out this article from the Harvard Business Review.

12. THINK BETTER : AN INNOVATOR'S GUIDE TO PRODUCTIVE THINKING

Tim Hurson details his own Productive Thinking Model at great length in this book from the author.

13. 5 STEPS TO SOLVING THE PROBLEMS WITH YOUR PROBLEM SOLVING INC MAGAZINE

This simple five-step process will help you break down the problem, analyze it, prioritize solutions, and sell them internally.

14. CRITICAL THINKING : A BEGINNER'S GUIDE TO CRITICAL THINKING, BETTER DECISION MAKING, AND PROBLEM SOLVING!

LOOKING FOR ASSISTANCE WITH YOUR PROBLEM-SOLVING PROCESS?

There's a lot to take in here, but following some of these methods are sure to improve your problem-solving process. However, if you really want to take problem-solving to the next level, InitiativeOne can come alongside your team to help you solve problems much faster than you ever have before.

There are several parts to this leadership transformation process provided by InitiativeOne, including a personal profile assessment, cognitive learning, group sessions with real-world challenges, personal discovery, and a toolkit to empower leaders to perform at their best.

There are really only two things stopping good teams from being great. One is how they make decisions and two is how they solve problems. Contact us today to grow your team’s leadership performance by making decisions and solving problems more swiftly than ever before!

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Problem-Solving Strategies and Obstacles

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• Application
• Improvement

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

What Is Problem-Solving?

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

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

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

The problem-solving process involves:

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

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

Problem-Solving Mental Processes

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

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

Problem-Solving Strategies

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

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

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

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

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

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

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

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

Trial and Error

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

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

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

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

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

How to Apply Problem-Solving Strategies in Real Life

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

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

Obstacles to Problem-Solving

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

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

How to Improve Your Problem-Solving Skills

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

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

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

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

Dunbar K. Problem solving . A Companion to Cognitive Science . 2017. doi:10.1002/9781405164535.ch20

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

Rosenbusch H, Soldner F, Evans AM, Zeelenberg M. Supervised machine learning methods in psychology: A practical introduction with annotated R code . Soc Personal Psychol Compass . 2021;15(2):e12579. doi:10.1111/spc3.12579

Mishra S. Decision-making under risk: Integrating perspectives from biology, economics, and psychology . Personal Soc Psychol Rev . 2014;18(3):280-307. doi:10.1177/1088868314530517

Csikszentmihalyi M, Sawyer K. Creative insight: The social dimension of a solitary moment . In: The Systems Model of Creativity . 2015:73-98. doi:10.1007/978-94-017-9085-7_7

Chrysikou EG, Motyka K, Nigro C, Yang SI, Thompson-Schill SL. Functional fixedness in creative thinking tasks depends on stimulus modality .  Psychol Aesthet Creat Arts . 2016;10(4):425‐435. doi:10.1037/aca0000050

Huang F, Tang S, Hu Z. Unconditional perseveration of the short-term mental set in chunk decomposition .  Front Psychol . 2018;9:2568. doi:10.3389/fpsyg.2018.02568

National Alliance on Mental Illness. Warning signs and symptoms .

Mayer RE. Thinking, problem solving, cognition, 2nd ed .

Schooler JW, Ohlsson S, Brooks K. Thoughts beyond words: When language overshadows insight. J Experiment Psychol: General . 1993;122:166-183. doi:10.1037/0096-3445.2.166

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

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• The Three Stages of the Problem-Solving Cycle

Essentially every problem-solving heuristic in mathematics goes back to George Polya’s How to Solve It ; my approach is no exception. However, this cyclic description might help to keep the process cognitively present.

A few months ago, I produced a video describing this the three stages of the problem-solving cycle: Understand, Strategize, and Implement. That is, we must first understand the problem, then we think of strategies that might help solve the problem, and finally we implement those strategies and see where they lead us. During two decades of observing myself and others in the teaching and learning process, I’ve noticed that the most neglected phase is often the first one—understanding the problem.

The Three Stages Explained

• What am I looking for?
• What is the unknown?
• Do I understand every word and concept in the problem?
• Am I familiar with the units in which measurements are given?
• Is there information that seems missing?
• Is there information that seems superfluous?
• Is the source of information bona fide? (Think about those instances when a friend gives you a puzzle to solve and you suspect there’s something wrong with the way the puzzle is posed.)
• Logical reasoning
• Pattern recognition
• Working backwards
• Adopting a different point of view
• Considering extreme cases
• Solving a simpler analogous problem
• Organizing data
• Making a visual representation
• Accounting for all possibilities
• Intelligent guessing and testing

I have produced videos explaining each one of these strategies individually using problems we have solved at the Chapel Hill Math Circle.

• Implementing : We now implement our strategy or set of strategies. As we progress, we check our reasoning and computations (if any). Many novice problem-solvers make the mistake of “doing something” before understanding (or at least thinking they understand) the problem. For instance, if you ask them “What are you looking for?”, they might not be able to answer. Certainly, it is possible to have an incorrect understanding of the problem, but that is different from not even realizing that we have to understand the problem before we attempt to solve it!

As we implement our strategies, we might not be able to solve the problem, but we might refine our understanding of the problem. As we refine our understanding of the problem, we can refine our strategy. As we refine our strategy and implement a new approach, we get closer to solving the problem, and so on. Of course, even after several iterations of this cycle spanning across hours, days, or even years, one may still not be able to solve a particular problem. That’s part of the enchanting beauty of mathematics.

I invite you to observe your own thinking—and that of your students—as you move along the problem-solving cycle!

[1] Problem-Solving Strategies in Mathematics , Posamentier and Krulik, 2015.

About the author: You may contact Hector Rosario at [email protected].

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7 Steps To Problem-Solving

The 7 steps to problem-solving is a disciplined and methodical approach to identifying and then addressing the root cause of problems. Instead, a more robust approach involves working through a problem using the hypothesis-driven framework of the scientific method. Each viable hypothesis is tested using a range of specific diagnostics and then recommendations are made.

Table of Contents

Understanding the 7 steps to problem-solving

The core argument of this approach is that the most obvious solutions to a problem are often not the best solutions. 

Good problem-solving in business is a skill that must be learned. Businesses that are adept at problem-solving take responsibility for their own decisions and have courage and confidence in their convictions. Ultimately, this removes doubt which can impede the growth of businesses and indeed employees alike.

Moving through the 7 steps to problem-solving

Although many versions of the 7-step approach exist, the McKinsey approach is the most widely used in business settings. Here is how decision makers can move through each of the steps systematically.

Step 1 – Define the problem

First, the scope and extent of the problem must be identified. Actions and behaviors of individuals must be the focus – instead of a focus on the individuals themselves. Whatever the case, the problem must be clearly defined and be universally accepted by all relevant parties.

Step 2 – Disaggregate the problem

In the second step, break down the problem (challenge) into smaller parts using logic trees and develop an early hypothesis. Here, economic and scientific principles can be useful in brainstorming potential solutions. Avoid cognitive biases, such as deciding that a previous solution should be used again because it worked last time.

Step 3 – Prioritize issues

Which constituent parts could be key driving factors of the problem? Prioritize each according to those which have the biggest impact on the problem. Eliminate parts that have negligible impact. This step helps businesses use their resources wisely.

Step 4 – Plan the analyses

Before testing each hypothesis, develop a work and process plan for each. Staff should be assigned to analytical tasks with unique output and completion dates. Hypothesis testing should also be reviewed at regular intervals to measure viability and adjust strategies accordingly.

Step 5 – Conduct the analyses

In step five, gather the critical data required to accept or reject each hypothesis. Data analysis methods will vary according to the nature of the project, but each business must understand the reasons for implementing specific methods. In question-based problem solving, the Five Whys or Fishbone method may be used. More complicated problems may require the use of statistical analysis . In any case, this is often the longest and most complex step of the process. 

Step 6 – Synthesise the results

Once the results have been determined, they must be synthesized in such a way that they can be tested for validity and logic. In a business context, assess the implications of the findings for a business moving forward. Does it solve the problem? 

Step 7 – Communicate

In the final step, the business must present the solutions in such a way that they link back to the original problem statement. When presenting to clients, this is vital. It shows that the business understands the problem and has a solution supported by facts or hard data. Above all, the data should be woven into a convincing story that ends with recommendations for future action.

Key takeaways

• 7 steps to problem-solving is a methodical approach to problem-solving based on the scientific method.
• Although a somewhat rigorous approach, the strategy can be learned by any business willing to devote the time and resources.
• Fundamentally, the 7 steps to problem-solving method involves formulating and then testing hypotheses. Through the process of elimination, a business can narrow its focus to the likely root cause of a problem.

Key Highlights

• Definition : The 7 Steps to Problem-Solving is a structured methodology rooted in the scientific method. It emphasizes systematic hypothesis testing and data analysis to identify and address the root cause of problems, avoiding surface-level solutions.
• Problem-Solving Skill : Effective problem-solving is a learned skill that fosters responsible decision-making, boosts confidence, and supports business growth .
• Define the Problem : Clearly outline the problem’s scope and impact, focusing on actions and behaviors rather than individuals.
• Disaggregate the Problem : Break down the problem into smaller parts using logic trees and form early hypotheses. Avoid biases from past solutions.
• Prioritize Issues : Identify key driving factors of the problem and prioritize them by impact. Eliminate parts with minimal impact to allocate resources efficiently.
• Plan the Analyses : Develop work and process plans for hypothesis testing, assigning staff and setting completion dates. Regularly review and adjust strategies.
• Conduct the Analyses : Gather critical data to accept or reject hypotheses. Use methods like Five Whys, Fishbone diagrams, or statistical analysis .
• Synthesize the Results : Combine and analyze results to determine their validity and implications for the business . Assess if the problem is solved.
• Communicate : Present solutions that link back to the original problem statement, supported by facts. Create a compelling story ending with recommendations.
• The 7 Steps to Problem-Solving is based on the scientific method.
• It requires a structured approach to formulating and testing hypotheses.
• Businesses willing to invest time and resources can learn and apply this method effectively.

Connected Decision-Making Frameworks

Cynefin Framework

SWOT Analysis

Personal SWOT Analysis

Pareto Analysis

Failure Mode And Effects Analysis

Blindspot Analysis

Comparable Company Analysis

Cost-Benefit Analysis

Agile Business Analysis

SOAR Analysis

STEEPLE Analysis

Pestel Analysis

DESTEP Analysis

Paired Comparison Analysis

Related Strategy Concepts:  Go-To-Market Strategy ,  Marketing Strategy ,  Business Models ,  Tech Business Models ,  Jobs-To-Be Done ,  Design Thinking ,  Lean Startup Canvas ,  Value Chain ,  Value Proposition Canvas ,  Balanced Scorecard ,  Business Model Canvas ,  SWOT Analysis ,  Growth Hacking ,  Bundling ,  Unbundling ,  Bootstrapping ,  Venture Capital ,  Porter’s Five Forces ,  Porter’s Generic Strategies ,  Porter’s Five Forces ,  PESTEL Analysis ,  SWOT ,  Porter’s Diamond Model ,  Ansoff ,  Technology Adoption Curve ,  TOWS ,  SOAR ,  Balanced

Read Next:  Mental Models ,  Biases ,  Bounded Rationality ,  Mandela Effect ,  Dunning-Kruger Effect ,  Lindy Effect ,  Crowding Out Effect ,  Bandwagon Effect ,  Decision-Making Matrix .

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Psychology Spot

All About Psychology

The 5 phases of problem solving

Problem solving is a complex psychological process through which we try to find the best way to overcome an obstacle or face a challenge. Unfortunately, this process is not always linear, but can follow tortuous paths, plunging us into a situation of psychological anguish when we believe that there is no possible solution.

On the other hand, knowing the phases of problem solving will save us a lot of headaches. Providing a coherent structure to the situation that concerns us, and having a common thread that guides us along the way, will help us to put some order in the mental chaos that problems usually generate.

To Solve a Problem, Experience Does not Always Work in Our Favor

Experience can be a plus or, on the contrary, become an impediment to solving problems. Psychologists from the universities of Hong Kong and Princeton examined how we implement problem-solving strategies by asking a group of people to solve a series of problems with matches.

Participants were presented with a series of linked squares. Each square in the matrix was made up of separate pieces, and people had to remove a certain number of matches while keeping a specified number of squares intact. The interesting thing about these types of problems is that they generally have more than one solution, different strategies can be used and these must change according to the configuration of the matrix, just as it usually happens with life problems.

These researchers found that participants went through two major stages in problem solving. At first they let themselves be carried away by the perceptual characteristics of the problem and began to explore different strategies, some successful and others not.

In a second moment they used the accumulated experience to narrow their options of strategies, focusing on those that were more successful. The problem is that the more the participants trusted their strategic knowledge, the more difficulties they had in solving problems that demanded the application of novel strategies. In practice, they suffered from a kind of functional fixation.

These series of experiments show us that to solve a problem we must keep an open mind because along the way circumstances are likely to change and we need the mental flexibility necessary to change our problem-solving strategies.

The Stages of Problem Solving We Can All Apply

1. Identify the problem

It may seem like a truism, but the truth is that identifying the real problem is not as easy as it seems, especially when it comes to a situation that affects us emotionally. In fact, when the problem is too scary or we sense that we do not have the psychological tools to solve it, we usually put into practice defense mechanisms such as displacement that allow us to erase the problematic situation from our conscious mind.

Instead, being able to identify the problem is the first step in finding a solution. Many times that means stopping looking outside for the culprits and searching within, wondering why a situation is particularly bothering or hindering us.

2. Understand the problem

Many times the problem brings with it the seed of the solution. So one of the steps in solving a problem is making sure we understand it. It is not enough to identify the problem, we need to define it. For this we need to analyze it from different perspectives.

For example, if we are trying to carry out a professional project that does not finish taking off, we have to clarify the reasons. Do we need more training? Are we in an overly competitive sector? Do we have enough resources? We need to understand the source of the problem.

Organizing the information available is another crucial step in the problem-solving process. We have to ask ourselves both, what we know about the problem and everything we do not know. Ultimately, the accuracy of the solution will largely depend on the amount of information available.

3. Assume a psychological distance

Most of the major problems in life have the potential to generate an emotional tsunami. However, many times that affective involvement obfuscates and prevents us from thinking clearly. That is why on many occasions one of the most important but least known phases for solving problems consists of moving away from what concerns us. To assume a psychological distance , we can take a few days away from the problematic environment or try to stop thinking about what worries us for a while.

During that time the unconscious mind will continue to work and is likely to generate creative and perfectly valid insights that lead to the solution of the problem. That distance to allow us to overcome the functional fixations that prevent us from thinking outside the box, giving way to a mental restructuring that will allow us to see the problem from another perspective.

4. Find solutions and develop strategies

Each problem is different, so it will require a specific solution. A solution cannot always be reached by insight, so it will be necessary to think of possible alternatives to solve the problem. Synectics , for example, is a problem-solving method that uses creativity to find original solutions.

The next step is to develop a strategy, since solutions that do not materialize in concrete steps are very difficult to implement. Therefore, we must ask ourselves how we are going to implement our solution. In this phase of problem solving it is important to be honest with ourselves and “land” that strategy taking into account our resources and real availability. It is useless to develop a great strategy if we cannot apply it later.

5. Evaluation of progress

Very few problems are solved overnight. These are generally complex situations that we must patiently “unwind” over time. Therefore, another of the phases to solve a problem consists of monitoring the results that we are achieving. This way we make sure that we are on the right track and we are not wasting energy and time uselessly.

In this last stage of problem solving it is important to be able to adapt our expectations. It is difficult for a professional project to take off in the blink of an eye, so we must focus on the small steps that indicate that the solution is paying off. To do this, it is important to sit down and reflect on the impact of the solution from time to time.

We must also bear in mind that circumstances often change, so we may need to make adjustments to our initial solution. This requires great mental flexibility to change course when we realize that the strategy is not as effective as we would like.

Fedor, A. et. Al. (2015) Problem solving stages in the five square problem.  Front. Psychol ; 6: 1050.

Louis Lee, N. Y. & Johnson-Laird, P. N. (2013) Strategic changes in problem solving.  Journal of Cognitive Psychology ; 25: 165–173. 

Gillen, G. (2009) Managing Executive Function Impairments to Optimize Function.  Cognitive and Perceptual Rehabilitation ; 245-283.

Jennifer Delgado

I am a psychologist and I spent several years writing articles for scientific journals specialized in Health and Psychology. I want to help you create great experiences. Learn more about me .

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What Is Problem Solving?

You will often see beach clean-up drives being publicized in coastal cities. There are already dustbins available on the beaches,…

You will often see beach clean-up drives being publicized in coastal cities. There are already dustbins available on the beaches, so why do people need to organize these drives? It’s evident that despite advertising and posting anti-littering messages, some of us don’t follow the rules.

Temporary food stalls and shops make it even more difficult to keep the beaches clean. Since people can’t ask the shopkeepers to relocate or prevent every single person from littering, the clean-up drive is needed.  This is an ideal example of problem-solving psychology in humans. ( 230-fifth.com ) So, what is problem-solving? Let’s find out.

What Is Problem-Solving?

At its simplest, the meaning of problem-solving is the process of defining a problem, determining its cause, and implementing a solution. The definition of problem-solving is rooted in the fact that as humans, we exert control over our environment through solutions. We move forward in life when we solve problems and make decisions. 

We can better define the problem-solving process through a series of important steps.

Identify The Problem: 

This step isn’t as simple as it sounds. Most times, we mistakenly identify the consequences of a problem rather than the problem itself. It’s important that we’re careful to identify the actual problem and not just its symptoms. 

Define The Problem: 

Once the problem has been identified correctly, you should define it. This step can help clarify what needs to be addressed and for what purpose.

Form A Strategy: 

Develop a strategy to solve your problem. Defining an approach will provide direction and clarity on the next steps. 

Organize The Information:  

Organizing information systematically will help you determine whether something is missing. The more information you have, the easier it’ll become for you to arrive at a solution.  

Allocate Resources:  

We may not always be armed with the necessary resources to solve a problem. Before you commit to implementing a solution for a problem, you should determine the availability of different resources—money, time and other costs.

Track Progress: 

The true meaning of problem-solving is to work towards an objective. If you measure your progress, you can evaluate whether you’re on track. You could revise your strategies if you don’t notice the desired level of progress. 

Evaluate The Results:  

After you spot a solution, evaluate the results to determine whether it’s the best possible solution. For example, you can evaluate the success of a fitness routine after several weeks of exercise.

Meaning Of Problem-Solving Skill

Now that we’ve established the definition of problem-solving psychology in humans, let’s look at how we utilize our problem-solving skills.  These skills help you determine the source of a problem and how to effectively determine the solution. Problem-solving skills aren’t innate and can be mastered over time. Here are some important skills that are beneficial for finding solutions.

Communication

Communication is a critical skill when you have to work in teams.  If you and your colleagues have to work on a project together, you’ll have to collaborate with each other. In case of differences of opinion, you should be able to listen attentively and respond respectfully in order to successfully arrive at a solution.

As a problem-solver, you need to be able to research and identify underlying causes. You should never treat a problem lightly. In-depth study is imperative because often people identify only the symptoms and not the actual problem.

Once you have researched and identified the factors causing a problem, start working towards developing solutions. Your analytical skills can help you differentiate between effective and ineffective solutions.

Decision-Making

You’ll have to make a decision after you’ve identified the source and methods of solving a problem. If you’ve done your research and applied your analytical skills effectively, it’ll become easier for you to take a call or a decision.

Organizations really value decisive problem-solvers. Harappa Education’s   Defining Problems course will guide you on the path to developing a problem-solving mindset. Learn how to identify the different types of problems using the Types of Problems framework. Additionally, the SMART framework, which is a five-point tool, will teach you to create specific and actionable objectives to address problem statements and arrive at solutions. 

Explore topics & skills such as Problem Solving Skills , PICK Chart , How to Solve Problems & Barriers to Problem Solving from our Harappa Diaries blog section and develop your skills.

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CBSE Class 11 | Problem Solving Methodologies

Problem solving process.

The process of problem-solving is an activity which has its ingredients as the specification of the program and the served dish is a correct program. This activity comprises of four steps : 1. Understanding the problem: To solve any problem it is very crucial to understand the problem first. What is the desired output of the code and how that output can be generated? The obvious and essential need to generate the output is an input. The input may be singular or it may be a set of inputs. A proper relationship between the input and output must be drawn in order to solve the problem efficiently. The input set should be complete and sufficient enough to draw the output. It means all the necessary inputs required to compute the output should be present at the time of computation. However, it should be kept in mind that the programmer should ensure that the minimum number of inputs should be there. Any irrelevant input only increases the size of and memory overhead of the program. Thus Identifying the minimum number of inputs required for output is a crucial element for understanding the problem.

2. Devising the plan: Once a problem has been understood, a proper action plan has to be devised to solve it. This is called devising the plan. This step usually involves computing the result from the given set of inputs. It uses the relationship drawn between inputs and outputs in the previous step. The complexity of this step depends upon the complexity of the problem at hand.

3. Executing the plan: Once the plan has been defined, it should follow the trajectory of action while ensuring the plan’s integrity at various checkpoints. If any inconsistency is found in between, the plan needs to be revised.

4. Evaluation: The final result so obtained must be evaluated and verified to see if the problem has been solved satisfactorily.

Problem Solving Methodology(The solution for the problem)

The methodology to solve a problem is defined as the most efficient solution to the problem. Although, there can be multiple ways to crack a nut, but a methodology is one where the nut is cracked in the shortest time and with minimum effort. Clearly, a sledgehammer can never be used to crack a nut. Under problem-solving methodology, we will see a step by step solution for a problem. These steps closely resemble the software life cycle . A software life cycle involves several stages in a program’s life cycle. These steps can be used by any tyro programmer to solve a problem in the most efficient way ever. The several steps of this cycle are as follows :

Step by step solution for a problem (Software Life Cycle) 1. Problem Definition/Specification: A computer program is basically a machine language solution to a real-life problem. Because programs are generally made to solve the pragmatic problems of the outside world. In order to solve the problem, it is very necessary to define the problem to get its proper understanding. For example, suppose we are asked to write a code for “ Compute the average of three numbers”. In this case, a proper definition of the problem will include questions like : “What exactly does average mean?” “How to calculate the average?”

Once, questions like these are raised, it helps to formulate the solution of the problem in a better way. Once a problem has been defined, the program’s specifications are then listed. Problem specifications describe what the program for the problem must do. It should definitely include :

what is the input set of the program

What is the desired output of the program and in what form the output is desired?

2. Problem Analysis (Breaking down the solution into simple steps): This step of solving the problem follows a modular approach to crack the nut. The problem is divided into subproblems so that designing a solution to these subproblems gets easier. The solutions to all these individual parts are then merged to get the final solution of the original problem. It is like divide and merge approach.

Modular Approach for Programming :

The process of breaking a large problem into subproblems and then treating these individual parts as different functions is called modular programming. Each function behaves independent of another and there is minimal inter-functional communication. There are two methods to implement modular programming :

• Top Down Design : In this method, the original problem is divided into subparts. These subparts are further divided. The chain continues till we get the very fundamental subpart of the problem which can’t be further divided. Then we draw a solution for each of these fundamental parts.
• Bottom Up Design : In this style of programming, an application is written by using the pre-existing primitives of programming language. These primitives are then amalgamated with more complicated features, till the application is written. This style is just the reverse of the top-down design style.

3. Problem Designing: The design of a problem can be represented in either of the two forms :

The ways to execute any program are of three categories:

• Sequence Statements Here, all the instructions are executed in a sequence, that is, one after the another, till the program is executed.
• Selection Statements As it is self-clear from the name, in these type of statements the whole set of instructions is not executed. A selection has to be made. A selected number of instructions are executed based on some condition. If the condition holds true then some part of the instruction set is executed, otherwise, another part of the set is executed. Since this selection out of the instruction set has to be made, thus these type of instructions are called Selection Statements.

Identification of arithmetic and logical operations required for the solution : While writing the algorithm for a problem, the arithmetic and logical operations required for the solution are also usually identified. They help to write the code in an easier manner because the proper ordering of the arithmetic and logical symbols is necessary to determine the correct output. And when all this has been done in the algorithm writing step, it just makes the coding task a smoother one.

• Flow Chart : Flow charts are diagrammatic representation of the algorithm. It uses some symbols to illustrate the starting and ending of a program along with the flow of instructions involved in the program.

4. Coding: Once an algorithm is formed, it can’t be executed on the computer. Thus in this step, this algorithm has to be translated into the syntax of a particular programming language. This process is often termed as ‘coding’. Coding is one of the most important steps of the software life cycle. It is not only challenging to find a solution to a problem but to write optimized code for a solution is far more challenging.

Writing code for optimizing execution time and memory storage : A programmer writes code on his local computer. Now, suppose he writes a code which takes 5 hours to get executed. Now, this 5 hours of time is actually the idle time for the programmer. Not only it takes longer time, but it also uses the resources during that time. One of the most precious computing resources is memory. A large program is expected to utilize more memory. However, memory utilization is not a fault, but if a program is utilizing unnecessary time or memory, then it is a fault of coding. The optimized code can save both time and memory. For example, as has been discussed earlier, by using the minimum number of inputs to compute the output , one can save unnecessary memory utilization. All such techniques are very necessary to be deployed to write optimized code. The pragmatic world gives reverence not only to the solution of the problem but to the optimized solution. This art of writing the optimized code also called ‘competitive programming’.

5. Program Testing and Debugging: Program testing involves running each and every instruction of the code and check the validity of the output by a sample input. By testing a program one can also check if there’s an error in the program. If an error is detected, then program debugging is done. It is a process to locate the instruction which is causing an error in the program and then rectifying it. There are different types of error in a program : (i) Syntax Error Every programming language has its own set of rules and constructs which need to be followed to form a valid program in that particular language. If at any place in the entire code, this set of rule is violated, it results in a syntax error. Take an example in C Language

In the above program, the syntax error is in the first printf statement since the printf statement doesn’t end with a ‘;’. Now, until and unless this error is not rectified, the program will not get executed.

Once the error is rectified, one gets the desired output. Suppose the input is ‘good’ then the output is : Output:

(ii) Logical Error An error caused due to the implementation of a wrong logic in the program is called logical error. They are usually detected during the runtime. Take an example in C Language:

In the above code, the ‘for’ loop won’t get executed since n has been initialized with the value of 11 while ‘for’ loop can only print values smaller than or equal to 10. Such a code will result in incorrect output and thus errors like these are called logical errors. Once the error is rectified, one gets the desired output. Suppose n is initialised with the value ‘5’ then the output is : Output:

(iii) Runtime Error Any error which causes the unusual termination of the program is called runtime error. They are detected at the run time. Some common examples of runtime errors are : Example 1 :

If during the runtime, the user gives the input value for B as 0 then the program terminates abruptly resulting in a runtime error. The output thus appears is : Output:

Example 2 : If while executing a program, one attempts for opening an unexisting file, that is, a file which is not present in the hard disk, it also results in a runtime error.

6. Documentation : The program documentation involves :

• Problem Definition
• Problem Design
• Documentation of test perform
• History of program development

7. Program Maintenance: Once a program has been formed, to ensure its longevity, maintenance is a must. The maintenance of a program has its own costs associated with it, which may also exceed the development cost of the program in some cases. The maintenance of a program involves the following :

• Detection and Elimination of undetected errors in the existing program.
• Modification of current program to enhance its performance and adaptability.
• Enhancement of user interface
• Enriching the program with new capabilities.
• Updation of the documentation.

Control Structure- Conditional control and looping (finite and infinite)

There are codes which usually involve looping statements. Looping statements are statements in which instruction or a set of instructions is executed multiple times until a particular condition is satisfied. The while loop, for loop, do while loop, etc. form the basis of such looping structure. These statements are also called control structure because they determine or control the flow of instructions in a program. These looping structures are of two kinds :

In the above program, the ‘for’ loop gets executed only until the value of i is less than or equal to 10. As soon as the value of i becomes greater than 10, the while loop is terminated. Output:

In the above code, one can easily see that the value of n is not getting incremented. In such a case, the value of n will always remain 1 and hence the while loop will never get executed. Such loop is called an infinite loop. Output:

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