when is problem solving used in everyday life

10 Everyday uses for Problem Solving Skills

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Many employers are recognizing the value and placing significant investments in developing the problem solving skills of their employees.  While we often think about these skills in the work context, problem solving isn’t just helpful in the workplace.  Here are 10 everyday uses for problem solving skills that can you may not have thought about

1. Stuck in traffic and late for work, again

With busy schedules and competing demands for your time, getting where you need to be on time can be a real challenge.  When traffic backs up, problem solving skills can help you figure out alternatives to avoid congestion, resolve the immediate situation and develop a solution to avoid encountering the situation in the future.

2. What is that stain on the living room carpet?

Parents, pet owners and spouses face this situation all the time.  The living room carpet was clean yesterday but somehow a mysterious stain has appeared and nobody is claiming it.  In order to clean it effectively, first you need to figure out what it is.  Problem solving can help you track down the culprit, diagnose the cause of the stain and develop an action plan to get your home clean and fresh again.

3. What is that smell coming from my garden shed?

Drawing from past experiences, the seasoned problem solver in you suspects that the source of the peculiar odor likely lurks somewhere within the depths of the shed. Your challenge now lies in uncovering the origin of this scent, managing its effects, and formulating a practical plan to prevent such occurrences in the future.

4. I don’t think the car is supposed to make that thumping noise

As with many problems in the workplace, this may be a situation to bring in problem solving experts in the form of your trusted mechanic.  If that isn’t an option, problem solving skills can be helpful to diagnose and assess the impact of the situation to ensure you can get where you need to be.

5. Creating a budget

Tap into your problem-solving prowess as you embark on the journey of budgeting. Begin by determining what expenses to include in your budget, and strategize how to account for unexpected financial surprises. The challenge lies in crafting a comprehensive budget that not only covers your known expenses but also prepares you for the uncertainties that may arise.

6. My daughter has a science project – due tomorrow

Sometimes the challenge isn’t impact, its urgency.  Problem solving skills can help you quickly assess the situation and develop an action plan to get that science project done and turned in on time.

7. What should I get my spouse for his/her birthday?

As with many problems, this one may not have a “right answer” or apparent solution.  Its time to apply those problem solving skills to evaluate the effects of past decisions combined with current environmental signals and available resources to select the perfect gift to put a smile on your significant other’s face.

8. The office printer suddenly stopped working, and there are important documents that need to be printed urgently.

Uh oh, time to think quickly.  There is an urgent situation that must be addressed to get things back to normal, a cause to be identified (what’s causing the printer issue), and an action plan to resolve it.  Problem solving skills can help you avoid stress and ensure that your documents are printed on time.

9. I’m torn between two cars! Which one should I choose?

In a world brimming with countless choices, employ decision analysis as your trusty tool to navigate the sea of options. Whether you’re selecting a car (or any other product), the challenge is to methodically identify and evaluate the best choices that align with your unique needs and preferences.

10. What’s for dinner?

Whether you are planning to eat alone, with family or entertaining friends and colleagues, meal planning can be a cause of daily stress.  Applying problem solving skills can put the dinner dilemma into perspective and help get the food on the table and keep everyone happy.

Problem Solving skills aren’t just for the workplace – they can be applied in your everyday life.  Kepner-Tregoe can help you and your team develop your problem solving skills through a combination of training and consulting with our problem solving experts.

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50 Problem-Solving and Critical Thinking Examples

Critical thinking and problem solving are essential skills for success in the 21st century. Critical thinking is the ability to analyze information, evaluate evidence, and draw logical conclusions. Problem solving is the ability to apply critical thinking to find effective solutions to various challenges. Both skills require creativity, curiosity, and persistence. Developing critical thinking and problem solving skills can help students improve their academic performance, enhance their career prospects, and become more informed and engaged citizens.

Sanju Pradeepa

In today’s complex and fast-paced world, the ability to think critically and solve problems effectively has become a vital skill for success in all areas of life. Whether it’s navigating professional challenges, making sound decisions, or finding innovative solutions, critical thinking and problem-solving are key to overcoming obstacles and achieving desired outcomes. In this blog post, we will explore problem-solving and critical thinking examples.

Table of Contents

Developing the skills needed for critical thinking and problem solving.

It is not enough to simply recognize an issue; we must use the right tools and techniques to address it. To do this, we must learn how to define and identify the problem or task at hand, gather relevant information from reliable sources, analyze and compare data to draw conclusions, make logical connections between different ideas, generate a solution or action plan, and make a recommendation.

The first step in developing these skills is understanding what the problem or task is that needs to be addressed. This requires careful consideration of all available information in order to form an accurate picture of what needs to be done. Once the issue has been identified, gathering reliable sources of data can help further your understanding of it. Sources could include interviews with customers or stakeholders, surveys, industry reports, and analysis of customer feedback.

After collecting relevant information from reliable sources, it’s important to analyze and compare the data in order to draw meaningful conclusions about the situation at hand. This helps us better understand our options for addressing an issue by providing context for decision-making. Once you have analyzed the data you collected, making logical connections between different ideas can help you form a more complete picture of the situation and inform your potential solutions.

Once you have analyzed your options for addressing an issue based on all available data points, it’s time to generate a solution or action plan that takes into account considerations such as cost-effectiveness and feasibility. It’s also important to consider the risk factors associated with any proposed solutions in order to ensure that they are responsible before moving forward with implementation. Finally, once all the analysis has been completed, it is time to make a recommendation based on your findings, which should take into account any objectives set out by stakeholders at the beginning of this process as well as any other pertinent factors discovered throughout the analysis stage.

By following these steps carefully when faced with complex issues, one can effectively use critical thinking and problem-solving skills in order to achieve desired outcomes more efficiently than would otherwise be possible without them, while also taking responsibility for decisions made along the way.

What Does Critical Thinking Involve: 5 Essential Skill

Problem-solving and critical thinking examples.

Problem-solving and critical thinking are key skills that are highly valued in any professional setting. These skills enable individuals to analyze complex situations, make informed decisions, and find innovative solutions. Here, we present 25 examples of problem-solving and critical thinking. problem-solving scenarios to help you cultivate and enhance these skills.

Ethical dilemma: A company faces a situation where a client asks for a product that does not meet quality standards. The team must decide how to address the client’s request without compromising the company’s credibility or values.

Brainstorming session: A team needs to come up with new ideas for a marketing campaign targeting a specific demographic. Through an organized brainstorming session, they explore various approaches and analyze their potential impact.

Troubleshooting technical issues : An IT professional receives a ticket indicating a network outage. They analyze the issue, assess potential causes (hardware, software, or connectivity), and solve the problem efficiently.

Negotiation : During contract negotiations, representatives from two companies must find common ground to strike a mutually beneficial agreement, considering the needs and limitations of both parties.

Project management: A project manager identifies potential risks and develops contingency plans to address unforeseen obstacles, ensuring the project stays on track.

Decision-making under pressure: In a high-stakes situation, a medical professional must make a critical decision regarding a patient’s treatment, weighing all available information and considering potential risks.

Conflict resolution: A team encounters conflicts due to differing opinions or approaches. The team leader facilitates a discussion to reach a consensus while considering everyone’s perspectives.

Data analysis: A data scientist is presented with a large dataset and is tasked with extracting valuable insights. They apply analytical techniques to identify trends, correlations, and patterns that can inform decision-making.

Customer service: A customer service representative encounters a challenging customer complaint and must employ active listening and problem-solving skills to address the issue and provide a satisfactory resolution.

Market research : A business seeks to expand into a new market. They conduct thorough market research, analyzing consumer behavior, competitor strategies, and economic factors to make informed market-entry decisions.

Creative problem-solvin g: An engineer faces a design challenge and must think outside the box to come up with a unique and innovative solution that meets project requirements.

Change management: During a company-wide transition, managers must effectively communicate the change, address employees’ concerns, and facilitate a smooth transition process.

Crisis management: When a company faces a public relations crisis, effective critical thinking is necessary to analyze the situation, develop a response strategy, and minimize potential damage to the company’s reputation.

Cost optimization : A financial analyst identifies areas where expenses can be reduced while maintaining operational efficiency, presenting recommendations for cost savings.

Time management : An employee has multiple deadlines to meet. They assess the priority of each task, develop a plan, and allocate time accordingly to achieve optimal productivity.

Quality control: A production manager detects an increase in product defects and investigates the root causes, implementing corrective actions to enhance product quality.

Strategic planning: An executive team engages in strategic planning to define long-term goals, assess market trends, and identify growth opportunities.

Cross-functional collaboration: Multiple teams with different areas of expertise must collaborate to develop a comprehensive solution, combining their knowledge and skills.

Training and development : A manager identifies skill gaps in their team and designs training programs to enhance critical thinking, problem-solving, and decision-making abilities.

Risk assessment : A risk management professional evaluates potential risks associated with a new business venture, weighing their potential impact and developing strategies to mitigate them.

Continuous improvement: An operations manager analyzes existing processes, identifies inefficiencies, and introduces improvements to enhance productivity and customer satisfaction.

Customer needs analysis: A product development team conducts extensive research to understand customer needs and preferences, ensuring that the resulting product meets those requirements.

Crisis decision-making: A team dealing with a crisis must think quickly, assess the situation, and make timely decisions with limited information.

Marketing campaign analysis : A marketing team evaluates the success of a recent campaign, analyzing key performance indicators to understand its impact on sales and customer engagement.

Constructive feedback: A supervisor provides feedback to an employee, highlighting areas for improvement and offering constructive suggestions for growth.

Conflict resolution in a team project: Team members engaged in a project have conflicting ideas on the approach. They must engage in open dialogue, actively listen to each other’s perspectives, and reach a compromise that aligns with the project’s goals.

Crisis response in a natural disaster: Emergency responders must think critically and swiftly in responding to a natural disaster, coordinating rescue efforts, allocating resources effectively, and prioritizing the needs of affected individuals.

Product innovation : A product development team conducts market research, studies consumer trends, and uses critical thinking to create innovative products that address unmet customer needs.

Supply chain optimization: A logistics manager analyzes the supply chain to identify areas for efficiency improvement, such as reducing transportation costs, improving inventory management, or streamlining order fulfillment processes.

Business strategy formulation: A business executive assesses market dynamics, the competitive landscape, and internal capabilities to develop a robust business strategy that ensures sustainable growth and competitiveness.

Crisis communication: In the face of a public relations crisis, an organization’s spokesperson must think critically to develop and deliver a transparent, authentic, and effective communication strategy to rebuild trust and manage reputation.

Social problem-solving: A group of volunteers addresses a specific social issue, such as poverty or homelessness, by critically examining its root causes, collaborating with stakeholders, and implementing sustainable solutions for the affected population.

Problem-Solving Mindset: How to Achieve It (15 Ways)

Risk assessment in investment decision-making: An investment analyst evaluates various investment opportunities, conducting risk assessments based on market trends, financial indicators, and potential regulatory changes to make informed investment recommendations.

Environmental sustainability: An environmental scientist analyzes the impact of industrial processes on the environment, develops strategies to mitigate risks, and promotes sustainable practices within organizations and communities.

Adaptation to technological advancements : In a rapidly evolving technological landscape, professionals need critical thinking skills to adapt to new tools, software, and systems, ensuring they can effectively leverage these advancements to enhance productivity and efficiency.

Productivity improvement: An operations manager leverages critical thinking to identify productivity bottlenecks within a workflow and implement process improvements to optimize resource utilization, minimize waste, and increase overall efficiency.

Cost-benefit analysis: An organization considering a major investment or expansion opportunity conducts a thorough cost-benefit analysis, weighing potential costs against expected benefits to make an informed decision.

Human resources management : HR professionals utilize critical thinking to assess job applicants, identify skill gaps within the organization, and design training and development programs to enhance the workforce’s capabilities.

Root cause analysis: In response to a recurring problem or inefficiency, professionals apply critical thinking to identify the root cause of the issue, develop remedial actions, and prevent future occurrences.

Leadership development: Aspiring leaders undergo critical thinking exercises to enhance their decision-making abilities, develop strategic thinking skills, and foster a culture of innovation within their teams.

Brand positioning : Marketers conduct comprehensive market research and consumer behavior analysis to strategically position a brand, differentiating it from competitors and appealing to target audiences effectively.

Resource allocation: Non-profit organizations distribute limited resources efficiently, critically evaluating project proposals, considering social impact, and allocating resources to initiatives that align with their mission.

Innovating in a mature market: A company operating in a mature market seeks to innovate to maintain a competitive edge. They cultivate critical thinking skills to identify gaps, anticipate changing customer needs, and develop new strategies, products, or services accordingly.

Analyzing financial statements : Financial analysts critically assess financial statements, analyze key performance indicators, and derive insights to support financial decision-making, such as investment evaluations or budget planning.

Crisis intervention : Mental health professionals employ critical thinking and problem-solving to assess crises faced by individuals or communities, develop intervention plans, and provide support during challenging times.

Data privacy and cybersecurity : IT professionals critically evaluate existing cybersecurity measures, identify vulnerabilities, and develop strategies to protect sensitive data from threats, ensuring compliance with privacy regulations.

Process improvement : Professionals in manufacturing or service industries critically evaluate existing processes, identify inefficiencies, and implement improvements to optimize efficiency, quality, and customer satisfaction.

Multi-channel marketing strategy : Marketers employ critical thinking to design and execute effective marketing campaigns across various channels such as social media, web, print, and television, ensuring a cohesive brand experience for customers.

Peer review: Researchers critically analyze and review the work of their peers, providing constructive feedback and ensuring the accuracy, validity, and reliability of scientific studies.

Project coordination : A project manager must coordinate multiple teams and resources to ensure seamless collaboration, identify potential bottlenecks, and find solutions to keep the project on schedule.  

These examples highlight the various contexts in which problem-solving and critical-thinking skills are necessary for success. By understanding and practicing these skills, individuals can enhance their ability to navigate challenges and make sound decisions in both personal and professional endeavors.

Conclusion:

Critical thinking and problem-solving are indispensable skills that empower individuals to overcome challenges, make sound decisions, and find innovative solutions. By honing these skills, one can navigate through the complexities of modern life and achieve success in both personal and professional endeavors. Embrace the power of critical thinking and problem-solving, and unlock the door to endless possibilities and growth.

• Problem solving From Wikipedia, the free encyclopedia
• Critical thinking From Wikipedia, the free encyclopedia
• The Importance of Critical Thinking and Problem Solving Skills for Students (5 Minutes)

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

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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Problem-Solving Strategies and Obstacles

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

What Is Problem-Solving?

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

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

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

The problem-solving process involves:

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

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

Problem-Solving Mental Processes

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

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

Problem-Solving Strategies

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

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

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

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

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

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

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

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

Trial and Error

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

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

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

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

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

How to Apply Problem-Solving Strategies in Real Life

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

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

Obstacles to Problem-Solving

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

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

How to Improve Your Problem-Solving Skills

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

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

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

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

Introduction to Problem Solving Skills

What is problem solving and why is it important.

The ability to solve problems is a basic life skill and is essential to our day-to-day lives, at home, at school, and at work. We solve problems every day without really thinking about how we solve them. For example: it’s raining and you need to go to the store. What do you do? There are lots of possible solutions. Take your umbrella and walk. If you don't want to get wet, you can drive, or take the bus. You might decide to call a friend for a ride, or you might decide to go to the store another day. There is no right way to solve this problem and different people will solve it differently.

Problem solving is the process of identifying a problem, developing possible solution paths, and taking the appropriate course of action.

Why is problem solving important? Good problem solving skills empower you not only in your personal life but are critical in your professional life. In the current fast-changing global economy, employers often identify everyday problem solving as crucial to the success of their organizations. For employees, problem solving can be used to develop practical and creative solutions, and to show independence and initiative to employers.

Throughout this case study you will be asked to jot down your thoughts in idea logs. These idea logs are used for reflection on concepts and for answering short questions. When you click on the "Next" button, your responses will be saved for that page. If you happen to close the webpage, you will lose your work on the page you were on, but previous pages will be saved. At the end of the case study, click on the "Finish and Export to PDF" button to acknowledge completion of the case study and receive a PDF document of your idea logs.

What Does Problem Solving Look Like?

The ability to solve problems is a skill, and just like any other skill, the more you practice, the better you get. So how exactly do you practice problem solving? Learning about different problem solving strategies and when to use them will give you a good start. Problem solving is a process. Most strategies provide steps that help you identify the problem and choose the best solution. There are two basic types of strategies: algorithmic and heuristic.

Algorithmic strategies are traditional step-by-step guides to solving problems. They are great for solving math problems (in algebra: multiply and divide, then add or subtract) or for helping us remember the correct order of things (a mnemonic such as “Spring Forward, Fall Back” to remember which way the clock changes for daylight saving time, or “Righty Tighty, Lefty Loosey” to remember what direction to turn bolts and screws). Algorithms are best when there is a single path to the correct solution.

But what do you do when there is no single solution for your problem? Heuristic methods are general guides used to identify possible solutions. A popular one that is easy to remember is IDEAL [ Bransford & Stein, 1993 ] :

• I dentify the problem
• D efine the context of the problem
• E xplore possible strategies
• A ct on best solution

IDEAL is just one problem solving strategy. Building a toolbox of problem solving strategies will improve your problem solving skills. With practice, you will be able to recognize and use multiple strategies to solve complex problems.

Watch the video

What is the best way to get a peanut out of a tube that cannot be moved? Watch a chimpanzee solve this problem in the video below [ Geert Stienissen, 2010 ].

[PDF transcript]

Describe the series of steps you think the chimpanzee used to solve this problem.

• [Page 2: What does Problem Solving Look Like?] Describe the series of steps you think the chimpanzee used to solve this problem.

Think of an everyday problem you've encountered recently and describe your steps for solving it.

• [Page 2: What does Problem Solving Look Like?] Think of an everyday problem you've encountered recently and describe your steps for solving it.

Developing Problem Solving Processes

Problem solving is a process that uses steps to solve problems. But what does that really mean? Let's break it down and start building our toolbox of problem solving strategies.

What is the first step of solving any problem? The first step is to recognize that there is a problem and identify the right cause of the problem. This may sound obvious, but similar problems can arise from different events, and the real issue may not always be apparent. To really solve the problem, it's important to find out what started it all. This is called identifying the root cause .

Example: You and your classmates have been working long hours on a project in the school's workshop. The next afternoon, you try to use your student ID card to access the workshop, but discover that your magnetic strip has been demagnetized. Since the card was a couple of years old, you chalk it up to wear and tear and get a new ID card. Later that same week you learn that several of your classmates had the same problem! After a little investigation, you discover that a strong magnet was stored underneath a workbench in the workshop. The magnet was the root cause of the demagnetized student ID cards.

The best way to identify the root cause of the problem is to ask questions and gather information. If you have a vague problem, investigating facts is more productive than guessing a solution. Ask yourself questions about the problem. What do you know about the problem? What do you not know? When was the last time it worked correctly? What has changed since then? Can you diagram the process into separate steps? Where in the process is the problem occurring? Be curious, ask questions, gather facts, and make logical deductions rather than assumptions.

Watch Adam Savage from Mythbusters, describe his problem solving process [ ForaTv, 2010 ]. As you watch this section of the video, try to identify the questions he asks and the different strategies he uses.

Adam Savage shared many of his problem solving processes. List the ones you think are the five most important. Your list may be different from other people in your class—that's ok!

• [Page 3: Developing Problem Solving Processes] Adam Savage shared many of his problem solving processes. List the ones you think are the five most important.

“The ability to ask the right question is more than half the battle of finding the answer.” — Thomas J. Watson , founder of IBM

Voices From the Field: Solving Problems

In manufacturing facilities and machine shops, everyone on the floor is expected to know how to identify problems and find solutions. Today's employers look for the following skills in new employees: to analyze a problem logically, formulate a solution, and effectively communicate with others.

In this video, industry professionals share their own problem solving processes, the problem solving expectations of their employees, and an example of how a problem was solved.

Meet the Partners:

• Taconic High School in Pittsfield, Massachusetts, is a comprehensive, fully accredited high school with special programs in Health Technology, Manufacturing Technology, and Work-Based Learning.
• Berkshire Community College in Pittsfield, Massachusetts, prepares its students with applied manufacturing technical skills, providing hands-on experience at industrial laboratories and manufacturing facilities, and instructing them in current technologies.
• H.C. Starck in Newton, Massachusetts, specializes in processing and manufacturing technology metals, such as tungsten, niobium, and tantalum. In almost 100 years of experience, they hold over 900 patents, and continue to innovate and develop new products.
• Nypro Healthcare in Devens, Massachusetts, specializes in precision injection-molded healthcare products. They are committed to good manufacturing processes including lean manufacturing and process validation.

Making Decisions

Now that you have a couple problem solving strategies in your toolbox, let's practice. In this exercise, you are given a scenario and you will be asked to decide what steps you would take to identify and solve the problem.

Scenario: You are a new employee and have just finished your training. As your first project, you have been assigned the milling of several additional components for a regular customer. Together, you and your trainer, Bill, set up for the first run. Checking your paperwork, you gather the tools and materials on the list. As you are mounting the materials on the table, you notice that you didn't grab everything and hurriedly grab a few more items from one of the bins. Once the material is secured on the CNC table, you load tools into the tool carousel in the order listed on the tool list and set the fixture offsets.

Bill tells you that since this is a rerun of a job several weeks ago, the CAD/CAM model has already been converted to CNC G-code. Bill helps you download the code to the CNC machine. He gives you the go-ahead and leaves to check on another employee. You decide to start your first run.

What problems did you observe in the video?

• [Page 5: Making Decisions] What problems did you observe in the video?
• What do you do next?
• Try to fix it yourself.
• Ask your trainer for help.

As you are cleaning up, you think about what happened and wonder why it happened. You try to create a mental picture of what happened. You are not exactly sure what the end mill hit, but it looked like it might have hit the dowel pin. You wonder if you grabbed the correct dowel pins from the bins earlier.

You can think of two possible next steps. You can recheck the dowel pin length to make sure it is the correct length, or do a dry run using the CNC single step or single block function with the spindle empty to determine what actually happened.

• Check the dowel pins.
• Use the single step/single block function to determine what happened.

You notice that your trainer, Bill, is still on the floor and decide to ask him for help. You describe the problem to him. Bill asks if you know what the end mill ran into. You explain that you are not sure but you think it was the dowel pin. Bill reminds you that it is important to understand what happened so you can fix the correct problem. He suggests that you start all over again and begin with a dry run using the single step/single block function, with the spindle empty, to determine what it hit. Or, since it happened at the end, he mentions that you can also check the G-code to make sure the Z-axis is raised before returning to the home position.

• Run the single step/single block function.
• Edit the G-code to raise the Z-axis.

You finish cleaning up and check the CNC for any damage. Luckily, everything looks good. You check your paperwork and gather the components and materials again. You look at the dowel pins you used earlier, and discover that they are not the right length. As you go to grab the correct dowel pins, you have to search though several bins. For the first time, you are aware of the mess - it looks like the dowel pins and other items have not been put into the correctly labeled bins. You spend 30 minutes straightening up the bins and looking for the correct dowel pins.

Finally finding them, you finish setting up. You load tools into the tool carousel in the order listed on the tool list and set the fixture offsets. Just to make sure, you use the CNC single step/single block function, to do a dry run of the part. Everything looks good! You are ready to create your first part. The first component is done, and, as you admire your success, you notice that the part feels hotter than it should.

You wonder why? You go over the steps of the process to mentally figure out what could be causing the residual heat. You wonder if there is a problem with the CNC's coolant system or if the problem is in the G-code.

• Look at the G-code.

After thinking about the problem, you decide that maybe there's something wrong with the setup. First, you clean up the damaged materials and remove the broken tool. You check the CNC machine carefully for any damage. Luckily, everything looks good. It is time to start over again from the beginning.

You again check your paperwork and gather the tools and materials on the setup sheet. After securing the new materials, you use the CNC single step/single block function with the spindle empty, to do a dry run of the part. You watch carefully to see if you can figure out what happened. It looks to you like the spindle barely misses hitting the dowel pin. You determine that the end mill was broken when it hit the dowel pin while returning to the start position.

After conducting a dry run using the single step/single block function, you determine that the end mill was damaged when it hit the dowel pin on its return to the home position. You discuss your options with Bill. Together, you decide the best thing to do would be to edit the G-code and raise the Z-axis before returning to home. You open the CNC control program and edit the G-code. Just to make sure, you use the CNC single step/single block function, to do another dry run of the part. You are ready to create your first part. It works. You first part is completed. Only four more to go.

As you are cleaning up, you notice that the components are hotter than you expect and the end mill looks more worn than it should be. It dawns on you that while you were milling the component, the coolant didn't turn on. You wonder if it is a software problem in the G-code or hardware problem with the CNC machine.

It's the end of the day and you decide to finish the rest of the components in the morning.

• You decide to look at the G-code in the morning.
• You leave a note on the machine, just in case.

You decide that the best thing to do would be to edit the G-code and raise the Z-axis of the spindle before it returns to home. You open the CNC control program and edit the G-code.

While editing the G-code to raise the Z-axis, you notice that the coolant is turned off at the beginning of the code and at the end of the code. The coolant command error caught your attention because your coworker, Mark, mentioned having a similar issue during lunch. You change the coolant command to turn the mist on.

• You decide to talk with your supervisor.
• You discuss what happened with a coworker over lunch.

As you reflect on the residual heat problem, you think about the machining process and the factors that could have caused the issue. You try to think of anything and everything that could be causing the issue. Are you using the correct tool for the specified material? Are you using the specified material? Is it running at the correct speed? Is there enough coolant? Are there chips getting in the way?

Wait, was the coolant turned on? As you replay what happened in your mind, you wonder why the coolant wasn't turned on. You decide to look at the G-code to find out what is going on.

From the milling machine computer, you open the CNC G-code. You notice that there are no coolant commands. You add them in and on the next run, the coolant mist turns on and the residual heat issues is gone. Now, its on to creating the rest of the parts.

Have you ever used brainstorming to solve a problem? Chances are, you've probably have, even if you didn't realize it.

You notice that your trainer, Bill, is on the floor and decide to ask him for help. You describe the problem with the end mill breaking, and how you discovered that items are not being returned to the correctly labeled bins. You think this caused you to grab the incorrect length dowel pins on your first run. You have sorted the bins and hope that the mess problem is fixed. You then go on to tell Bill about the residual heat issue with the completed part.

Together, you go to the milling machine. Bill shows you how to check the oil and coolant levels. Everything looks good at the machine level. Next, on the CNC computer, you open the CNC G-code. While looking at the code, Bill points out that there are no coolant commands. Bill adds them in and when you rerun the program, it works.

Bill is glad you mentioned the problem to him. You are the third worker to mention G-code issues over the last week. You noticed the coolant problems in your G-code, John noticed a Z-axis issue in his G-code, and Sam had issues with both the Z-axis and the coolant. Chances are, there is a bigger problem and Bill will need to investigate the root cause .

Talking with Bill, you discuss the best way to fix the problem. Bill suggests editing the G-code to raise the Z-axis of the spindle before it returns to its home position. You open the CNC control program and edit the G-code. Following the setup sheet, you re-setup the job and use the CNC single step/single block function, to do another dry run of the part. Everything looks good, so you run the job again and create the first part. It works. Since you need four of each component, you move on to creating the rest of them before cleaning up and leaving for the day.

It's a new day and you have new components to create. As you are setting up, you go in search of some short dowel pins. You discover that the bins are a mess and components have not been put away in the correctly labeled bins. You wonder if this was the cause of yesterday's problem. As you reorganize the bins and straighten up the mess, you decide to mention the mess issue to Bill in your afternoon meeting.

You describe the bin mess and using the incorrect length dowels to Bill. He is glad you mentioned the problem to him. You are not the first person to mention similar issues with tools and parts not being put away correctly. Chances are there is a bigger safety issue here that needs to be addressed in the next staff meeting.

In any workplace, following proper safety and cleanup procedures is always important. This is especially crucial in manufacturing where people are constantly working with heavy, costly and sometimes dangerous equipment. When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost, and save money.

You now know that the end mill was damaged when it hit the dowel pin. It seems to you that the easiest thing to do would be to edit the G-code and raise the Z-axis position of the spindle before it returns to the home position. You open the CNC control program and edit the G-code, raising the Z-axis. Starting over, you follow the setup sheet and re-setup the job. This time, you use the CNC single step/single block function, to do another dry run of the part. Everything looks good, so you run the job again and create the first part.

At the end of the day, you are reviewing your progress with your trainer, Bill. After you describe the day's events, he reminds you to always think about safety and the importance of following work procedures. He decides to bring the issue up in the next morning meeting as a reminder to everyone.

In any workplace, following proper procedures (especially those that involve safety) is always important. This is especially crucial in manufacturing where people are constantly working with heavy, costly, and sometimes dangerous equipment. When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost, and save money. One tool to improve communication is the morning meeting or huddle.

The next morning, you check the G-code to determine what is wrong with the coolant. You notice that the coolant is turned off at the beginning of the code and also at the end of the code. This is strange. You change the G-code to turn the coolant on at the beginning of the run and off at the end. This works and you create the rest of the parts.

Throughout the day, you keep wondering what caused the G-code error. At lunch, you mention the G-code error to your coworker, John. John is not surprised. He said that he encountered a similar problem earlier this week. You decide to talk with your supervisor the next time you see him.

You are in luck. You see your supervisor by the door getting ready to leave. You hurry over to talk with him. You start off by telling him about how you asked Bill for help. Then you tell him there was a problem and the end mill was damaged. You describe the coolant problem in the G-code. Oh, and by the way, John has seen a similar problem before.

Your supervisor doesn't seem overly concerned, errors happen. He tells you "Good job, I am glad you were able to fix the issue." You are not sure whether your supervisor understood your explanation of what happened or that it had happened before.

The challenge of communicating in the workplace is learning how to share your ideas and concerns. If you need to tell your supervisor that something is not going well, it is important to remember that timing, preparation, and attitude are extremely important.

It is the end of your shift, but you want to let the next shift know that the coolant didn't turn on. You do not see your trainer or supervisor around. You decide to leave a note for the next shift so they are aware of the possible coolant problem. You write a sticky note and leave it on the monitor of the CNC control system.

How effective do you think this solution was? Did it address the problem?

In this scenario, you discovered several problems with the G-code that need to be addressed. When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring and avoid injury to personnel. The challenge of communicating in the workplace is learning how and when to share your ideas and concerns. If you need to tell your co-workers or supervisor that there is a problem, it is important to remember that timing and the method of communication are extremely important.

You are able to fix the coolant problem in the G-code. While you are glad that the problem is fixed, you are worried about why it happened in the first place. It is important to remember that if a problem keeps reappearing, you may not be fixing the right problem. You may only be addressing the symptoms.

You decide to talk to your trainer. Bill is glad you mentioned the problem to him. You are the third worker to mention G-code issues over the last week. You noticed the coolant problems in your G-code, John noticed a Z-axis issue in his G-code, and Sam had issues with both the Z-axis and the coolant. Chances are, there is a bigger problem and Bill will need to investigate the root cause .

Over lunch, you ask your coworkers about the G-code problem and what may be causing the error. Several people mention having similar problems but do not know the cause.

You have now talked to three coworkers who have all experienced similar coolant G-code problems. You make a list of who had the problem, when they had the problem, and what each person told you.

When you see your supervisor later that afternoon, you are ready to talk with him. You describe the problem you had with your component and the damaged bit. You then go on to tell him about talking with Bill and discovering the G-code issue. You show him your notes on your coworkers' coolant issues, and explain that you think there might be a bigger problem.

You supervisor thanks you for your initiative in identifying this problem. It sounds like there is a bigger problem and he will need to investigate the root cause. He decides to call a team huddle to discuss the issue, gather more information, and talk with the team about the importance of communication.

Root Cause Analysis

Root cause analysis ( RCA ) is a method of problem solving that identifies the underlying causes of an issue. Root cause analysis helps people answer the question of why the problem occurred in the first place. RCA uses clear cut steps in its associated tools, like the "5 Whys Analysis" and the "Cause and Effect Diagram," to identify the origin of the problem, so that you can:

• Determine what happened.
• Determine why it happened.
• Fix the problem so it won’t happen again.

RCA works under the idea that systems and events are connected. An action in one area triggers an action in another, and another, and so on. By tracing back these actions, you can discover where the problem started and how it developed into the problem you're now facing. Root cause analysis can prevent problems from recurring, reduce injury to personnel, reduce rework and scrap, and ultimately, reduce cost and save money. There are many different RCA techniques available to determine the root cause of a problem. These are just a few:

• Root Cause Analysis Tools
• 5 Whys Analysis
• Fishbone or Cause and Effect Diagram
• Pareto Analysis

How Huddles Work

Communication is a vital part of any setting where people work together. Effective communication helps employees and managers form efficient teams. It builds trusts between employees and management, and reduces unnecessary competition because each employee knows how their part fits in the larger goal.

One tool that management can use to promote communication in the workplace is the huddle . Just like football players on the field, a huddle is a short meeting where everyone is standing in a circle. A daily team huddle ensures that team members are aware of changes to the schedule, reiterated problems and safety issues, and how their work impacts one another. When done right, huddles create collaboration, communication, and accountability to results. Impromptu huddles can be used to gather information on a specific issue and get each team member's input.

The most important thing to remember about huddles is that they are short, lasting no more than 10 minutes, and their purpose is to communicate and identify. In essence, a huddle’s purpose is to identify priorities, communicate essential information, and discover roadblocks to productivity.

Who uses huddles? Many industries and companies use daily huddles. At first thought, most people probably think of hospitals and their daily patient update meetings, but lots of managers use daily meetings to engage their employees. Here are a few examples:

• Brian Scudamore, CEO of 1-800-Got-Junk? , uses the daily huddle as an operational tool to take the pulse of his employees and as a motivational tool. Watch a morning huddle meeting .
• Fusion OEM, an outsourced manufacturing and production company. What do employees take away from the daily huddle meeting .
• Biz-Group, a performance consulting group. Tips for a successful huddle .

Brainstorming

One tool that can be useful in problem solving is brainstorming . Brainstorming is a creativity technique designed to generate a large number of ideas for the solution to a problem. The method was first popularized in 1953 by Alex Faickney Osborn in the book Applied Imagination . The goal is to come up with as many ideas as you can in a fixed amount of time. Although brainstorming is best done in a group, it can be done individually. Like most problem solving techniques, brainstorming is a process.

• Define a clear objective.
• Have an agreed a time limit.
• During the brainstorming session, write down everything that comes to mind, even if the idea sounds crazy.
• If one idea leads to another, write down that idea too.
• Combine and refine ideas into categories of solutions.
• Assess and analyze each idea as a potential solution.

When used during problem solving, brainstorming can offer companies new ways of encouraging staff to think creatively and improve production. Brainstorming relies on team members' diverse experiences, adding to the richness of ideas explored. This means that you often find better solutions to the problems. Team members often welcome the opportunity to contribute ideas and can provide buy-in for the solution chosen—after all, they are more likely to be committed to an approach if they were involved in its development. What's more, because brainstorming is fun, it helps team members bond.

• Watch Peggy Morgan Collins, a marketing executive at Power Curve Communications discuss How to Stimulate Effective Brainstorming .
• Watch Kim Obbink, CEO of Filter Digital, a digital content company, and her team share their top five rules for How to Effectively Generate Ideas .

Importance of Good Communication and Problem Description

Communication is one of the most frequent activities we engage in on a day-to-day basis. At some point, we have all felt that we did not effectively communicate an idea as we would have liked. The key to effective communication is preparation. Rather than attempting to haphazardly improvise something, take a few minutes and think about what you want say and how you will say it. If necessary, write yourself a note with the key points or ideas in the order you want to discuss them. The notes can act as a reminder or guide when you talk to your supervisor.

Tips for clear communication of an issue:

• Provide a clear summary of your problem. Start at the beginning, give relevant facts, timelines, and examples.
• Avoid including your opinion or personal attacks in your explanation.
• Avoid using words like "always" or "never," which can give the impression that you are exaggerating the problem.
• If this is an ongoing problem and you have collected documentation, give it to your supervisor once you have finished describing the problem.
• Remember to listen to what's said in return; communication is a two-way process.

Not all communication is spoken. Body language is nonverbal communication that includes your posture, your hands and whether you make eye contact. These gestures can be subtle or overt, but most importantly they communicate meaning beyond what is said. When having a conversation, pay attention to how you stand. A stiff position with arms crossed over your chest may imply that you are being defensive even if your words state otherwise. Shoving your hands in your pockets when speaking could imply that you have something to hide. Be wary of using too many hand gestures because this could distract listeners from your message.

The challenge of communicating in the workplace is learning how and when to share your ideas or concerns. If you need to tell your supervisor or co-worker about something that is not going well, keep in mind that good timing and good attitude will go a long way toward helping your case.

Like all skills, effective communication needs to be practiced. Toastmasters International is perhaps the best known public speaking organization in the world. Toastmasters is open to anyone who wish to improve their speaking skills and is willing to put in the time and effort to do so. To learn more, visit Toastmasters International .

Methods of Communication

Communication of problems and issues in any workplace is important, particularly when safety is involved. It is therefore crucial in manufacturing where people are constantly working with heavy, costly, and sometimes dangerous equipment. As issues and problems arise, they need to be addressed in an efficient and timely manner. Effective communication is an important skill because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost and save money.

There are many different ways to communicate: in person, by phone, via email, or written. There is no single method that fits all communication needs, each one has its time and place.

In person: In the workplace, face-to-face meetings should be utilized whenever possible. Being able to see the person you need to speak to face-to-face gives you instant feedback and helps you gauge their response through their body language. Be careful of getting sidetracked in conversation when you need to communicate a problem.

Email: Email has become the communication standard for most businesses. It can be accessed from almost anywhere and is great for things that don’t require an immediate response. Email is a great way to communicate non-urgent items to large amounts of people or just your team members. One thing to remember is that most people's inboxes are flooded with emails every day and unless they are hyper vigilant about checking everything, important items could be missed. For issues that are urgent, especially those around safety, email is not always be the best solution.

Phone: Phone calls are more personal and direct than email. They allow us to communicate in real time with another person, no matter where they are. Not only can talking prevent miscommunication, it promotes a two-way dialogue. You don’t have to worry about your words being altered or the message arriving on time. However, mobile phone use and the workplace don't always mix. In particular, using mobile phones in a manufacturing setting can lead to a variety of problems, cause distractions, and lead to serious injury.

Written: Written communication is appropriate when detailed instructions are required, when something needs to be documented, or when the person is too far away to easily speak with over the phone or in person.

There is no "right" way to communicate, but you should be aware of how and when to use the appropriate form of communication for your situation. When deciding the best way to communicate with a co-worker or manager, put yourself in their shoes, and think about how you would want to learn about the issue. Also, consider what information you would need to know to better understand the issue. Use your good judgment of the situation and be considerate of your listener's viewpoint.

Did you notice any other potential problems in the previous exercise?

• [Page 6:] Did you notice any other potential problems in the previous exercise?

Summary of Strategies

In this exercise, you were given a scenario in which there was a problem with a component you were creating on a CNC machine. You were then asked how you wanted to proceed. Depending on your path through this exercise, you might have found an easy solution and fixed it yourself, asked for help and worked with your trainer, or discovered an ongoing G-code problem that was bigger than you initially thought.

When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost, and save money. Although, each path in this exercise ended with a description of a problem solving tool for your toolbox, the first step is always to identify the problem and define the context in which it happened.

There are several strategies that can be used to identify the root cause of a problem. Root cause analysis (RCA) is a method of problem solving that helps people answer the question of why the problem occurred. RCA uses a specific set of steps, with associated tools like the “5 Why Analysis" or the “Cause and Effect Diagram,” to identify the origin of the problem, so that you can:

Once the underlying cause is identified and the scope of the issue defined, the next step is to explore possible strategies to fix the problem.

If you are not sure how to fix the problem, it is okay to ask for help. Problem solving is a process and a skill that is learned with practice. It is important to remember that everyone makes mistakes and that no one knows everything. Life is about learning. It is okay to ask for help when you don’t have the answer. When you collaborate to solve problems you improve workplace communication and accelerates finding solutions as similar problems arise.

One tool that can be useful for generating possible solutions is brainstorming . Brainstorming is a technique designed to generate a large number of ideas for the solution to a problem. The method was first popularized in 1953 by Alex Faickney Osborn in the book Applied Imagination. The goal is to come up with as many ideas as you can, in a fixed amount of time. Although brainstorming is best done in a group, it can be done individually.

Depending on your path through the exercise, you may have discovered that a couple of your coworkers had experienced similar problems. This should have been an indicator that there was a larger problem that needed to be addressed.

In any workplace, communication of problems and issues (especially those that involve safety) is always important. This is especially crucial in manufacturing where people are constantly working with heavy, costly, and sometimes dangerous equipment. When issues and problems arise, it is important that they be addressed in an efficient and timely manner. Effective communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost and save money.

One strategy for improving communication is the huddle . Just like football players on the field, a huddle is a short meeting with everyone standing in a circle. A daily team huddle is a great way to ensure that team members are aware of changes to the schedule, any problems or safety issues are identified and that team members are aware of how their work impacts one another. When done right, huddles create collaboration, communication, and accountability to results. Impromptu huddles can be used to gather information on a specific issue and get each team member's input.

To learn more about different problem solving strategies, choose an option below. These strategies accompany the outcomes of different decision paths in the problem solving exercise.

• View Problem Solving Strategies Select a strategy below... Root Cause Analysis How Huddles Work Brainstorming Importance of Good Problem Description Methods of Communication

Communication is one of the most frequent activities we engage in on a day-to-day basis. At some point, we have all felt that we did not effectively communicate an idea as we would have liked. The key to effective communication is preparation. Rather than attempting to haphazardly improvise something, take a few minutes and think about what you want say and how you will say it. If necessary, write yourself a note with the key points or ideas in the order you want to discuss them. The notes can act as a reminder or guide during your meeting.

• Provide a clear summary of the problem. Start at the beginning, give relevant facts, timelines, and examples.

In person: In the workplace, face-to-face meetings should be utilized whenever possible. Being able to see the person you need to speak to face-to-face gives you instant feedback and helps you gauge their response in their body language. Be careful of getting sidetracked in conversation when you need to communicate a problem.

There is no "right" way to communicate, but you should be aware of how and when to use the appropriate form of communication for the situation. When deciding the best way to communicate with a co-worker or manager, put yourself in their shoes, and think about how you would want to learn about the issue. Also, consider what information you would need to know to better understand the issue. Use your good judgment of the situation and be considerate of your listener's viewpoint.

"Never try to solve all the problems at once — make them line up for you one-by-one.” — Richard Sloma

Problem Solving: An Important Job Skill

Problem solving improves efficiency and communication on the shop floor. It increases a company's efficiency and profitability, so it's one of the top skills employers look for when hiring new employees. Recent industry surveys show that employers consider soft skills, such as problem solving, as critical to their business’s success.

The 2011 survey, "Boiling Point? The skills gap in U.S. manufacturing ," polled over a thousand manufacturing executives who reported that the number one skill deficiency among their current employees is problem solving, which makes it difficult for their companies to adapt to the changing needs of the industry.

In this video, industry professionals discuss their expectations and present tips for new employees joining the manufacturing workforce.

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Everyday problem solving across the adult life span: solution diversity and efficacy

Everyday problem solving involves examining the solutions that individuals generate when faced with problems that take place in their everyday experiences. Problems can range from medication adherence and meal preparation to disagreeing with a physician over a recommended medical procedure or compromising with extended family members over where to host Thanksgiving dinner. Across the life span, research has demonstrated divergent patterns of change in performance based on the type of everyday problems used as well as based on the way that problem-solving efficacy is operationally defined. Advancing age is associated with worsening performance when tasks involve single-solution or fluency-based definitions of effectiveness. However, when efficacy is defined in terms of the diversity of strategies used, as well as by the social and emotional impact of solution choice on the individual, performance is remarkably stable and sometimes even improves in the latter half of life. This article discusses how both of these approaches to everyday problem solving inform research on the influence that aging has on everyday functioning.

Introduction

As mentioned in many chapters in this review volume, a common theme of the cognitive aging literature is a steady decline in functioning. As we get older, we experience changes in processing speed, 1 – 3 memory, 4 reasoning, 5 attention, 6 , 7 and executive functioning. 8 – 10 Underlying such decline is a series of structural changes in the brain 11 , 12 as well as shifts in what motivates us to think and act as we grow older. 13 – 15 Despite these declines, older adults are often autonomous, independent, and well adjusted. They live full lives and occupy as many roles in society as younger individuals, if not more roles, and they are relied upon as authority figures—leaders, advisors, employers, parents, and grandparents. This divergence between declines in lab-assessed cognitive functioning and maintained interpersonal influence is what fuels research on everyday problem solving across the adult half of the life span. 16 , 17 The need to assess everyday functioning independently of traditional measures of primary mental abilities led to the creation of everyday problem solving batteries that displayed higher levels of ecological validity, more closely resembling challenges that are part of our day-to-day existence. Research in this field focuses on defining the conditions under which older adults may have difficulties with these problems (e.g., physical limitations and comprehension of sophisticated instructions) so that interventions can be established to ameliorate such difficulties and promote a higher quality of life. In addition, research in this field also focuses on examining how those processes that we use to solve problems change across the adult life span and lead us to implement different types of strategies based upon the goals that we set at each stage of life. 18 , 19 Here, research is reviewed that discusses the challenges faced by older individuals when managing everyday problems as well as the differences that have been found in how young and older adults approach the process of solving everyday problems.

Everyday problems are the circumstances that we find ourselves in on a daily basis that involve using the skills, accumulated knowledge, and resources (e.g., time, money, and friends) that we have available to us to reach our goals and to side step obstacles to these goals. 17 Everyday problems vary in terms of their problem space, or the possible solutions that an individual can reach given the contextual features and demands of the situation. 16 Everyday problems sometimes have a clear outcome, or goal state, that all individuals will work toward. For instance, if you return to your automobile at the airport to find that you have a flat tire, the steps that are required to effectively resolve the problem so that you can be on your way are quite clear. Success depends upon your ability to implement these steps (e.g., use of physical strength to remove lug nuts). On the other hand, everyday problems sometimes create obstacles that cannot be directly removed and require a careful balance of knowing not just what to do but when to do it. For example, should you find yourself in a disagreement with your partner on what to give your child as a gift on a birthday, you can each give the child your respective preferred gifts. However, how will you resolve the negativity that emerged as a result of conflicting preferences? What if you have a limited number of resources to devote to a gift and a compromise is necessary to resolve the conflict? If you have to involve others in the problem-solving process, it is challenging to ensure that all parties have the same goals in mind. Moreover, you cannot proceed forward to acquire the gift until you have buy-in from others. When problems are ill-defined, the timing of your actions is important because you may have to refrain from acting until a negotiation can take place. In such a situation, it is important to recognize how to regulate your own emotions and how to influence the emotions and thought processes of others. 18

In this review, how everyday problem solving changes across the adult half of the life span will be discussed. Included is (a) a description of the methods used to assess everyday problem-solving performance and the diversity in findings that emerges when age's impact on everyday problem solving is gauged using well-defined versus ill-defined problems as well as different operational definitions of efficacy, (b) a description of the contextual factors that lead to age differences in everyday problem solving, and (c) a brief assessment of the future directions of the field.

Assessing age differences in everyday problem-solving performance

As mentioned earlier, decades of research on cognitive aging demonstrate gradual decline in functioning over time. This decline, however, runs counter to the notion that with age comes wisdom, or at least an accumulation of experiences that can help us determine how to continue to function when faced with problems. Baltes referred to these divergent trends as multidirectionality, and he believed that two distinct systems of cognition existed to capture these trends: pragmatic knowledge and structural mechanics. 20 Accumulated experience or pragmatic knowledge (sometimes called tacit knowledge or crystallized intelligence) continues to grow throughout the life span given the novel circumstances and ever-expanding culture to which we are exposed year by year. Conversely, the hard-wired, biologically determined mechanisms that support cognition (sometimes called fluid intelligence) slowly degrade as our cells and tissues wear out over time. Key to successful aging is how the change that takes place in these two systems balance against one another. 21 – 23 Ultimately, each person has a limited pool of resources to devote to all aspects of their life at any given moment. 20 Consequently, throughout the life span, we set goals for ourselves that shape our behavior by prioritizing some pursuits over others. This selection process limits the number of goals that we consider at any given stage of our life so as to make it possible to optimize the investment of our resources to maintain the greatest level of successful functioning as is possible. 20 With respect to everyday problem solving, this poses some interesting questions: (a) To what extent does decline in cognitive functioning (especially rooted in one's neural mechanics) affect the resources that are available to individuals in the latter half of life when faced with complex everyday problems that are vital to autonomous functioning, and (b) How does one's changing goals and accumulated experience across the life span influence the process by which we solve problems? These two questions have dominated research on everyday problem solving and aging over the past 25 years.

Consistent with the need to map cognitive decline onto everyday problem solving, many everyday problem-solving tasks consist of a pool of well-defined problems from multiple domains (e.g., nutrition, health, and finance) that reflect the activities that an autonomous individual will engage in when caring for themselves. 24 A well-defined problem is a problem that has a constrained problem space (i.e., number of possible responses limited by the features of the question asked) with a single correct solution. For instance, the Everyday Cognition Battery (ECB) includes items that ask participants to compare the nutritional value of two brands of chili. 25 Participants are asked to use nutrition labels to determine which brand has less fat and to compare the statistics provided on each label for each of the other listed categories of dietary information. They might also be asked specific questions about what the categories listed on the labels refer to as a way to assess the participants' general knowledge about food labels. Additional items in the battery focus on medication use and understanding financial information. Overall, the problems included in the ECB capture functioning that contributes to many of the domains found in the assessment of Instrumental Activities of Daily Living. 26 Studies using this battery or similar tasks with similar well-defined problems demonstrate decline in everyday functioning with advancing age. 27 Also, performance on the different components of the battery (e.g., everyday inductive reasoning or everyday knowledge) are significantly correlated with performance on corresponding psychometric tests of intelligence, 28 like lab-based assessments of inductive reasoning and verbal knowledge commonly used to track intelligence. 29 However, performance on the practical problems included in the ECB better predicts actual everyday functioning than does performance on the standard psychometric tests of intelligence. Overall, well-defined problems are used to trace how age-related cognitive decline affects the specific abilities that are vital to maintaining an individual's autonomy over and above those abilities measured by tests of primary mental abilities. 24 , 28 , 30 Often, researchers who use tasks that include well-defined everyday problems are trying to replicate specific activities from everyday life within the lab to systematically examine where functional deficits may occur. These tasks provide useful information as to which skills might be most affected in an individual, 31 opening up the possibility for future skills training geared toward forestalling further losses. 32 , 33

In addition to assessing individuals' ability to generate the single correct solution found in each well-defined everyday problem, other researchers assess everyday problem-solving performance by posing ill-defined hypothetical problems and counting the number of safe and effective solutions that can be generated by each participant. In an ill-defined problem, participants are asked to identify all of the ways that they might overcome an obstacle to a goal to reach an acceptable outcome. 34 , 35 The participants' solutions are then examined by coders to ensure that they are in fact safe and effective ways to resolve the problem before being tallied as an indicator of everyday problem-solving ability. A sample problem from such a test might ask the participants to consider ways in which a man with heart problems might still be able to complete summer maintenance and landscaping duties around his house even though his doctor has told him to refrain from strenuous physical activity and even though he does not have enough money to hire someone to do the work for him. 36 Researchers use everyday problem-solving assessments that consist of ill-defined problems in order to allow participant-specific experiences to inform the solutions that are generated. For instance, suppose that one is asked to balance a checkbook in a well-defined everyday problem-solving task, this activity requires that the individual demonstrate addition and subtraction skills. If an ill-defined problem involved balancing one's checkbook or managing finances, then recommending the addition of deposits and subtraction of expenditures would be an effective solution. However, recommending that one seek assistance from someone who has experience balancing a checkbook would also be an effective solution. Ultimately, tasks using ill-defined problems have the potential to capture other solutions that a person may find that go beyond the most common strategy for resolving the issue at hand.

From young adulthood until middle age, the fluency of solution generation increases, possibly reflecting the appropriate balance between gains stemming from pragmatic life experience and only minimal structural or neurological decline. However, performance declines slightly in one's 50s and throughout the remainder of one's years. 35 Similarly, when social problem solving was examined via ill-defined problems, again an inverted U-shaped function characterized performance, with solution fluency peaking in one's 40s and 50s, and declining thereafter. 37 This finding is important because perceived quality of life is closely linked to one's ability to function independently 38 – 40 and solve everyday problems that might emerge on occasion 41 , 42 that are both linked to mortality. 43 – 45 Despite there being numerous studies that link advancing age to declines in everyday problem-solving ability, 46 , 47 other studies have identified areas in which we improve in everyday problem solving with age. Studies that do not demonstrate the similar levels of age-related decline in problem-solving performance often rely on an operational definition of problem solving efficacy that differs from a focus on solution fluency (i.e., the number of safe and effective solutions generated). Table 1 includes some of the ways that researchers have defined everyday problem-solving effectiveness.

Operationalizing effective everyday problem solving

Everyday problem-solving performance dependent on manner of assessment

What defines success when solving everyday problems? In the aforementioned studies, when faced with a well-defined problem, success was based on whether the participant provided the single best solution. When faced with an ill-defined problem, success was based on the overall number of safe and effective solutions that the individual offered as potential ways of managing the problem. In general, with these definitions of success, advancing age is associated with a decline in everyday problem solving performance. 46 Although these definitions of effectiveness provide a useful metric for problem solving success, they are not without their limitations. The one-solution definition of success assumes that there may only be one way to solve a well-defined problem and that such problems are generally solved in isolation instead of with the assistance of others or with supplemental information. Additionally, the solution-fluency definition of success assumes that the solutions that are generated reflect the maximum number of solutions accessible to the participants when in actuality they may reflect those solutions that the participants believed to be most relevant to or efficacious for a given problem.

When you examine the actual strategies that young and older individuals use (or recommend) to solve problems, older adults may fare better than expected because the previously mentioned techniques for assessing everyday problem-solving performance underestimate the value of the behaviors evinced by older adults when they are coping with an everyday problem. 17 , 18 Specifically, the conventional ways of operationalizing everyday problem solving success fail to account for the quality of individual solutions that are generated. They also do not account for the evolving nature of the everyday problem solving process, including the temporal and environmental limitations on direct action that might be imposed on the problem solver by the problem space. Finally, they ignore the impact that nominated solutions have on the participants' well-being and on their ability to meet the goals that they have set for resolving the problem. Given these limitations, additional definitions of everyday problem-solving success have emerged in order to broaden the scope with which age differences in the everyday problem-solving process are examined.

For instance, Cornelius and Caspi defined everyday problem solving success in terms of the degree to which participants' recommended solutions matched those of an expert panel consisting of developmental psychologists as well as young, middle-aged, and older adult lay people. They asked participants ranging in age from 20 to 78 years to consider 48 hypothetical, ill-defined problems from six domains of everyday functioning (i.e., family, friend, work, home, consumer, and information gathering) included in their Everyday Problem Solving Inventory (EPSI). 48 Participants indicated the extent to which they might use each of four specific strategies, tailored to each problem, in an attempt to reach a resolution: purposeful action (self-initiated action to directly resolve the problem), cognitive analysis (planning action and thinking about the situation to better understand it), passive-dependent behavior (doing nothing to change the situation or relying on others to step in), and avoidant thinking and denial (distracting one's attention away from the problem, avoiding responsibility for the problem, or denying one's emotions). Other studies conducted at this point in time were also relying on similar coping-based techniques for operationalizing the diversity of problem-solving strategies that may be employed to manage stressors like those in the EPSI. 49 , 50 After the participants responded, their recommended strategies were compared to those selected by an expert panel as ideal, and an effectiveness correlation was calculated and examined by age group. Overall, older individuals chose strategies that more closely matched those recommended by the expert panel than did younger age groups. This finding runs counter to previous findings that have been discussed demonstrating that problem-solving ability peaks in mid-life and then declines.

This age-related enhancement in everyday problem solving was later replicated using the same set of problems from the EPSI, parsimoniously redistributing them into achievement-oriented and interpersonal domains. 51 Again, older adults were more effective than young adults in their overall choice of strategies for solving everyday problems. Moreover, older adults were more effective than young adults in choosing strategies to resolve hypothetical social conflicts (e.g., how to react when your peers gossip about one of your closest friends). The major reason for this outcome is that older adults were more likely to implement combinations of strategies that included both problem-focused solutions (e.g., purposeful action) and emotion-focused solutions (avoidance and passive dependence). As had been noted by Blanchard-Fields and her colleagues in prior research, older adults approach everyday problems involving interpersonal conflict in ways that are fundamentally different from young adults and in ways that possibly reflect age-appropriate differences in social motivation and experience that guide older adults to be more mindful of the emotions evoked by problems. 19 , 52

Although older adults are less accurate than young adults when solving well-defined instrumental everyday problems and less fluent when generating solutions for ill-defined everyday problems in tasks that do not recognize the value of emotion recognition in the problem-solving process, 46 older adults display a consistent advantage over young adults when problem solving success is defined in terms of one's ability to implement a diverse repertoire of strategies that meet the practical and emotional challenges created by problems. 18 This divergence in outcomes emerges because of the differences that exist in the two dominant approaches to research on everyday problem solving and aging. The method of investigation used, including the operational definition of problem-solving success, influences the conclusions that are drawn about how everyday problem solving performance changes across the adult half of the life span. This can make it quite challenging to compare outcomes across tasks. 53 Ultimately, though, each technique seeks to characterize the diversity of solutions offered by the population to manage everyday problems. Errors that individuals make while completing well-defined problems can help inform the research and development conducted by those who design consumer products, financial forms, and even home environments by specifying which parameters need to be changed to promote a more user friendly experience for people of all ages. Additionally, the breadth of emotion-focused coping strategies offered by individuals facing challenging interpersonal conflicts can be used to develop age-specific norms that can inform mental health professionals of those strategies that would be most relevant to patients at different points in their life. In their own ways, each technique strives to add more information to the existing literature on ways that people of all ages can elevate their sense of well-being while continuing to maintain their autonomy and social functioning.

Contextual factors that contribute to age differences in everyday problem solving

Over the past two decades, researchers have recognized that everyday problem solving can be influenced by many person-specific (e.g., sensory abilities and level of cognitive functioning) and age-typical (e.g., communion-oriented goals or time constraints imposed by thoughts about the end of life) contextual factors. Consequently, the literature is replete with examples of studies that attempt to measure the correlational impact of contextual factors on everyday functioning or that directly manipulate context to track how such interventions affect solution quality and strategy preference. These studies are valuable to the field because they inform practitioners (e.g., medical doctors, nurses, rehabilitation therapists, mental health professionals, and financial advisors) about the roles that cognitive ability and personal motivation play in driving adult decision making. Earlier, it was already noted that cognitive functioning predicts everyday problem-solving performance. 25 , 28 , 33 In fact, recent research suggests that individual differences in cognitive functioning mediate the relationship between poor health status and poor everyday problem-solving performance. 47 Some possible factors that underlie this mediation effect include wide variation (or inconsistency) in response time and age-associated decline in sensory abilities. 54 – 56 These findings tie back to Baltes' hypothesis that we become most susceptible to functional deficits in old age when our neurological architecture degrades to the point where we have difficulty implementing the knowledge that we have gained from our past experiences as we cope with current obstacles to our goals. 20 Consistent with the idea that our own personal goals and our appraisals of problems matter and shape our choices, other researchers have proceeded forward knowing that, although cognitive ability can factor into everyday problem-solving performance, personal relevance and social context also influence how we solve everyday problems. Figure 1 illustrates the mediating role that social context can have on everyday problem-solving performance.

Contextual factors that influence solution implementation in everyday problem-solving tasks.

When faced with a challenge that is not personally meaningful to us, it is reasonable to expect that our feelings of self-efficacy toward our solutions might be less than they would have otherwise been if we were faced with a problem that was more relevant to our own personal history. This prediction is supported by the work of Artistico et al ., who identified that age differences in everyday problem-solving performance map on to the divergent feelings of self-efficacy held by young and older adults when solving problems that either were age relevant or were not relevant to their own age group. 57 , 58 Problems that are more relevant to our current stage of life might be easier to resolve because (a) the problem's context may be more familiar to use, (b) solutions to past similar problems are still accessible, and (c) our peers may also be familiar with these problems and could offer instrumental and emotional support. Intuitively, how much personal experience we have with a given problem should predict how successful we are at solving it. However, Berg et al . have found that experience with the problem itself matters less in producing age differences in everyday problem solving than does the heuristic-oriented (or experiential-based) reasoning implemented by older adults and not younger adults when completing problem solving tasks. 59 Specifically, Berg et al . demonstrated that older adults may be less motivated than young adults to produce as exhaustive of a list of potential solutions to problems or to consider as much information when generating solutions. This behavioral tendency of older adults has appeared in decision making research over the past 20 years and is discussed throughout this review volume. Ultimately, future research will continue to examine whether this practice is being driven by cognitive decline or by a fundamental shift in the reward structure that motivates decisions in the latter half of life. 60 – 62

The impact that personal relevance has on everyday problem solving may stem from how it facilitates several other appraisal processes that force us to examine the contextual features of problems in more details. Specifically, we have to assess what may be the source of a problem (e.g., domain and cause), our goals for coping with the problem, and the types of solutions that may lead to the best outcomes for the problem. Blanchard-Fields and colleagues have identified that younger and older adults choose similar forms of purposeful action- and planning-oriented strategies (also known as problem-focused strategies) when faced with instrumental problems, or problems that merely present some obstacle to the individual who is trying to achieve some personal goal that does not involve other people or relationships, neither directly nor indirectly. 18 , 63 This finding is not surprising given that it is most adaptive to combat the source of the problem directly in these types of situations (e.g., a flat tire on a car or a broken iPod). 64 Interestingly, younger adults are more likely than older adults to use emotion-focused strategies when faced with instrumental problems. 63 This may occur because young people do not have the same personal freedom (e.g., time constraints) and monetary resources at their disposal as older individuals do to invest in clearing obstacles to achievement-oriented problems. If you cannot do something to resolve the problem yourself, you may have to depend on others for assistance. Consequently, passive dependence or attempts to avoid or deny the existence of the obstacle can be an effective way to reduce the disappointment or frustration that one experiences when a goal is thwarted. 18 Developmentally, we would expect young and older adults to offer different solutions to instrumental problems.

Likewise, when faced with interpersonal problems, we might predict that how one responds may depend upon where they currently fall along the developmental spectrum. Early in life, individuals are focused on gathering information, seeking novel experiences, and meeting new people. In the latter half of life, however, the focus shifts toward investing resources in our current relationships to maintain strong socioemotional bonds. 15 , 64 This means that young adults have more social capital to spare and can afford to engage in more argumentative or confrontational strategies for resolving interpersonal problems than can older adults. 65 Whereas young adults focus on balancing short-term negativity with long-term happiness, older adults are focused on being happy today. Simply put, older adults are more likely than young adults to focus on strategies that squelch those negative emotions that are toxic or threaten relationships because they do not have as much time left in life to enjoy these relationships. 15 , 18 For example, in a seminal paper in everyday problem solving and aging, Blanchard-Fields and colleagues found that older adults were more likely thanyoung adults to engage inavoidant-denial strategies when faced with interpersonal problems that were emotionally evocative. 66 Older adults appear to be more keenly aware of when it is important to step away from a conflict to cool off and when it is valuable to delay reacting so as to avoid from fanning the flames. 52 , 67 Consistent with this interpretation, older adults have been found to experience less anger during interpersonal conflicts. 68 , 69 More-over, from middle adulthood through old age, there is a greater emphasis placed on secondary control striving, or the need to internally regulate our reactivity to an environment that might fall outside of our control. 70 With respect to interpersonal everyday problems, the latter half of life is when we realize that attempting to change the behaviors of others might be counterproductive because doing so might exacerbate conflict. A substantial component of this is recognizing that interpersonal harmony requires working within the boundaries of relationships and considering the mutual goals that we have with our relationship partners.

Future directions

The research reviewed up to this point has highlighted how the methods used to assess everyday problem solving contribute to age differences in everyday problem solving performance. It has also presented some of the factors that are responsible for eliciting age differences in strategy selection when researchers focus on the dynamics of how young and older adults react to everyday problems. With the emergence of socioemotional selectivity theory in cognitive aging, there has been a renewed focus on the role that age differences in goals play in motivating everyday decisions. 15 Specifically, an increased emphasis has been placed on trying to gain a deeper understanding of the ways that emotion regulatory and relational communion goals drive older adults' behavioral tendencies when faced with stress or everyday problems. Strough, Berg, and Sansone were among the first to provide evidence that young and older adults approached interpersonal interactions with different goal sets in mind. 71 Their research suggested that older adults were more supportive of social others than were young adults when pursuing the resolution to everyday problems. They interpreted this to suggest that older adults were more focused on generativity, whereas young adults were focused on independence. What is most remarkable about this finding is that, in old age, when individuals face the greatest potential for cognitive and physical decline as well as thwarted instrumental goals, they realign their priorities in order to provide support to their friends and family. Future research in this field will examine how older adults capitalize on their interpersonal focus to live happy and healthy lives. 72 It will also characterize the relational contexts under which older adults are most at risk for stress or which predispose older adults to health problems.

Emerging from the discussion on how we should define successful everyday problem solving was the recognition that individuals would experience the greatest sense of well-being when they selected problem solving strategies that matched their personal goals for the situation in which they found themselves. 18 , 71 , 73 In other words, if your chosen course of action allowed you to meet your goal for the problem, then you will be successful at resolving that problem. Although shockingly simple in theory, in practice, this perspective creates some challenging methodological and statistical hurdles for the researcher to negotiate. For instance, if you want to assess the match between goals and strategies in real time, you have to collect information on the participant's current goals, carefully distinguishing between short-term interests and longer-term life philosophies. Next, you have to wait for a problem to arise and then track how the participant resolves it. If the problem involves someone else, then you have to determine if there is a match between the goals of both parties involved and then examine the strategies of each individual to see how they contribute to individual and collective goals. Time-sampling studies, which ask people to report their goals, the obstacles that they experience to their goals, their emotional reactions to such obstacles, as well as the strategies that they are using to manage these obstacles are currently in progress. 74 Using archival data from a study in which participants ranging in age from 15 to 84 years were asked to discuss a problem from their own lives, Hoppmann, Coats, and Blanchard-Fields found that younger individuals were most likely to match autonomy goals (e.g., independence of action) with self-focused strategies, whereas older adults matched generativity goals with other-focused strategies. 75 These findings highlight the importance of considering goals when trying to account for why young and older adults may arrive at different resolutions to their problems.

Although numerous studies have examined the types of problem- and emotion-focused coping strategies that young and older adults endorse when faced with everyday problems, few studies have examined the interpersonal interactions that occur between individuals as they collaboratively solve everyday problems. As mentioned earlier, older adults display passive dependent strategies at times during a conflict when action may worsen the negativity experienced by both interaction partners, whereas young adults are willing to be confrontational. For instance, when working with a friend to generate as many solutions as possible to hypothetical interpersonal problems, older adults were more likely than young adults to recommend help seeking and careful planning, whereas young adults were more likely to recommend verbally aggressive self-assertion. 76 In other words, when collaborating with a friend, older adults are more likely than young adults to agree that interpersonally destructive strategies are not the best way to resolve conflict. This may reflect a shared recognition in the importance of reducing the potential for making the problem worse. Aside from looking at the strategies nominated by collaborators, Berg et al . have also examined the ways that collaborators treat one another while working to solve problems. In a study examining how partners in older couples collaboratively coped with prostate cancer, husbands and wives both benefited emotionally from working with one another if they were satisfied with their marriage. 77 In a second study, middle-aged and older married couples were asked to discuss an ongoing conflict and to also collaborate with one another to complete an instrumental planning task. 78 Older couples experienced less negative affect during the conflict if they were satisfied with their marriage. However, contrary to the prediction that older couples may behave more passively toward one another during conflict, older couples did express negativity toward one another (especially wives) during the discussion of their conflict. Additionally, when working on the instrumental task, members of older adult couples were warm when attempting to exert control over their partner during the task. When taken together, these findings suggest that jointly reported marital satisfaction can be important for fostering collaborative efforts between partners when coping with health problems, resolving an interpersonal spat, and even when dealing with the daily chores and errands of everyday life. 79 Future research should continue to examine the dynamic role of partner involvement in everyday problem solving performance to identify which relationship factors are most valuable for predicting long-term health and well-being.

Conclusions

One of the central themes of research examining everyday problem solving across the life span has been to identify the trajectory of change in performance throughout the years as we gain experience and knowledge while simultaneously displaying cognitive and physical declines. The impact of cognitive decline on everyday problem solving is most evident when examining the outcomes of studies that use tasks consisting of well-defined problems. Studies using tasks consisting of ill-defined problems produce mixed evidence of both decline and maintenance, depending on the manner with which problem-solving success is operationally defined. Based on more recent findings, however, it is clear that those individuals in their latter half of life are motivated by interpersonal factors that are important to young people but just are not prioritized to the same degree. Future research needs to further clarify the role that interpersonal interaction plays in promoting successful everyday problem solving. Outside of the lab environment, older adults continue to make autonomous choices while also working interdependently with members of their social network. Although cognitive and physical decline are inevitable to some degree for all of us, it seems that a shared decision space between close partners may go a long way to promote sustained well-being, physical health, and everyday cognition.

Conflicts of interest The author declares no conflicts of interest.

• For Parents

Math in Action: Problem Solving Skills for Everyday Life

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Author: BYJU’S Math Companion Tutor

How is math problem-solving commonly used in everyday life?

• Budgeting: Teach children how to manage allowances, savings, and expenses. Discussing budgeting strategies helps them make wise financial decisions.
• Cooking: Cooking involves precise measurements and conversions. Baking a cake, for instance, is a delicious way to apply math skills.
• Shopping: Explain how discounts, percentages, and sales tax work. Involve children in calculating discounts to make shopping both educational and fun.
• Travel planning: Planning a road trip requires understanding distance, time, and fuel consumption. Map reading and calculating travel expenses provide real-life math lessons.
• Time management: Teach children to use schedules and timetables. Managing their time effectively prepares them for future responsibilities.
• Problem-solving games: Encourage board games like chess, Sudoku, or logic puzzles. These games sharpen analytical thinking and math skills.

Math problem-solving skills that are essential for real-life challenges for children

• Critical thinking and analysis: Encourage children to dissect complex problems into smaller, manageable parts. This skill enables them to analyze situations, identify key variables, and approach challenges with clarity.
• Logical reasoning: Logical thinking helps your little one evaluate the relationships between different components of a problem. It guides them in determining cause-and-effect patterns and making informed decisions.
• Pattern recognition: Patterns are everywhere in our world, from nature’s symmetries to data trends. Teaching children to recognize and use patterns equips them with a powerful tool for problem-solving.
• Creative problem solving: Foster creativity by encouraging children to explore various approaches to a problem. This allows them to think outside the box and devise innovative solutions.
• Numerical fluency: Strong numerical skills are fundamental. Proficiency in addition, subtraction, multiplication, and division forms the basis for solving a wide range of everyday problems.
• Measurement and estimation: Understanding measurement units and making reasonable estimations are essential for tasks like cooking, DIY projects, and understanding sizes and quantities.
• Spatial awareness: Geometry plays a significant role in real-life situations, from arranging furniture to reading maps. Developing spatial skills enhances a child’s ability to navigate physical spaces efficiently.
• Time management: The skill of managing time effectively is essential for scheduling daily activities, setting goals, and adhering to deadlines.
• Probability and risk assessment: Understanding probability helps children assess risks and make decisions in uncertain situations, such as games of chance or investments.
• Measurement conversions: Being able to convert units, such as ounces to grams or miles to kilometers, is valuable in daily life.
• Algebraic thinking: Basic algebraic concepts can be applied to real-life situations, such as solving for an unknown variable in a recipe or a budget.

5 ways children use math in everyday life

• Money matters: Understanding and managing allowances, budgeting for spending, and calculating change while shopping.
• Time management: Reading clocks and calendars, scheduling activities, and tracking time spent on tasks.
• Homework and tests: Solving math problems for assignments and taking math tests and quizzes at school.
• Playing games : Board games, card games, and video games often involve counting, calculating scores, and making strategic moves.
• Sports and activities: Keeping score in sports, tracking statistics, and understanding game strategies that involve math.

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What Are Problem-Solving Skills? Definition and Examples

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Forage puts students first. Our blog articles are written independently by our editorial team. They have not been paid for or sponsored by our partners. See our full  editorial guidelines .

Why do employers hire employees? To help them solve problems. Whether you’re a financial analyst deciding where to invest your firm’s money, or a marketer trying to figure out which channel to direct your efforts, companies hire people to help them find solutions. Problem-solving is an essential and marketable soft skill in the workplace. 

So, how can you improve your problem-solving and show employers you have this valuable skill? In this guide, we’ll cover:

Problem-Solving Skills Definition

Why are problem-solving skills important, problem-solving skills examples, how to include problem-solving skills in a job application, how to improve problem-solving skills, problem-solving: the bottom line.

Problem-solving skills are the ability to identify problems, brainstorm and analyze answers, and implement the best solutions. An employee with good problem-solving skills is both a self-starter and a collaborative teammate; they are proactive in understanding the root of a problem and work with others to consider a wide range of solutions before deciding how to move forward. 

Examples of using problem-solving skills in the workplace include:

• Researching patterns to understand why revenue decreased last quarter
• Experimenting with a new marketing channel to increase website sign-ups
• Brainstorming content types to share with potential customers
• Testing calls to action to see which ones drive the most product sales
• Implementing a new workflow to automate a team process and increase productivity

Problem-solving skills are the most sought-after soft skill of 2022. In fact, 86% of employers look for problem-solving skills on student resumes, according to the National Association of Colleges and Employers Job Outlook 2022 survey . 

It’s unsurprising why employers are looking for this skill: companies will always need people to help them find solutions to their problems. Someone proactive and successful at problem-solving is valuable to any team.

“Employers are looking for employees who can make decisions independently, especially with the prevalence of remote/hybrid work and the need to communicate asynchronously,” Eric Mochnacz, senior HR consultant at Red Clover, says. “Employers want to see individuals who can make well-informed decisions that mitigate risk, and they can do so without suffering from analysis paralysis.”

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Problem-solving includes three main parts: identifying the problem, analyzing possible solutions, and deciding on the best course of action.

>>MORE: Discover the right career for you based on your skills with a career aptitude test .

Research is the first step of problem-solving because it helps you understand the context of a problem. Researching a problem enables you to learn why the problem is happening. For example, is revenue down because of a new sales tactic? Or because of seasonality? Is there a problem with who the sales team is reaching out to? 

Research broadens your scope to all possible reasons why the problem could be happening. Then once you figure it out, it helps you narrow your scope to start solving it. 

Analysis is the next step of problem-solving. Now that you’ve identified the problem, analytical skills help you look at what potential solutions there might be.

“The goal of analysis isn’t to solve a problem, actually — it’s to better understand it because that’s where the real solution will be found,” Gretchen Skalka, owner of Career Insights Consulting, says. “Looking at a problem through the lens of impartiality is the only way to get a true understanding of it from all angles.”

Decision-Making

Once you’ve figured out where the problem is coming from and what solutions are, it’s time to decide on the best way to go forth. Decision-making skills help you determine what resources are available, what a feasible action plan entails, and what solution is likely to lead to success.

On a Resume

Employers looking for problem-solving skills might include the word “problem-solving” or other synonyms like “ critical thinking ” or “analytical skills” in the job description.

“I would add ‘buzzwords’ you can find from the job descriptions or LinkedIn endorsements section to filter into your resume to comply with the ATS,” Matthew Warzel, CPRW resume writer, advises. Warzel recommends including these skills on your resume but warns to “leave the soft skills as adjectives in the summary section. That is the only place soft skills should be mentioned.”

On the other hand, you can list hard skills separately in a skills section on your resume .

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In a Cover Letter or an Interview

Explaining your problem-solving skills in an interview can seem daunting. You’re required to expand on your process — how you identified a problem, analyzed potential solutions, and made a choice. As long as you can explain your approach, it’s okay if that solution didn’t come from a professional work experience.

“Young professionals shortchange themselves by thinking only paid-for solutions matter to employers,” Skalka says. “People at the genesis of their careers don’t have a wealth of professional experience to pull from, but they do have relevant experience to share.”

Aaron Case, career counselor and CPRW at Resume Genius, agrees and encourages early professionals to share this skill. “If you don’t have any relevant work experience yet, you can still highlight your problem-solving skills in your cover letter,” he says. “Just showcase examples of problems you solved while completing your degree, working at internships, or volunteering. You can even pull examples from completely unrelated part-time jobs, as long as you make it clear how your problem-solving ability transfers to your new line of work.”

Learn How to Identify Problems

Problem-solving doesn’t just require finding solutions to problems that are already there. It’s also about being proactive when something isn’t working as you hoped it would. Practice questioning and getting curious about processes and activities in your everyday life. What could you improve? What would you do if you had more resources for this process? If you had fewer? Challenge yourself to challenge the world around you.

Think Digitally

“Employers in the modern workplace value digital problem-solving skills, like being able to find a technology solution to a traditional issue,” Case says. “For example, when I first started working as a marketing writer, my department didn’t have the budget to hire a professional voice actor for marketing video voiceovers. But I found a perfect solution to the problem with an AI voiceover service that cost a fraction of the price of an actor.”

Being comfortable with new technology — even ones you haven’t used before — is a valuable skill in an increasingly hybrid and remote world. Don’t be afraid to research new and innovative technologies to help automate processes or find a more efficient technological solution.

Collaborate

Problem-solving isn’t done in a silo, and it shouldn’t be. Use your collaboration skills to gather multiple perspectives, help eliminate bias, and listen to alternative solutions. Ask others where they think the problem is coming from and what solutions would help them with your workflow. From there, try to compromise on a solution that can benefit everyone.

If we’ve learned anything from the past few years, it’s that the world of work is constantly changing — which means it’s crucial to know how to adapt . Be comfortable narrowing down a solution, then changing your direction when a colleague provides a new piece of information. Challenge yourself to get out of your comfort zone, whether with your personal routine or trying a new system at work.

Put Yourself in the Middle of Tough Moments

Just like adapting requires you to challenge your routine and tradition, good problem-solving requires you to put yourself in challenging situations — especially ones where you don’t have relevant experience or expertise to find a solution. Because you won’t know how to tackle the problem, you’ll learn new problem-solving skills and how to navigate new challenges. Ask your manager or a peer if you can help them work on a complicated problem, and be proactive about asking them questions along the way.

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Step 1 of 3

Companies always need people to help them find solutions — especially proactive employees who have practical analytical skills and can collaborate to decide the best way to move forward. Whether or not you have experience solving problems in a professional workplace, illustrate your problem-solving skills by describing your research, analysis, and decision-making process — and make it clear that you’re the solution to the employer’s current problems. 

Image Credit: Christina Morillo / Pexels 

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10 Problem-solving strategies to turn challenges on their head

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What is an example of problem-solving?

What are the 5 steps to problem-solving, 10 effective problem-solving strategies, what skills do efficient problem solvers have, how to improve your problem-solving skills.

Problems come in all shapes and sizes — from workplace conflict to budget cuts.

Creative problem-solving is one of the most in-demand skills in all roles and industries. It can boost an organization’s human capital and give it a competitive edge. 

Problem-solving strategies are ways of approaching problems that can help you look beyond the obvious answers and find the best solution to your problem . 

Let’s take a look at a five-step problem-solving process and how to combine it with proven problem-solving strategies. This will give you the tools and skills to solve even your most complex problems.

Good problem-solving is an essential part of the decision-making process . To see what a problem-solving process might look like in real life, let’s take a common problem for SaaS brands — decreasing customer churn rates.

To solve this problem, the company must first identify it. In this case, the problem is that the churn rate is too high. 

Next, they need to identify the root causes of the problem. This could be anything from their customer service experience to their email marketing campaigns. If there are several problems, they will need a separate problem-solving process for each one. 

Let’s say the problem is with email marketing — they’re not nurturing existing customers. Now that they’ve identified the problem, they can start using problem-solving strategies to look for solutions. 

This might look like coming up with special offers, discounts, or bonuses for existing customers. They need to find ways to remind them to use their products and services while providing added value. This will encourage customers to keep paying their monthly subscriptions.

They might also want to add incentives, such as access to a premium service at no extra cost after 12 months of membership. They could publish blog posts that help their customers solve common problems and share them as an email newsletter.

The company should set targets and a time frame in which to achieve them. This will allow leaders to measure progress and identify which actions yield the best results.

Perhaps you’ve got a problem you need to tackle. Or maybe you want to be prepared the next time one arises. Either way, it’s a good idea to get familiar with the five steps of problem-solving. 

Use this step-by-step problem-solving method with the strategies in the following section to find possible solutions to your problem.

1. Identify the problem

The first step is to know which problem you need to solve. Then, you need to find the root cause of the problem. 

The best course of action is to gather as much data as possible, speak to the people involved, and separate facts from opinions. 

Once this is done, formulate a statement that describes the problem. Use rational persuasion to make sure your team agrees .

2. Break the problem down 

Identifying the problem allows you to see which steps need to be taken to solve it. 

First, break the problem down into achievable blocks. Then, use strategic planning to set a time frame in which to solve the problem and establish a timeline for the completion of each stage.

3. Generate potential solutions

At this stage, the aim isn’t to evaluate possible solutions but to generate as many ideas as possible. 

Encourage your team to use creative thinking and be patient — the best solution may not be the first or most obvious one.

Use one or more of the different strategies in the following section to help come up with solutions — the more creative, the better.

4. Evaluate the possible solutions

Once you’ve generated potential solutions, narrow them down to a shortlist. Then, evaluate the options on your shortlist. 

There are usually many factors to consider. So when evaluating a solution, ask yourself the following questions:

• Will my team be on board with the proposition?
• Does the solution align with organizational goals ?
• Is the solution likely to achieve the desired outcomes?
• Is the solution realistic and possible with current resources and constraints?
• Will the solution solve the problem without causing additional unintended problems?

5. Implement and monitor the solutions

Once you’ve identified your solution and got buy-in from your team, it’s time to implement it. 

But the work doesn’t stop there. You need to monitor your solution to see whether it actually solves your problem. 

Request regular feedback from the team members involved and have a monitoring and evaluation plan in place to measure progress.

If the solution doesn’t achieve your desired results, start this step-by-step process again.

There are many different ways to approach problem-solving. Each is suitable for different types of problems. 

The most appropriate problem-solving techniques will depend on your specific problem. You may need to experiment with several strategies before you find a workable solution.

Here are 10 effective problem-solving strategies for you to try:

• Use a solution that worked before
• Brainstorming
• Work backward
• Use the Kipling method
• Draw the problem
• Use trial and error
• Sleep on it
• Get advice from your peers
• Use the Pareto principle
• Add successful solutions to your toolkit

Let’s break each of these down.

1. Use a solution that worked before

It might seem obvious, but if you’ve faced similar problems in the past, look back to what worked then. See if any of the solutions could apply to your current situation and, if so, replicate them.

2. Brainstorming

The more people you enlist to help solve the problem, the more potential solutions you can come up with.

Use different brainstorming techniques to workshop potential solutions with your team. They’ll likely bring something you haven’t thought of to the table.

3. Work backward

Working backward is a way to reverse engineer your problem. Imagine your problem has been solved, and make that the starting point.

Then, retrace your steps back to where you are now. This can help you see which course of action may be most effective.

4. Use the Kipling method

This is a method that poses six questions based on Rudyard Kipling’s poem, “ I Keep Six Honest Serving Men .” 

• What is the problem?
• Why is the problem important?
• When did the problem arise, and when does it need to be solved?
• How did the problem happen?
• Where is the problem occurring?
• Who does the problem affect?

Answering these questions can help you identify possible solutions.

5. Draw the problem

Sometimes it can be difficult to visualize all the components and moving parts of a problem and its solution. Drawing a diagram can help.

This technique is particularly helpful for solving process-related problems. For example, a product development team might want to decrease the time they take to fix bugs and create new iterations. Drawing the processes involved can help you see where improvements can be made.

6. Use trial-and-error

A trial-and-error approach can be useful when you have several possible solutions and want to test them to see which one works best.

7. Sleep on it

Finding the best solution to a problem is a process. Remember to take breaks and get enough rest . Sometimes, a walk around the block can bring inspiration, but you should sleep on it if possible.

A good night’s sleep helps us find creative solutions to problems. This is because when you sleep, your brain sorts through the day’s events and stores them as memories. This enables you to process your ideas at a subconscious level. 

If possible, give yourself a few days to develop and analyze possible solutions. You may find you have greater clarity after sleeping on it. Your mind will also be fresh, so you’ll be able to make better decisions.

8. Get advice from your peers

Getting input from a group of people can help you find solutions you may not have thought of on your own. 

For solo entrepreneurs or freelancers, this might look like hiring a coach or mentor or joining a mastermind group. 

For leaders , it might be consulting other members of the leadership team or working with a business coach .

It’s important to recognize you might not have all the skills, experience, or knowledge necessary to find a solution alone. 

9. Use the Pareto principle

The Pareto principle — also known as the 80/20 rule — can help you identify possible root causes and potential solutions for your problems.

Although it’s not a mathematical law, it’s a principle found throughout many aspects of business and life. For example, 20% of the sales reps in a company might close 80% of the sales. 

You may be able to narrow down the causes of your problem by applying the Pareto principle. This can also help you identify the most appropriate solutions.

10. Add successful solutions to your toolkit

Every situation is different, and the same solutions might not always work. But by keeping a record of successful problem-solving strategies, you can build up a solutions toolkit. 

These solutions may be applicable to future problems. Even if not, they may save you some of the time and work needed to come up with a new solution.

Improving problem-solving skills is essential for professional development — both yours and your team’s. Here are some of the key skills of effective problem solvers:

• Critical thinking and analytical skills
• Communication skills , including active listening
• Decision-making
• Planning and prioritization
• Emotional intelligence , including empathy and emotional regulation
• Time management
• Data analysis
• Research skills
• Project management

And they see problems as opportunities. Everyone is born with problem-solving skills. But accessing these abilities depends on how we view problems. Effective problem-solvers see problems as opportunities to learn and improve.

Ready to work on your problem-solving abilities? Get started with these seven tips.

1. Build your problem-solving skills

One of the best ways to improve your problem-solving skills is to learn from experts. Consider enrolling in organizational training , shadowing a mentor , or working with a coach .

2. Practice

Practice using your new problem-solving skills by applying them to smaller problems you might encounter in your daily life. 

Alternatively, imagine problematic scenarios that might arise at work and use problem-solving strategies to find hypothetical solutions.

3. Don’t try to find a solution right away

Often, the first solution you think of to solve a problem isn’t the most appropriate or effective.

Instead of thinking on the spot, give yourself time and use one or more of the problem-solving strategies above to activate your creative thinking. 

4. Ask for feedback

Receiving feedback is always important for learning and growth. Your perception of your problem-solving skills may be different from that of your colleagues. They can provide insights that help you improve. 

5. Learn new approaches and methodologies

There are entire books written about problem-solving methodologies if you want to take a deep dive into the subject. 

We recommend starting with “ Fixed — How to Perfect the Fine Art of Problem Solving ” by Amy E. Herman. 

6. Experiment

Tried-and-tested problem-solving techniques can be useful. However, they don’t teach you how to innovate and develop your own problem-solving approaches. 

Sometimes, an unconventional approach can lead to the development of a brilliant new idea or strategy. So don’t be afraid to suggest your most “out there” ideas.

7. Analyze the success of your competitors

Do you have competitors who have already solved the problem you’re facing? Look at what they did, and work backward to solve your own problem. 

For example, Netflix started in the 1990s as a DVD mail-rental company. Its main competitor at the time was Blockbuster. 

But when streaming became the norm in the early 2000s, both companies faced a crisis. Netflix innovated, unveiling its streaming service in 2007. 

If Blockbuster had followed Netflix’s example, it might have survived. Instead, it declared bankruptcy in 2010.

Use problem-solving strategies to uplevel your business

When facing a problem, it’s worth taking the time to find the right solution. 

Otherwise, we risk either running away from our problems or headlong into solutions. When we do this, we might miss out on other, better options.

Use the problem-solving strategies outlined above to find innovative solutions to your business’ most perplexing problems.

If you’re ready to take problem-solving to the next level, request a demo with BetterUp . Our expert coaches specialize in helping teams develop and implement strategies that work.

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Elizabeth Perry, ACC

Elizabeth Perry is a Coach Community Manager at BetterUp. She uses strategic engagement strategies to cultivate a learning community across a global network of Coaches through in-person and virtual experiences, technology-enabled platforms, and strategic coaching industry partnerships. With over 3 years of coaching experience and a certification in transformative leadership and life coaching from Sofia University, Elizabeth leverages transpersonal psychology expertise to help coaches and clients gain awareness of their behavioral and thought patterns, discover their purpose and passions, and elevate their potential. She is a lifelong student of psychology, personal growth, and human potential as well as an ICF-certified ACC transpersonal life and leadership Coach.

8 creative solutions to your most challenging problems

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When it comes to everyday problems in your life, some are easier to fix than you might think, like not having enough lighting in your kitchen or losing items in your purse. Amazon is a handy site when looking for solutions, as they have tons of products to help solve those pesky common issues.

In this list, you’ll find a bunch of simple life solutions , at home and on the go. In the kitchen, you can improve your dish-drying setup with this silicone drying mat that’s easy to clean. Make it easier to add sugar to your coffee or tea with this glass container that dispenses from the bottom.

Forgetting where to be and when? Keep your appointments and events more organized with this magnetic whiteboard calendar that’s perfect for attaching to your fridge. Is your closet becoming an issue? You can better organize your shoes with this bamboo shoe rack that looks great wherever it’s placed.

Whether your problems are in the kitchen, the closet, or your own purse, you’ll find plenty of solutions that make your life just a little bit easier in this list.

1 Problem: You Can’t Reach The Candle Wick Solution: This Electric Lighter With A Flexible Neck

After you’ve burned a candle for a while, it can be tricky to light without burning your hand. This electric lighter has a long, bendable neck, so you can adjust it based on the size and depth of your candle. Since it’s electric, the lighter is rechargeable using a USB charging port and doesn’t use lighter fluid.

2 Problem: Your Half-Eaten Bag Of Chips Went Stale Solution: This Mini Snack Sealer

Keep your snacks fresh with this mini bag sealer . The device uses heat to reseal the packaging of chips, cookies, and other snacks, so they don’t go stale. It heats up in just a few seconds and seals almost instantly. It’s also lightweight, so you can take it to work or while traveling.

3 Problem: Necklaces Are Getting Tangled Solution: This Clasp That Keeps Necklaces Separated

A layered necklace look is always chic — unless, of course, your necklaces get tangled. This clasp allows you to clip three necklaces onto little rings that keep the chains separated. It clasps together with a magnet, so it’s easy to take on and off. It’s also great for bracelets and comes in silver and gold.

4 Problem: Inside Your Bag Is A Mess Solution: This Purse Organizer With 10 Pockets

Having an organized purse is a rare skill that most of us don’t possess — it doesn’t help that many bags (looking at you totes!) don’t even have any inner pockets or storage. This purse organizer insert has 10 pockets, including a zippered one, so you can keep your wallet, makeup, gum, and other items in their own pockets. The organizer is made from a sturdy felt material and comes in 19 colors and designs, including snakeskin and polka dot.

5 Problem: Burning Your Fingers & Forearms Solution: These Silicone Oven Mitts With An Extra Thick Lining

When it comes to kitchen tools, oven mitts are not somewhere you want to skimp, since they protect you from burning yourself. These silicone oven mitts have an extra thick padded lining, so they keep your hands and arms safe, but they also have a silicone layer on the outside which makes them heat resistant up to 450 degrees. Aside from the brilliant red shade featured, you can also buy them in aqua, gray, and black.

6 Problem: Charging Cables Everywhere Solution: This 3-in-1 Charging Station

Keep all your devices at 100% with this 3-in-1 charging station. With a spot for your phone, smartwatch, and earbuds, this charging station is perfect for keeping in your home or office. It uses wireless charging, so it also means you won’t have a huge mess of cords. It’s compatible with most smart devices, including Apple, Android, and Samsung.

7 Problem: Poorly Lit Cabinets & Closets Solution: These Lights That Fit Under The Cabinet

Add more light to your closets, cabinets — or anywhere that needs a little extra light — without having to install a whole light fixture. These under the cabinet lights come with adhesive tape, so they’re easy to install. A remote is included, so the brightness can be easily adjusted.

8 Problem: Bugs Getting In The House Solution: This Screen Door With A Magnetic Closure

When the weather’s nice out, it’s the perfect time to leave your door open to let the warm breeze in. Of course, the open air comes with bugs — unless you have one of these magnetic screen doors . Made from a fine mesh, the screen lets air in but keeps bugs and debris out. It also has a magnetic closure so you can enter and exit even if your hands are full.

9 Problem: Running Out Of Paper Towels Solution: These Reusable Dish Cloths

Paper towels are handy, but they eventually run out. These Swedish dishcloths , on the other hand, are machine washable and reusable up to 100 times. Plus they come in a pack of 10, so they can take the place of several paper towel rolls. The cloths are stiff when dry but become soft and pliable when wet.

10 Problem: Overbooking Your Schedule Solution: Getting An Accessible Whiteboard Calendar

If you have a hard time keeping track of your schedule, then this magnetic whiteboard calendar will come in handy. The calendar is ideal for attaching to the fridge, or any other magnetic surface. It can be filled in and erased each month to keep track of appointments and events. You can use it immediately, as it comes with six dry erase markers.

11 Problem: Having Noisy Housemates Solution: This Door Insulator That Blocks Out Sound

Keep your room quiet with this door draft stopper that blocks out noise and insulates. This stopper has a velcro strip that makes it more adjustable. It also helps keep cold air out and keep heat in. For those with noisy roommates, this can offer a bit more peace at a low price.

12 Problem: Losing Your Luggage Solution: This Luggage Tag With Your Initial

It can be hard to keep track of your luggage when so many suitcases look alike. Set yours apart with this luggage tag that has a big colorful letter on it to match your initial on your first or last name. The tag is made of rubber, so it won’t be easily damaged, and includes a card for writing down your contact information in the chance your luggage gets misplaced.

13 Problem: Not Being Able To Properly Clean Your Reusable Straws (Or Not Having Them At All) Solution: These Reusable Straws That Come With A Cleaning Tool

Reusable straws are great for reducing single-use plastic, but they can be a pain to clean. These silicone straws come with their own cleaning brush that gets into the narrow cavity of the straws. They can be used for hot and cold drinks and are safe to throw in the dishwasher. They also come in a 2-pack, with 20 straws total.

14 Problem: Breaking Dishes Because You Don’t Have A Proper Place To Dry Them Solution: This Silicone Dish-Drying Mat

If you’re playing Jenga with your dishes when you’re setting them on your counter to dry then chances are you’ve broken more than a few. But that is where this silicone dish drying mat comes in: It’s soft but non-slip so you can set your wet dishes on it without them slipping around, cracking, and shattering. It is easy to clean, so it won’t build up dirt and grime like a cloth drying mat. It’s dishwasher safe and heat-resistant, so you can also use it to support hot plates.

15 Problem: Getting Syrup Or Honey All Over Your Hands Solution: This Dispenser That’s Keeps Your Hands From Getting All Sticky

When it gets on your hands, syrup seems to multiply — making everything you touch sticky for the rest of the day. But with this syrup/honey dispenser , you can keep your hands clean. The dispenser has a lever you can pull that releases syrup from the bottom of the bottle. Dispensing from the bottom also means you’ll be able to get every last drop of the sticky sweet liquid sugar without having to shake the bottle or awkwardly balance it on its head while it slowly drips towards the opening at the top. This dispenser comes with a stand with a reservoir to catch any syrup drips.

16 Problem: Running Out Of Aluminum Foil Solution: This Reusable Beeswax Food Wrap

Never worry about running out of foil or plastic wrap again with this reusable food wrap made from beeswax. These wraps are moldable to your needs, so they can cover a large bowl of salad or wrap around a leftover piece of fruit. They’re washable and reusable, plus biodegradable, so they’re better for the environment.

17 Problem: Your Rugs Are Sliding Around Solution: These Rug Pads That Are Non-Slip

Keep your rugs from slipping around the floor with this rug pad that can be cut to fit any size you need. The pad is made from a non-slip foam that can be used on wood floors, tile, and other materials. It automatically sticks to the rug and the floor, so there’s no special installation required.

18 Problem: There’s Not Enough Storage Space In The Living Room Solution: This Ottoman With Hidden Storage

Use this storage ottoman to hold blankets, books, pillows, and other items that don’t necessarily have a good home in your living room. The ottoman has a faux leather cushioned top, which is perfect for resting your feet on. The lid is removable with a collapsible base.

19 Problem: Figuring Out Where To Put Your Phone During Workouts Solution: These Leggings with Built-In Pockets

Workout clothes don’t always have pockets for holding your phone the way a pair of jeans does. Luckily, these high-waisted leggings have pockets on the thigh, so your phone will be safe and secure while you’re going on a walk or run. They’re made from a soft, stretchy fabric made from a spandex and polyester blend for maximum comfort.

• Available sizes: One Size and One Size Plus
• Available colors: 51

20 Problem: It’s Too Bright To Nap Solution: These Window Shades That Are Easy To Install

Darken your room without the hassle of professionally installing shades. This set of six window shades comes with sticky adhesive for easy installation. They can also be cut to size, so you can fit them exactly to your window. They also come with clips to help you easily adjust the height.

21 Problem: You’re Not Able To Find Your Keys After Dropping Them Solution: This Magnetic Pickup Tool With A Flashlight

Dropping your keys in the dark can be a huge pain, but this magnetic pickup tool will help save the day. The tool has a long arm, bright flashlight, and magnetic surface to pick up whatever you dropped. Use it to safely collect anything metal, or magnetically attach it to a metal surface, like the hood of your car, for better vision.

22 Problem: There’s No Way To Store Canned Pet Food Solution: These Covers That Fit Multiple Can Sizes

I recently started feeding my dog canned wet food, and having can covers makes it so much easier. This set of five covers is made from food-safe silicone and fits three different sizes of cans. They’re dishwasher safe and come in an array of colors. They also have a cute paw tab that makes removal a breeze.

23 Problem: You Slept In And It’s Too Late To Get Coffee Solution: This Milk Frother That Upgrades Your Homemade Lattes

We can’t all get up early to make it to the coffee shop before work. Make your own fancy latte at home with this milk frother . The lightweight device is easy to use and turns milk into foam in just a few seconds. It’s portable, so you can even take it with you to work or on vacation. It also comes with its own metal stand.

24 Problem: There’s Nowhere To Put Your Essentials When Going For A Walk Solution: This Water-Resistant Fanny Pack

Sometimes you want to go on a walk or hike, but don’t want to drag around a heavy backpack. Did you know that fanny packs are back in style? This fanny pack is the perfect option for holding your phone, wallet, keys, and other essentials. The fanny pack is made from durable nylon that is water-resistant. It has six zippered pockets, so your things will be safe and sound.

25 Problem: Breaking Eggs When Storing Them In The Fridge Solution: These Sturdy Egg Trays That Will Keep Them Safe

Cardboard egg cartons are flimsy — stack them in your fridge and chances are you’re probably going to end up breaking an egg or two — which is why these plastic egg cartons are so genius. They’re sturdy and stackable, so you can organize your fridge and protect your eggs. The trays come in a pack of two and hold 12 eggs each.

26 Problem: You’re Dropping Nails & Screws While Working Solution: This Magnetic Wristband That Holds Your Tools

If you like to spend time working on DIY projects or doing repairs, then this magnetic wristband will come in handy. The wristband attaches with velcro and is handy for holding screws, nails, or other tools you’re using while working. The wristband is equipped with 10 strong magnets, but it’s still lightweight.

27 Problem: You’re Spending Too Much On Cold Brew Solution: This Large Cold Brew Maker & Dispenser

Save yourself time in the morning and ditch the coffee shop. This cold brew maker has a stainless steel filter and holds up to 12 cups, so you can make cold brew for the whole week. Just put your favorite coffee grounds in the filter, add water, and put it in the fridge to steep. It can also be used for making iced tea. It comes in two sizes — two liters and a gallon.

28 Problem: You Always Drop Your Soap In The Shower Solution: This Soap Holder That Gives You More Grip

A bar of soap can be hard to hold onto in the shower, but these soap saver bags are easier to grip. The five-bag set is made from natural sisal plants, which help the soap lather and produce foam. The bags are also ideal for when the bar of soap gets too small, but you’re not ready to throw it out just yet.

29 Problem: There’s Nowhere To Store Leftover Food Solution: This Set Of 24 Food Storage Containers

A good set of food containers serve as one of the most useful tools in any kitchen. These glass storage containers come in a set of 24, with a range of sizes to fit everything from leftover salmon to half a lemon. The containers have an airtight seal that is leakproof, so it’s perfect for storing leftovers to take for lunch.

30 Problem: The Sheets Keep Coming Off The Bed Solution: These Straps That Keep Your Sheets Secure

It’s a pain when your fitted sheets don’t stay fitted. These sheet holder straps clip onto the corner of your sheets, holding them in place so they don’t slip off. The straps have metal clips and elastic bands, which are easy to install. They’re basically like little suspenders for your sheets.

31 Problem: You Can’t Find Your Shoes Solution: This Shoe Rack That Keeps Them Organized

If you have a habit of misplacing your shoes around the house, then this shoe shelf will help keep them organized. Made from sturdy bamboo, the shelf holds three or four pairs of shoes on each tier and is perfect for keeping in the entryway or bedroom. If you need three or more tiers, Amazon offers those options as well.

32 Problem: Misplacing Your Keys Solution: This Bluetooth Tracker That Attaches To Your Keychain

Attach this Tile Bluetooth tracker to your keyring and you won’t have to dig through all your purses to find your keys. The small, lightweight tracker connects to the Tile app on your phone, so it can help you find your keys in your home, or if you left them in your bag somewhere while out and about. It’s incredible how much time you’ll save (and how many appointments you’ll be on time for.)

33 Problem: Uneven Winged Eyeliner Solution: This Winged Eyeliner Stamp

Unless you’re a professional makeup artist, getting the perfect winged eyeliner can be tricky. This eyeliner stamp makes it so much easier by literally stamping the shape of the wing on the corner of your eye. Each liner has two ends, one for the stamp and one with a fine point for refining the edges. It’s also waterproof and smudge-proof.

34 Problem: Forgetting A Good Pillow While Traveling Solution: A Great Travel Pillow You Can Store In Your Car

One of the worst feelings in the world is needing a pillow, but not having a pillow. Luckily, you can prep ahead of time by storing this compressible memory foam pillow in the trunk of your car. It doesn’t take up a lot of room but will offer a ton of comfort in a pinch. It’s also machine washable.

35 Problem: Getting Sauce On The Counter Solution: This Spoon Rest With 4 Slots

The problem with most spoon rests is that they only hold one spoon. This silicone utensil rest has four slots, which is perfect if you’re the kind of cook (like me) who cooks with a spatula and two spoons at the same time. The utensil rest has a large drip pad to catch any sauce or liquid that drips off. The best part is that you can easily throw it in the dishwasher to clean.

36 Problem: Avocados Going Bad Too Quickly Solution: This Avocado Safer That Keeps Them Fresh

Avocados are an odd shape, so they don’t always fit in a typical storage container. This avocado saver is designed to preserve the fruit with an indent designed to fit around the pit (leaving the pit in helps it from going brown) The container also has an adjustable strap to keep the avocado in place, like a little seatbelt.

37 Problem: Having Too Much Produce You Didn’t Finish Solution: This Silicone Food Savers That Keep Produce Fresh

These silicone food huggers are a versatile kitchen accessory and can be used to preserve half an apple, a partially used onion, or as a replacement lid on a jar. They come in a set of five of varying sizes, and are a great solution for replacing plastic wrap or foil, and help reduce single-use plastic in your home.

38 Problem: You Can’t Get All The Toothpaste Out Solution: These Tube Squeezers Get Out Every Last Drop

Get the most out of your toothpaste with these tube squeezers . Just like the name implies, these handy tools squeeze out every last drop from the tube, and can also be used for makeup, lotion, or anything else that comes in a tube. They come in a pack of four, so you’ll have plenty at hand.

39 Problem: You Can’t Find Your Earrings Solution: This Jewelry Organizer With 80 Pockets

Make it easier to find the pair of earrings or that necklace you want to wear with this jewelry organizer . With 80 clear vinyl pockets, this organizer makes it easy to find the piece you’re looking for while also keeping them from getting tangled with each other. The organizer also has a hook at the top, making it easy to hang.

40 Problem: The Duvet Getting Scrunched Up In Its Cover Solution: These Magnetic Clips That Keep Your Duvet Secure

Keeping your duvet in place inside a duvet cover is no easy feat. Luckily, these magnetic duvet clips are an easy solution. The clips secure your duvet with a magnetic pin, and each pin can secure up to 10 pounds. They come in a set of eight, so you can secure the whole edge.

41 Problem: Accidentally Shrinking Cotton Clothes Solution: This Folding Drying Rack

Not all fabrics are suitable for a dryer. This Amazon Basics laundry rack is perfect for hanging shrinkable fabrics like cotton, delicate undergarments, or other items that you want to air-dry. The steel rack can support up to 32 pounds and is collapsible, so you can store it away when not in use.

42 Problem: Leaving The Lights On Solution: These Smart Lightbulbs You Can Adjust With Your Phone

Once you leave the house, there’s no way to know whether or not you left any lights on. That is, unless you use these smart lightbulbs that you can control from your phone. These bulbs connect to an app (and can even connect to Alexa and Google Home) where you can turn them on and off, adjust the brightness, and even change the color of the light.

43 Problem: Losing Jewelry While Traveling Solution: This Portable Jewelry Organizer

If you take your favorite jewelry with you on a trip, then you’re gonna want a safe place to store it. This travel jewelry organizer has compartments to hold rings, necklaces, and other assorted jewelry. It has a zipper closure and is compact enough to fit in a purse. Plus, it comes in 17 colors.

44 Problem: Pants That Are Too Long Solution: A Hem Tape That Quickly Adjusts Length

Adjust the length of your pants without going to a tailor using this double-sided clothing tape . It’s safe to use on both your skin and clothing without damaging either. It can also be used to keep clothing in place, like a dress strap or a low-cut blouse. Each pack comes with 50 pieces of tape.

45 Problem: Wrinkly Clothing Solution: A Spray That Removes Wrinkles Without An Iron

It can be a whole ordeal to pull out the iron just to remove a few wrinkles. This crease release spray works without an iron. Just spray it on the fabric and smooth your hand over it to remove the wrinkles. Plus, it has a clean, fresh laundry scent.

22 Examples of Mathematics in Everyday Life

Let’s read further to know the real-life situations where maths is applied.

1. Making Routine Budgets

How much should I spend today? When I will be able to buy a new car? Should I save more? How will I be able to pay my EMIs? Such thoughts usually come into our minds. The simple answer to such type of question is maths. We prepare budgets based on simple calculations with the help of simple mathematical concepts. So, we can’t say, I am not going to study maths ever! Everything which is going around us is somehow related to maths only.

Application: 

• Basic mathematical operations (addition, subtraction, multiplication, and division)
• Calculation of percentage
• Arithmetic calculations

2. Construction Purpose

You know what, maths is the basis of any construction work. A lot of calculations, preparations of budgets, setting targets, estimating the cost, etc., are all done based on maths. If you don’t believe it, ask any contractor or construction worker, and they will explain as to how important maths is for carrying out all the construction work.

Application:

• Preparing budgets
• Taking measurements
• Estimating the cost and profit
• Calculus and Statistics
• Trigonometry

3. Exercising and Training

I should reduce some body fat! Will I be able to achieve my dream body ever? How? When? Will I be able to gain muscles? Here, the simple concept that is followed is maths. Yes! based on simple mathematical concepts, we can answer to above-mentioned questions. We set our routine according to our workout schedule, count the number of repetitions while exercising, etc., just based on maths.

• Basic Mathematical Operations (additions, subtraction, multiplication, and division)
• Logical and Analogical Reasoning

4. Interior Designing

Interior designing seems to be a fun and interesting career but, do you know the exact reality? A lot of mathematical concepts, calculations, budgets, estimations, targets, etc., are to be followed to excel in this field. Interior designers plan the interiors based on area and volume calculations to calculate and estimate the proper layout of any room or building. Such concepts form an important part of maths.

• Ratios and Percentages
• Mathematical Operations

5. Fashion Designing

Just like interior design, maths is also an essential concept of fashion design. From taking measurements, estimating the quantity and quality of clothes, choosing the color theme, and estimating the cost and profit, to producing cloth according to the needs and tastes of the customers, maths is followed at every stage.

• Basic Mathematical Operations
• Rations and Percentages

6. Shopping at Grocery Stores and Supermarkets

The most obvious place where you would see the application of basic mathematical concepts is your neighborhood grocery store and supermarket. The schemes like ‘Flat 50% off, ‘Buy one get one free, etc., are seen in most of the stores. Customers visit the stores, see such schemes, estimate the quantity to be bought, the weight, the price per unit, discount calculations, and finally the total price of the product, and buy it. The calculations are done based on basic mathematical concepts. Thus, here also, maths forms an important part of our daily routine.

• Ratio and Percentage

7. Cooking and Baking

In your kitchen also, the maths is performed. For cooking or baking anything, a series of steps are followed, telling us how much of the quantity is to be used for cooking, the proportion of different ingredients, methods of cooking, the cookware to be used, and many more. Such are based on different mathematical concepts. Indulging children in the kitchen while cooking anything, is a fun way to explain maths as well as basic cooking methods.

• Mathematical Algorithm
• Ratios and Proportions

Maths improves the cognitive and decision-making skills of a person. Such skills are very important for a sportsperson because by this he can take the right decisions for his team. If a person lacks such abilities, he won’t be able to make correct estimations. So, maths also forms an important part of the sports field.

• Probability
• Mathematical Operations and Algorithm
• Logical Reasoning
• Game Theory

9.  Management of Time

Now managing time is one of the most difficult tasks which is faced by a lot of people. An individual wants to complete several assignments in a limited time. Not only the management, but some people also are not even able to read the timings on an analog clock. Such problems can be solved only by understanding the basic concepts of maths. Maths not only helps us to understand the management of time but also to value it.

10. Driving

‘Speed, Time, and Distance’ are all these three things that are studied in mathematical subjects, which are the basics of driving irrespective of any mode of transportation. Maths helps us to answer the following question;

• How much should be the speed to cover any particular distance?
• How much time would be taken?
• Whether to turn left or right?
• When to stop the car?
• When to increase or decrease the speed?
• Logical reasoning
• Numerical Reasoning

11. Automobiles Industry

The different car manufacturing companies produce cars based on the demands of the customers. Every company has its category of cars ranging from microcars to luxury SUVs. In such companies, basic mathematical operations are being applied to gain knowledge about the different demands of the customers.

12. Computer Applications

Ever wondered how a computer works? How easily it completes every task in a proper series of actions? The simple reason for this is the application of maths. The fields of mathematics and computing intersect both in computer science. The study of computer applications is next to impossible without maths. Concepts like computation, algorithms and many more forms the base for different computer applications like PowerPoint, word, excel, etc. are impossible to run without maths.

Applications:

• Computation
• Coding Methods
• Cryptography

13. Planning a Trip

We all are bored with our monotonous life and we wish to go on long vacations. For this, we have to plan things accordingly. We need to prepare the budget for the trip, the number of days, the destinations, and hotels adjust our other work accordingly, and many more. Here comes the role of maths. Basic mathematical concepts and operations are required to be followed to plan a successful trip.

14. Hospitals

Every Hospital has to make the schedule the timings of the doctors available, the systematic methods of conducting any major surgery, keeping the records of the patients, records of the success rate of surgeries, number of ambulances required, training for the use of medicines to nurses, prescriptions, and scheduling all tasks, etc. All these are done based on Mathematical concepts.

• Body Mass Index

15. Video Games

Playing video games is one of the most favorite entertainment activities done all over the world, irrespective of the fact that whether you are a kid or an adult. Students usually skip their maths classes to play video games. But, do you know here also they are learning maths? Here, they learn about the different steps and techniques to be followed to win any game. Not only while playing, but the engineers who introduce different games for people also follow the different mathematical concepts.

16. Weather Forecasting

The weather forecasting is all done based on the probability concept of maths. Through this, we get to know about the weather conditions like whether it’s going to be a sunny day or rainfall will come So, next time you plan your outing, don’t forget to see the weather forecasting.

Application:    

17. Base of Other Subjects

Though maths is itself a unique subject. But, you would be surprised to know that it forms the base for every subject. The subjects like physics, chemistry, economics, history, accountancy, and statistics every subject is based upon maths. So, next time you say, “I’m not going to study this maths subject ever!” remember, this subject will not going to leave you ever.

• Operations Research
• Linear Programming

18. Music and Dance

Listening to music and dancing is one of the most common hobbies of children. Here also, they learn maths while singing and learning different dance steps. Coordination in any dance can be gained by simple mathematical steps.

19. Manufacturing Industry

The part of maths called ‘Operations Research is an important concept that is being followed at every manufacturing unit. This concept of maths gives the manufacturer a simple idea of performing several tasks under the manufacturing unit like,

• What quantity is to be produced?
• What methods are to be followed?
• How to increase production?
• How the cost of production can be reduced?
• Removing unnecessary tasks.
• Following methods like target costing, ABC costing, cost-profit budgeting, and many more.
• Ratios and Probability

20. Planning of Cities

Urban planning includes the concepts of budgeting, planning, setting targets, and many more which all forms part of mathematics. No activity is possible without maths.

21. Problem-solving skills

Problem-solving skills are one of the most important skills which every individual should possess to be successful in life. Such skills help the individual in taking correct decisions in life, let it be professional or personal. This is all done when the person has the correct knowledge of basic mathematical concepts.

• Mathematical Reasoning

22. Marketing

The marketing agencies make the proper plans as to how to promote any product or service. The tasks like promoting a product online, use of social media platforms, following different methods of direct and indirect marketing, door-to-door sales, sending e-mails, making calls, and providing several schemes like ‘Buy one get one free, ‘Flat 50% off, offering discounts on special occasions, etc. are all done based on simple mathematical concepts. Thus, maths is present everywhere.

• Percentages
• Mathematical Operations  

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16 comments.

very good and rare found examples are here to be learned here.

Really informative and knowledgeable

I never realized how much math we use every day.

Example of cost

It nice and great! Idea

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Ideas Made to Matter

How to use algorithms to solve everyday problems

Kara Baskin

May 8, 2017

How can I navigate the grocery store quickly? Why doesn’t anyone like my Facebook status? How can I alphabetize my bookshelves in a hurry? Apple data visualizer and MIT System Design and Management graduate Ali Almossawi solves these common dilemmas and more in his new book, “ Bad Choices: How Algorithms Can Help You Think Smarter and Live Happier ,” a quirky, illustrated guide to algorithmic thinking. 

For the uninitiated: What is an algorithm? And how can algorithms help us to think smarter?

An algorithm is a process with unambiguous steps that has a beginning and an end, and does something useful.

Algorithmic thinking is taking a step back and asking, “If it’s the case that algorithms are so useful in computing to achieve predictability, might they also be useful in everyday life, when it comes to, say, deciding between alternative ways of solving a problem or completing a task?” In all cases, we optimize for efficiency: We care about time or space.

Note the mention of “deciding between.” Computer scientists do that all the time, and I was convinced that the tools they use to evaluate competing algorithms would be of interest to a broad audience.

Why did you write this book, and who can benefit from it?

All the books I came across that tried to introduce computer science involved coding. My approach to making algorithms compelling was focusing on comparisons. I take algorithms and put them in a scene from everyday life, such as matching socks from a pile, putting books on a shelf, remembering things, driving from one point to another, or cutting an onion. These activities can be mapped to one or more fundamental algorithms, which form the basis for the field of computing and have far-reaching applications and uses.

I wrote the book with two audiences in mind. One, anyone, be it a learner or an educator, who is interested in computer science and wants an engaging and lighthearted, but not a dumbed-down, introduction to the field. Two, anyone who is already familiar with the field and wants to experience a way of explaining some of the fundamental concepts in computer science differently than how they’re taught.

I’m going to the grocery store and only have 15 minutes. What do I do?

Do you know what the grocery store looks like ahead of time? If you know what it looks like, it determines your list. How do you prioritize things on your list? Order the items in a way that allows you to avoid walking down the same aisles twice.

For me, the intriguing thing is that the grocery store is a scene from everyday life that I can use as a launch pad to talk about various related topics, like priority queues and graphs and hashing. For instance, what is the most efficient way for a machine to store a prioritized list, and what happens when the equivalent of you scratching an item from a list happens in the machine’s list? How is a store analogous to a graph (an abstraction in computer science and mathematics that defines how things are connected), and how is navigating the aisles in a store analogous to traversing a graph?

Nobody follows me on Instagram. How do I get more followers?

The concept of links and networks, which I cover in Chapter 6, is relevant here. It’s much easier to get to people whom you might be interested in and who might be interested in you if you can start within the ball of links that connects those people, rather than starting at a random spot.

You mention Instagram: There, the hashtag is one way to enter that ball of links. Tag your photos, engage with users who tag their photos with the same hashtags, and you should be on your way to stardom.

What are the secret ingredients of a successful Facebook post?

I’ve posted things on social media that have died a sad death and then posted the same thing at a later date that somehow did great. Again, if we think of it in terms that are relevant to algorithms, we’d say that the challenge with making something go viral is really getting that first spark. And to get that first spark, a person who is connected to the largest number of people who are likely to engage with that post, needs to share it.

With [my first book], “Bad Arguments,” I spent a month pouring close to $5,000 into advertising for that project with moderate results. And then one science journalist with a large audience wrote about it, and the project took off and hasn’t stopped since.

What problems do you wish you could solve via algorithm but can’t?

When we care about efficiency, thinking in terms of algorithms is useful. There are cases when that’s not the quality we want to optimize for — for instance, learning or love. I walk for several miles every day, all throughout the city, as I find it relaxing. I’ve never asked myself, “What’s the most efficient way I can traverse the streets of San Francisco?” It’s not relevant to my objective.

Algorithms are a great way of thinking about efficiency, but the question has to be, “What approach can you optimize for that objective?” That’s what worries me about self-help: Books give you a silver bullet for doing everything “right” but leave out all the nuances that make us different. What works for you might not work for me.

Which companies use algorithms well?

When you read that the overwhelming majority of the shows that users of, say, Netflix, watch are due to Netflix’s recommendation engine, you know they’re doing something right.

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How is Algebra Used in Real Life – 10 Practical Examples Explained

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The Role of Algebra in Everyday Life

Role of algebra in budgeting and expenses, role of algebra in managing loans and interest rates, role of algebra in investment and profits, role of algebra in construction and engineering, role of algebra in travel planning and scheduling, role of algebra in computer programming and technology, role of algebra in logical thinking and critical analysis, role of algebra in patterns, formulas, and rules, role of algebra in gaming, sports, and hobbies, role of algebra in cooking, crafting, and interior decorating.

To use algebra in real life , I first grasp the fundamental concepts of variables and equations. Algebra stretches far beyond the walls of my classroom, seamlessly integrating into my daily routines and responsibilities. It’s the silent partner in my budgeting, where balancing expenses becomes a balancing act of numbers.

In my career, algebra unlocks a deeper understanding of various systems . For example, robotics use algebraic geometry to study the motion of robots with multidimensional search spaces. By applying algebra , I can model and solve problems with an array of possible outcomes and constraints. 

Algebra is a cornerstone of mathematics that pops up in numerous daily activities , often without my even noticing. From budgeting to cooking, the use of variables , equations , and the algebraic expressions simplifies complex tasks.

Knowing how to manipulate these allows me to solve practical problems effectively. Here’s how I apply algebra in real life:

Budgeting : Crafting a monthly budget requires balancing income and expenses . Variables represent the amounts, while equations make sure everything adds up. For example, if my income is $I$ and my monthly expenses are a sum of individual costs $c_1, c_2, …, c_n$, the algebraic expression looks like this: $I = c_1 + c_2 + … + c_n$.

Cooking : Modifying a recipe based on servings involves ratios and proportions , which are algebraic concepts. For a recipe that serves $4$ and I need it for $6$, I’ll use a simple formula : Multiply each ingredient quantity by $\frac{6}{4}$.

Shopping Discounts : When I’m out shopping and there’s a $20%$ sale, I calculate the discounted price using the original price $P$. The sale price $S$ is $S = P – (0.20 \times P)$ or simply $S = 0.80P$.

Fitness Tracking : Keeping up with my fitness regimen involves calculating calories and exercise durations. If a workout burns $C$ calories per minute and I exercise for $t$ minutes, the total calories burned is $Ct$.

Here’s a quick table summarizing the use of algebra in everyday situations:

Algebra is not just an abstract tool; it is a vital part of managing finances in my everyday life. When I sit down to create a budget, I’m essentially using algebraic equations to plan my spending, savings, and investments.

For example, when planning monthly expenses, I might use a simple equation:

 $\text{Income} – \text{Expenses} = \text{Savings}$

Here’s how algebra becomes practical:

• Income : I calculate my total income from different sources, such as my salary, freelance work, and any other passive income.
• Expenses : I then sum up my monthly bills, groceries, transport, and other known costs.
• Savings : What I aim to save is the variable I need to solve for in the equation.

I use algebra to calculate my monthly payments using the formula for an ordinary annuity, which is:

$M = P \frac{r(1 + r)^n}{(1 + r)^n – 1}$

• ( M ) is the monthly payment,
• ( P ) is the principal loan amount,
• ( r ) is the monthly interest rate (annual rate divided by 12 months),
• ( n ) is the number of payments (loan term in years multiplied by 12 months).

By plugging in the values, I can budget my monthly expenses effectively, ensuring I don’t overspend and land myself in financial hot water.

When I assess the impact of an interest rate on my loan, I recognize that a lower rate can significantly reduce the total amount of interest I’ll pay over time. For instance, if I consider two loans with different interest rates, algebra helps me determine which is more cost-effective for my budget and long-term financial goals.

Here’s a quick comparison of two different interest rates on a $10,000 car loan over 5 years:

Investing is a financial strategy I use to grow my income and savings over time. To make informed decisions, I rely heavily on algebra to predict potential profits and manage my investments. For instance, when considering the future value of an investment, I calculate compound interest using the formula:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Here’s a breakdown of this equation:

• ( A ) is the amount of money accumulated after ( n ) years, including interest.
• ( P ) is the principal amount (the initial money I put in).
• ( r ) is the annual interest rate (decimal).
• ( n ) is the number of times that interest is compounded per year.
• ( t ) is the time in years.

When planning my budget, algebra aids me in balancing my income, expenses, and savings. The basic structure of a budget can be summarized by:

$\text{Income} – \text{Expenses} = \text{Savings}$

I also assess loans and manage finances by understanding the interest rates and calculating monthly payments using amortization formulas.

The formula for figuring out the monthly payment (( PMT )) on a loan is:

$PMT = \frac{P \times \frac{r}{n}}{1 – (1 + r)^{-n}}$

Calculating taxes is another essential use of algebra. To find out my after-tax income, I subtract the tax, which is a percentage of my income, as follows:

$\text{After-Tax Income} = \text{Income} – (\text{Income} \times \text{Tax Rate}) $

By mastering these algebraic operations , I ensure my investments are profitable and my financial future secure.

In my career as a construction engineer, I’ve constantly engaged with algebra. It’s vital for creating stable structures and ensuring buildings can withstand stress. For example, calculating loads involves algebraic equations, so I can determine if a beam will support the weight using the formula:

$$ Load = \frac{Weight}{Area} $$

In the realm of construction scheduling, I integrate algebra to manage timelines efficiently. By establishing critical paths and resource allocations, I can pinpoint areas that need attention, making sure that my projects stay on track.

In my approach to technology and computer programming, I’ve also noticed a strong reliance on algebra. Whether it’s algorithm development or designing complex structures through Computer-Aided Design (CAD) software, algebraic concepts are crucial. Let me give you a brief glimpse at how algebra intersects across various applications:

When I plan a trip, algebra becomes a trusty companion, particularly in managing schedules and budgets. The use of algebra in travel planning is not just theoretical; it’s a practical tool that helps me make the most of my time and money.

To start with, creating a travel schedule can often feel like a puzzle. I use algebra to calculate travel times between destinations, accounting for layovers and connections. For example, if my flight from A to B takes 3 hours and my layover in B before flying to C is 2 hours, I can figure out my total travel time with a simple algebraic expression, ($ t_{\text{total}} = t_{\text{A to B}} + t_{\text{layover}} + t_{\text{B to C}}$ ).

In budgeting, I list all expenses such as transportation, accommodation, and activities. Then I sum them up, letting algebra help me keep a tight rein on spending. Here’s a small table I might create:

The application of algebra extends to more complex scenarios in engineering and construction , where it assists in optimizing project schedules and resource allocations. In computer science , algorithms for scheduling are embedded in various applications, using algebraic formulas to automate and enhance the planning process.

Algebra is a cornerstone in the realm of computer programming and technology. I often see it as the hidden hero in various applications spanning from simple software to complex engineering systems. It forms the backbone of algorithms, which are the step-by-step instructions I follow when writing code for anything from sorting data to encrypting information.

In computer science, I leverage algebraic structures to optimize code and solve computational problems. For example, the boolean algebra helps me in creating logic circuits and program decision-making capabilities in software. Here’s how algebraic concepts are applied:

Binary Operations : These allow me to perform tasks in programming languages, using operators such as $+$, $-$, $\times$, and $\div$.

Linear Algebra : It’s crucial in the construction of 3D graphics and animations, which are essential in video games and simulations.

Matrices : I use these for data organization and to perform multiple calculations at once, which is integral in image processing and machine learning tasks.

Algebra has its applications in scheduling and optimization algorithms too. Whether it’s assigning resources efficiently or finding the quickest routes for travel, algebra provides me with methods to compute optimal solutions.

Let me give you an example: when I’m dealing with robotics, I apply algebraic geometry to study the dynamics of robotic mechanisms. This involves handling a myriad of dimensional states and motions—something that is made manageable through algebraic principles.

In technology-enhanced education, algebra facilitates better learning tools, offering both visually engaging and interactive ways for students to grasp mathematical concepts. This contributes to a deeper understanding, heightened interest, and improved proficiency in mathematics.

Algebra is much more than just manipulating symbols and solving equations for me. It’s the backbone of my logical thinking and critical analysis skills. When I tackle an algebraic problem, I’m engaging with an entire system of logic and patterns that help build my reasoning abilities. 

For instance, consider the simple algebraic formula for solving for ( x ) in a linear equation: ( ax + b = c ). This equation might represent a real-life problem, like calculating the price after a discount (where ( x ) is the original price). Stringently following algebraic rules, I rearrange the formula to ( x = $\frac{c – b}{a}$ ), a process that reinforces my understanding of operations and the order in which they should be conducted.

Algebra strengthens my critical thinking by requiring me to apply sets of rules—properties of operations, for example—to various problems. These formulas and rules are not arbitrary; they are logical structures that I can rely on to find clarity in confusion.

Algebra serves as the foundation for problem-solving in various everyday scenarios. When I encounter patterns , algebra helps me to recognize and understand the structure behind these arrangements. For instance, a simple pattern like an increasing sequence of odd numbers can be represented algebraically as (2n + 1), where n represents the position in the sequence. This aids in predicting subsequent numbers, demonstrating a relationship ruled by algebra.

In my daily life, I use formulas to calculate things like interest rates or to determine the distance I travel. This use of formulas represents a set of rules that guide my critical thinking and enable accurate problem-solving. Here’s a snapshot of how I might use a formula:

Logic and reasoning intersect with algebra when I face a problem requiring a structured approach. Algebraic expressions give me a powerful language to describe relationships and solve problems methodically. This intersection fosters my critical thinking , which becomes instrumental when I’m trying to discover a rule through an observed pattern. It’s exciting to deduce a formula from scattered information, and algebra is my go-to toolkit for doing just that.

In gaming, I often find algebra underlying the design and development of many video games, particularly when programming movements or scoring systems. For instance, in a platformer, the character’s jump might be calculated using the formula ( s = ut + $\frac{1}{2}at^2$ ), where ( s ) is displacement, ( u ) is the initial velocity, ( a ) is the acceleration due to gravity, and ( t ) is time.

Sports analytics use algebra to enhance team performance and strategy. Take basketball, where player efficiency is often computed using a complex algebraic formula to analyze performance statistics.

As for cooking, algebra helps in scaling recipes. If I want to double a recipe, I apply proportional reasoning, a fundamental algebraic concept, to adjust ingredient quantities. With crafting and art, algebra assists in planning layouts and dimensions, ensuring symmetrical designs or patterns.

For children’s education and hobbies, algebra fosters problem-solving skills. It might be as simple as figuring out the right amount of paint for a color mix, calculated by a ratio or equation.

Cooking: When preparing a meal, algebra helps me adjust recipes. For instance, if a recipe calls for 4 cups of flour to serve 8 people, and I only need to serve 2, I use the algebraic equation ($ \text{required flour} = \frac{4}{8} \times 2 $) to determine that I need 1 cup of flour.

• Original servings: ( $s_1$ )
• Desired servings: ( $s_2$)
• Original ingredient amount: ( $a_1 $)
• New ingredient amount: ($ a_2 = \frac{a_1 \times s_2}{s_1}$ )

Crafting: Algebra aids me in creating and executing my designs accurately. If I’m designing a quilt, the number of squares (( q )) I need will depend on the size of the quilt and the size of each square. The equation ($ q = \frac{\text{total area of quilt}}{\text{area of one square}} $) saves time and materials.

• Total area of project: ( $A_t $)
• Area per piece: ($A_p$ )
• Pieces required: ( P =$ \frac{A_t}{A_p}$ )

Interior Decorating: When redecorating my living space, algebra helps me maximize the area and aesthetics. If I need to cover a wall with wallpaper, I need to know how many rolls to purchase. I’ll use the equation ($ \text{rolls needed} = \frac{\text{wall area}}{\text{coverage per roll}} $) to get the right quantity.

In exploring the intersection of algebra and daily life , I’ve highlighted its undeniable presence in the routines and decisions we navigate. From managing personal finances to interpreting data trends in work settings, algebra is not confined to textbooks—it thrives in the world around us.

I’ve found that recognizing variables and constants, denoted as $x$ and $c$ respectively, equips us with the insight to forecast outcomes. In doing so, we harness the capability to plan and strategize more effectively. Whether we’re considering the purchase of a new home, conserving gas based on our vehicle’s efficiency, or baking with precision, algebraic principles guide us.

Appreciating that a formula such as $distance = speed \times time$ can determine travel details, or that calculating an unknown expenditure with $income – expenses = savings$, is practical algebra at play. My experiences have shown that algebra isn’t just about solving equations; it’s a toolkit for problem-solving.

• Pre Calculus
• Probability
• Sets & Set Theory
• Trigonometry

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47 Things To Solve Everyday (And Even Not-So-Everyday) Problems

We found a trash can for your car, a moisture meter for your plants, a squirting spoon for your baby, and a Samsung Frame for you.

BuzzFeed Staff

1. A genius T-shirt roll holder that'll keep all your shirts neat and easily accessible. If folding is your kryptonite and digging through your shirt drawer is your biggest pet peeve, this nifty hanger is about to save you from yourself.

The Roll Keeper is owned by Kelso, Washington's resident crafter, Traci. Traci has been crafting for over 40 years and created her storage design to help organize vinyl, soon realizing that it was the perfect organization solution for much more. Her shop has versions for bottles, wrapping paper, pens, and more. Don't miss checking out this small business!

Before getting this I was driving myself up the wall with my bad folding habits. I basically shoved all my shirts into the storage drawers under my bed, because I have a teeny tiny closet (the picture above gives you a solid idea of how small it is). This has given me a massive amount of clothing storage I didn't have before. The quality is stellar and Traci is 10/10 the most thoughtful person I've purchased an Etsy product from!

Get it from The Roll Keeper on Etsy for $15.99 .

2. A squirting spoon with a squeezable silicone pouch that's gonna make feeding your baby pureed meals cleaner and easier both at home and on-the-go.

This comes with a hard plastic lid so you can seal it up and save it for snack time.

Promising review: "This product is Amazing!!! I now have kids in sports/activities and I am always on the go. I put my baby's food in one of these and take it to go in my diaper bag. It comes with a spoon cover that is hard plastic that covers the hole where the food comes out. The body of the spoon is a soft silicone that you gently squeeze to get the pureed food out. The spoon itself is a hard plastic but we had no issues. It is easy to clean and comes apart in two pieces. Seriously, this is the best gadget ever! This is coming from a mother of four who has probably owned and purchased every gadget out there to make life easier !!" — castgirl

Get it from Amazon for $8.82+ (available in two colors).

3. A booster seat diaper bag — a classic diaper bag that transforms into a secure seat (including chair straps) so your kiddo can sit up at the table and thus, off of your lap, when you're out and about. Even when used as a seat, the hollow center can be filled with all the things you need throughout your day.

The booster seat pops up and has adjustable straps to secure onto any chair. The bag itself has plenty of space for both you and your kiddo's things. Plus it's machine-washable, padded, water-resistant, and supports up to 60 pounds.

Get it on sale from Ashley Homestore for $49.99 (originally $84.99).

4. An elasticity repair hair treatment for anyone who has fried their hair with chemical treatments and heat tools. This quinoa-rich solution repairs hair right at the cuticle, making hair color look shinier, reducing split ends, and strengthening strands right at their core.

Here's a useful trick I learned back in my hair school days. If you're wondering whether or not your hair is chemically damaged, you can do a simple test at home. Grab a single strand of hair and pull it on either end. If the hair seems to slowly pull apart rather than bounce back...you've got some chemical damage and would benefit from an elasticity treatment. Now you know.

Promising review: "I bought this recently and I love love love it. My hair feels strong and healthy and now has a fantastic shine. This is definitely a must." —Barti7

Get it from Beauty Pie for $40 (or become a member and pay $4.93).

5. A moisture meter you can place deep down into the soil to know exactly how much water your plant is getting. Under- and overwatering is a thing of the past, people!

I love having this tool in my home! I jumped on the 2020 plant trend fast and have filled my home with tons of botanicals (that all have different watering schedules). The meter tells me if a plant is being over-watered or under-watered right down to the root, which is very necessary for a plant parent (who used to be a plant murderer) like myself. My home is going to be even greener in 2021.

Promising review: "This item is great. I can check how wet my plants are down where the roots are. So no more overwatering! It is very accurate. This works great!!" — Terri Carlson

Get it from Amazon for $11.97 (available in two colors).

6. A subscription to NordVPN — a service that uses an encrypted tunnel of online traffic for extra privacy online. With this, you're able to do things like enter your credit card info while on public Wi-Fi and feel safe and secure while you're at it!

The application works on Windows, macOS, and Linux, and has apps for iOS, Android, and Android TV. It also has encrypted proxy extensions for Chrome and Firefox. Secure up to six devices!

Get it from NordVPN for $3.71+ /month (available in multiple plans).

7. A maternity bodysuit that'll give you a chance to throw on something a little spicier than the hospital diapers you've been rockin' postpartum. The best part? You'll be able to wear this *while* also feeding a tiny human from your body.

PSA: word on the street is those hospital diaper pad deals are *very* comfy. You just had a baby. Wear extra comfortable clothes as long as you dang well please!

Promising review: " This is super comfortable, practical, and makes you feel sexy ! It's easy to pull up and down to nurse and it comes in beautiful colors." —Kim W.

Get it from Lively for $45 (available in two colors and sizes XS–XL).

8. A car trash can sure to save the day (and your upholstery) from suckers, soda bottles, and all the other sticky substances your kids sneak into the car.

Promising review: "This is the most useful little item I have EVER placed in my car for litter management. It's easy to use, easy to empty, AND it doubles as a spare cup holder when needed. I've ordered more for our other cars. The kids have really improved their management of basic tidiness in the car with this in our family vehicle. My husband has managed to keep the passenger seat easy for me to join him in his car, and now our teens will enjoy an uncluttered life in the 'teen mobile .'" — DW

Get it from Amazon for $7.99 .

9. A water-gel SPF 35 — a daily formula that's hypoallergenic, cruelty-free, vegan, and works great under makeup. Is your skin gonna be the envy of all your sunburnt besties? Why yes, yes it is.

To learn more, be sure to check out " Just 9 Glossier Products We Really Love ."

Promising review: "I've been searching for the longest time for a sunscreen that doesn't feel greasy, make me oily, or cause me to breakout. I was hesitant to purchase this because of the higher price point and small size, but it is totally worth it. This is the only sunscreen I've tried that feels nice on my skin! I use it daily and haven't experienced any breakouts or sunburn." —mckenna

Get it from Glossier for $25 .

10. Or an avocado oil SPF 30 specifically designed to blend in with dark skin, helping you avoid chalky buildup while still protecting your skin from the sun. Plus, this stuff is super moisturizing!

Promising review: "This is the only sunscreen that hasn’t given me a white cast! It absorbs and clears with no ashy look! I’ve already been through two tubes. I love this product!" —Anon

Get it from Target for $15.99 .

11. A pack of dander reducing wipes that'll help your kitto have a clean coat this winter without any bath time drama.

Each pack has 50 wipes. BTW, you can also get grooming wipes from Burt's Bees for your dog .

Promising review: "I was skeptical at first, but am so glad I decided to get these. Burt's Bees make excellent products. My apartment is so dry in the cold seasons, even with running multiple vaporizers. My cat was getting very bad dry skin and dander, as you can see in the first image (pictured above, left). After one use her fur is soft, silky, and the dander is so much better! This product will be a regular purchase and a must for my pets!" — Magpie

Get them from Amazon for $5.83 .

12. A pack of five produce bags made with a washable 100% cotton material, so you can carry produce in the grocery store, wash it in the sink at home, and keep it organized in the fridge — all while keeping it in one bag.

Promising review: "It seems like such a small thing, bringing your own bags to the store, but over time it saves so much plastic. In addition to bringing grocery bags, these little bags allow you to bag your own vegetables and fruits. The bags come in three different sizes (small, medium, and large) and they are color-coded by the size. Red is small, blue is medium and green is large. Due to the soft mesh the bags are made out of, they do not bruise the item and they allow it to breathe. It is easy to close these bags, you just pull tight the drawstring. I had no issues with washing the bags, just throw them into the laundry. I do recommend washing them out in the sink before throwing them into the wash. For drying, just let them hang dry." — CNV

Get them from BuzzFeed's Goodful collection on Amazon for $12.99 .

13. A pocket-sized Tile Mate — using your smartphone, these trackers are gonna "ring" to help figure out where you last left your purse, keys, wallet...basically whatever you hook them to! I can't even remember where I've left my lunch most days. Time to buy this.

BTW, this'll even help find your phone (even when it's on silent).

Promising review: "One of the best decisions I have ever made was purchasing a Tile. It's easy to use and does exactly what it's designed for. I HIGHLY recommend it." —Layne

Get it on sale from Tile for $17.99 (originally $24.99).

14. A bag of strawberry peanuts that'll satisfy all your PB&J cravings, whether you're trying out a low carb life or simply want a protein-filled snack that is *ridiculously* delicious.

I am a *major* PB&J fan and I swear these little peanuts taste exactly like the real thing. IDK how there isn't bread stuffed into each nut. These have been a great solution for me because I often skip breakfast, but am happy to munch on these in the mornings. They're the #1 snack in my home.

Promising review: "These are wonderful! Delicious! They really do taste just like PB&J! Shipping was very fast. I will definitely be purchasing again." —Em

Get a 24 bag mini pack for $24.99 from SkinnyDipped (available in two flavors and pack sizes).

15. A menstrual cup with a flat design that'll last up to 12 hours. You'll even be able to keep it in during intercourse! Science just made this the best time in history to be a person with a menstrual cycle. Period.

Promising review: "I bought this about month ago and at this very moment in time (9/12/20) I'm on day three, which is normally a heavy day, and I've had no leaks at all ." —Nicole

Get it from Intimina for $39.95 .

16. A splurge-worthy Samsung Frame for those of us who don't want quality wall space taken over by a big blank screen. With this, you just happen to get a luxury television while you're at it.

This is honest and truly the best splurge I have ever made. It has massively upgraded the look in my living room. My husband loves the photography options and I love all the classical paintings – as someone who loves changing up my decor, being able to update the display images has been so fun. The quality is fantastic while watching movies and TV...but I'm pretty sure I love it as a piece of art in my home even more.

Promising review: "This is a brilliant TV! It looks great in art mode. If your primary goal is to have the TV look less like a TV, I think you’ll be pleased with this one. There are some reviews that point out some downsides (like a small amount of local storage), but I’ve had no problems. The pictures make the screen look brighter than it is but with the right pictures, it looks matte and brilliant in art mode; like a framed print ." — N B

Get it from Amazon for $676.91+ (available in four colors and six sizes).

17. A car headrest pillow to save your neck from the awkward nap angles you usually end up in during long road trips. Don't let neck pain put a kink in your future travel plans!

Promising review: "I almost dozed off the first time I tested it in the driveway, lol. It was easy to install and adjustable for a 6'3" adult all the way down to a small child very easily. It took me less than 10 minutes to unbox and set it up perfectly with all adjustments." — Edward

Get it from Amazon for $30.90+ (available in four colors).

18. A fabric defuzzer that'll clean up sweaters, sofas, and other aging fabrics that have been a real ~pill~ lately.

Promising review: "I didn't think it through when I threw some dark shirts and sweaters in the wash with a couple of light towels. They came out with all those fuzzies. I ordered one of these based on the price and customer reviews and I can see why this is rated so high. Since it's so portable, I just sat on the couch and shaved two shirts and a pair of cottony exercise pants while watching tv. I probably would have never worn these items (at least not outside the house!) again if it wasn't for this great little gadget." — Paula Nelson

Get it from Amazon for $12.88 (available in six colors).

19. An Instant Pot magnetic cheat sheet you can stick right on your machine, giving you a helpful source that's far more reliable than asking Alexa for recipe directions every step of the way.

This includes 95 common food ingredients with their liquid ratios and cooking times. There's info for pasta and grains, seafood and fish, pork, beans and legumes, vegetables, chicken, beef, and other meats.

Promising review: "I am so happy that I decided to give this product a try! What an amazing idea. I placed the smaller magnet right on the Instant Pot and use it daily for a quick reference. Instead of searching the cookbook or the internet, I can just glance over and know in an instant how to program my Instant Pot for that particular product ." — Olesya

Get it from Amazon for $9.99+ (available in two sizes).

20. A USB cord bracelet great for vacations or for anyone who seems to need a charge at a moment's notice.

This specific bracelet is compatible with Apple, but you can also get one for Samsung products .

Promising review: "I usually have every sort of cable that I could possibly need when I'm at work, but I don't usually carry one on my person when I'm elsewhere. It looks sharp, and isn't obviously a cable, but its always available should you need it. One thing I have found is that the cable is compatible with Apple CarPlay, and when plugged into a computer will function like a default Apple cable. I am incredibly happy with it and would recommend it to anyone who might ask." — Patt Duffy

Get it from Amazon for $14.99+ (available in seven colors).

21. A multi-tier drinking fountain — it's gonna help keep your cat hydrated, because cats' instincts tell them that moving water is cleaner than still water. This thing looks great, is whisper-quiet, and even dishwasher-safe!

P.S. This is also a great choice for small dogs!

Promising reviews: "My Jake loves his new water dish! The constant flow keeps the water fresh and clean. I filled it and, just to test it, emptied it two days later. There was no scum and the water was clean. I am now confident I can just replenish the water lost. Jake drinks more water than before, which is good for him. I would recommend this to any pet owner." —RescueMom

"Our little dog, who is 15 years old, was starting to have trouble seeing and drinking from her normal water bowl, so we ordered this to see if it would help! It is perfect! Not only is it higher than a bowl on the floor, which helps her neck pain but the water also moves and she loves drinking from the top part. This is great for an aging pet! " —Happypetparent

Get it from Chewy for $29.95 (originally $64.99).

22. A nose butter that'll soothe your dog's schnoz if it gets dry or cracked this winter.

Promising review: "I received this item yesterday, so I have been using it three times a day for two days. My poor, beautiful English mastiff has had a horrible nose for so long. I have talked to the vet and researched on forums, but had yet to find a solution that actually worked. My husband was skeptical when I stumbled across this product but said to try it. I am amazed and recommend this to anyone who has a pup in need. Two days and my puppy's nose is almost as good as new! This stuff is a miracle-worker! I have attached a photo of the before and after so you can see the results too (pictured above). A huge thank you from my pup and myself!" — Bleeding Rose

Get it from Amazon for $7.19+ (available in several packaging styles based on breed).

23. An oven thermometer for folks who find their rental's ancient oven finicky at best. Use this for making sure you know the *actual* temperature, preventing any further cooking fails — courtesy of your oven.

Promising review: "This is a great value for the product. The ovens I have used have always seemed to be a bit off, so this was very important to have around the house especially for recipes that need a very specific temperature. My wife bakes a lot and before having an oven thermometer, she often times over-baked or under-baked her recipes. This thermostat can hang easily on the oven rack and is easy to read, making it helpful for any dish that needs to be baked at a certain temperature. Highly recommend this product!" — Abe

Get it from Amazon for $7.79 .

24. An anti-fog spray to give responsible folks who have been wearing face masks despite their glasses constantly fogging up — you deserve to see the light!

Promising review: "I bought this product because wearing a face mask makes my glasses fog, even with the metal strip to form around the bridge of my nose. It works all day with only one application, unless I have been doing a lot of activity, then I might have to re-apply. Just spray it on the clean lenses of your glasses then wipe dry with a clean dry lintless cloth, as simple as that. I was so impressed that I gave my second bottle to my team members for them to use. Delivery was fast. I highly recommend this product from this company. I would not hesitate to buy this again when I need more in the future." — Tonya Crippen

Get it from Amazon for $10.55 .

25. A ring-size adjuster for helping you wear oversized rings without spending a bundle on getting them fitted.

Promising review: "This is so simple yet so efficient! I have thin fingers (size 4) and my rings always spin all the way around. This product was very easy to use. I used both sizes, one for my bridal set that is soldered together and the thin one for my other ring. You can customize the fit by using more or less turns of the twine. It will be fairly easy to remove and attach again on swollen finger days. And it's super cheap. I think I should be able to resize 10 rings without having to reuse any of the twine. I'm very satisfied!" — new mom 2

Get four from Amazon for $4.99 .

26. A roll of glow in-the-dark tape you can basically use any time you'd rather not trip or stub your toe in the dark. This stuff really is, ahem, a ~bright~ idea.

Promising review: " I bought this tape hoping I could use it to label switches on a guitar effects pedalboard (above, right) so I could identify them on a dark stage while playing. It works perfectly! It was easy to trim the length and width neatly, thanks to the lines marked on the reverse backing. Sharpie ink goes on easily, with no smearing, and it's high contrast and easy to read in both light and dark environments.

When I tested 'supercharging' the tape with a bright pocket flashlight just before playing, the glow was a really bright green and it was incredibly easy to read the labeling – even in total darkness. I am really impressed with this tape. It performed much better than I had hoped for. I am going to give strips to my friends so they can label their boards as well." — Shopper

Get it from Amazon for $13.97 .

27. A double-sided exfoliating lip brush with a side that scrubs and another that stimulates circulation — both are gonna help make your lips look smoother and fuller.

Promising review: " I admit I was skeptical about this product but my desperation to regain my soft lips made me click the 'buy' button. My lips were dried, cracked, and even bleeding — very painful. Even my tried-and-true expensive-as-heck lip moisturizer I use couldn't help. Having this lip brush did the trick and made all the difference. The exfoliation must have allowed my lip moisturizer to get better absorbed. I was able to see results in just a couple days . Now I have soft and supple lips again . And it was so easy to clean the brush afterwards. Where has this thing been all my life? I don't think I can live without it now." — Double-J

Get it from Amazon for $7.99 (available in three colors).

28. A pack of six furniture markers that's gonna delight your kids when you tell them they actually ~can~ draw on the furniture.

Promising review: "I am thoroughly impressed! We have a 115-plus-year-old house and we only have hardwood in our downstairs hall and den. We didn't want to spend tons of money because we are probably going to be replacing the flooring in a few years. I'm actually still working on this as I'm writing this, but I am so impressed that I just had to write a review right away. The only 'negative' I have is that the colors are darker than the caps show, but not a big deal. For the money, you can't go wrong." — Borg

Get them from Amazon for $8.99 .

29. A tiny Jibbitz accessory to put on your Crocs to let everyone know (in the most meta way) just how much you love your Crocs.

Those are my Crocs! And *my* accessory of choice. The only thing better than Crocs is MORE CROCS.

Get it from Crocs for $4.99 .

30. A nail and cuticle oil made from jojoba oil, sweet almond oil, and vitamin E that'll strengthen chipped, cracking, dry, and brittle nails.

Promising review: "I had peeling, weak nails for years. This size bottle lasted a bit more than a month while I was religiously applying it two-three times a day in February. I was really seeing great improvements, so I bought another bottle in late March. By May, all the peeling had grown out and my nails were getting stronger every day. Cannot recommend this stuff enough!" — Diana

Get it from Amazon for $8.50 .

31. A bed bridge to turn two twins into a king and truly help you out if you go to bed wondering how to build bridges in your life. I mean, here's one way.

Promising review: "I love this bed bridge. I bought two twin XL, adjustable beds and didn't realize the gap it would leave. My husband and I would always find each other in the abyss between our beds. Then this came to the rescue! Now there is no more gap in the bed and it's strong enough to keep us from sinking into it! My husband and I can now cuddle comfortably!" — Cami

Get it from Amazon for $40.95 .

32. A hand massager designed to relax your joints and ease pressure. Use this spiffy tool once a day and you're sure to be ~on a roll~ again in no time.

Promising review: "This is self-care at its best. I like using it on the side of my poor, arthritic fingers. It really feels good over my knuckles. It feels good. Hand arthritis hurts and it is nice to have some relief." — M. V. Kolar

Get it from Amazon for $9.98 .

33. A bottle of wine drops , a natural sulfite and tannin remover — a few drops of this will let you enjoy your drink without worrying about getting a headache afterwards.

One of these will treat up to 55 glasses of wine (up to nine bottles!). You need 1-2 drops for a white wine and 2-3 for a red.

Promising review: "This product was really amazing. I buy a lot of stuff on Amazon and never write a review, however this product is worth writing one. I've used the Wand as well and like it, however the biggest drawback of the Wand is having to explain why I'm using it to others and causing undue attention. This is a quick solution to that issue. The product itself works great. I get bad headaches whenever I drink wine, however with this product I'm able to drink two to three glasses without the headaches . I'm not sure exactly what causes the headaches, whether it's tannins, sulfites, etc., however I just know this cures the issue. I'm sure there are those who are skeptical, I certainly was, but I can truly say it works for me and hopefully others will find success using it as well. " — luke

Get it from Amazon for $14.99 .

34. A pack of lobe support patches to ease the weight of your earrings, keeping your lobes from getting stretched and making sure your cutest accessories aren't a weight on your shoulders.

Promising review: "Amazing. Literal lifesavers. I LOVE my heavy Kendra Scott earrings, but I’m pretty sure they’re the culprit of why my right earring hole has ripped slightly. Using these support patches, it’s as if the earrings don’t even exist. I am going to tell all of my friends to get these for their heavy statement earrings!!" — Donthemom50

Get a box of 60 patches from Amazon for $9.91 .

35. A sliding webcam cover so you can show off your WFH lewk when you want to, and never when you don't. No more worries about forgetting to turn off the camera. We've been doing this too long at this point. It's time to bring in the hardware solutions.

Promising review: "The device sticks well to the computer and is thinner than any other one I purchased in the past. It's been doing a great job of covering my camera ; it slides easily when I want to use the camera, and it's so thin there are no issues closing the laptop . I tend to be kind of hard on my laptop, and I'm impressed with the durability ." — Sha

Get it from Amazon for $5.95+ (available in three colors).

36. An eye primer for anyone who spends way too much time on their smokey eye to have it sweat off the minute they hit the dance floor.

Promising review: "So I use this primer for my eyeliner AND eyebrows, and it is a life-changer !!! I work jobs and a majority of the day I'm waitressing outside on the patio in the humidity. I needed something to keep my eyeliner intact so I didn't look like a raccoon by the end of my shift. It literally kept my makeup looking like I just put it on allllll day no matter how bad I sweat in the heat!!! I used it only on my eyes first just to try and I was amazed. So the next day I tried it as a primer for my eyebrows too before I filled them in and it does the same for my eyebrows! I'm in love with this product. Hopefully my picture will prove it!!" — Molly

Get it from Amazon for $13.48 .

37. A set of carriage door magnets — throw these snazzy things on your garage and you're gonna make your sedan feel sensational every time you pull into the driveway.

Promising review: " These really dressed up our garage door!!!! UPDATE!! It has been almost a year since I purchased these. They have faded ever so slightly but still hold on to the metal of the garage door and have not cracked with the cold of winter or heat of summer. Very pleased!!!" — Robert R

Get a set of four hinges and two handles on Amazon for $11.68 .

38. A stress vest to keep your K-9 calm when thunder starts rumbling or in other high-stress situations.

Promising review: " I’m a little weirded-out by how well this works. It's a lifesaver! I bought it knowing I’d probably send it back. My schnauzer destroys my house when I leave and I don’t want him to spend his life in a crate. I bought this as a last-ditch effort before having him medicated to keep him from freaking out when we leave. It works. 100%. We’ve had it for about four weeks and tested it. If we leave and he’s wearing it he won’t touch ANYTHING. He’s very calm and collected. If he’s not wearing it he is antsy and we come home to DVDs destroyed, picture frames torn apart, his toys gutted and piled in the middle of the room, and hats chewed beyond saving. I’d recommend this to anyone with an anxious dog." — Amazon Customer

Get it from Amazon for $39.95+ (available in two colors and seven sizes).

39. A cast-iron stake to let your neighbors know your yard is not their basset hound's bathroom...without taking away from your *gorge* rhododendrons.

Promising review: "I love this little sign! It's such a polite way to tell your neighbors not to let their dogs go on your lawn. We had a problem with one particular neighbor who wouldn't pick up after her two small dogs and this has totally alleviated that. She simply walks past our yard now. It's cute, the perfect size, and effective!" — MO x CO x KO

Get it from Amazon for $8.73 .

40. A bug bite suction tool that'll remove the venom from any stings and help reduce itchiness, pain, and swollen skin.

Promising review: "I am a magnet for bites of all kinds and carry topical and medicines with me at all times — so I figured this would be a good product to see if it really works. It arrived on Monday and on Tuesday morning I woke up with a bug bite on my arm. I used this little tool (three times, per the instructions) and documented with photos. Immediately after using, it stopped itching! And less than 24 hours later the bump/bite was gone! There is a very faint red mark from using the thing but a small price to pay IMO. Bottom line: it’s awesome. I’m carrying it with me everywhere!" — Rebecca

Get it from Amazon for $9.95 (available in two colors).

41. A tie hanger that can hold up to 20 ties, keeping your favorite accessories neat and tie -dy all the time.

Promising review: "Good quality, small, and compact. I own about 10 of these now." –Target reviewer

Get it from Target for $7 .

42. A pack of five elastic scrunchies for anyone who is ready to break up with breakage caused by tight elastics. These are also great for preventing tension headaches if you like having your hair up when you sleep!

Promising review: "Reader, I love these scrunchies for my curly-frizzy-coarse and dry dry dry hair. I travel in them (they saved my hair on a looooooong set of flights to and from Australia this past January), sleep in them EVERY NIGHT, and I even wear them out when my hair is dirty and it's ~low bun time~ to dress it up a bit. I have absolutely noticed a reduction in breakage and the strands that cascade to the floor when I take my hair down in the morning for styling. If you're looking for a budget-friendly option to just add a little TLC to your hair care, I absolutely recommend these bbs. And in several months of constant use, there's been no stretching out, even though I have quite a bit of hair." — Maitland Quitmeyer , BuzzFeed Staff

Get them from Amazon for $7.99 .

43. A versatile bag clip for treating your Gucci dupe with the love and respect it deserves — it's hard work looking that pretty!

Promising review: "I have a very heavy, large purse that is a bottomless pit. One time I put my purse on the back of my chair at a cafe and the whole chair flipped over, that is how heavy my bag is. I was looking for something so that I could hook my purse on things so it wasn’t sitting on the floor and was more accessible. I love this little gadget. I have used it on everything from bathroom stalls to tables to grocery carts. This thing really grips. All of my girlfriends love it and have gotten it for themselves." — Jennifer

Get it from Amazon for $15.95 (available in five colors).

44. A pasta measuring tool for cooks who are incapable of using their ~noodle~ when it comes to solving the dreaded "how much dry pasta is too much cooked pasta" life quiz.

Promising review: "This is a lifesaver. I used to make more pasta than was necessary. Now I can make the perfect amount of pasta without looking like I’m trying to feed a whole army." — ashting

Get it from Amazon for $6.99 .

45. A clever pack of baby clothes dividers for organizing your newborn's outfits by month — making sure you have the clothes you need when baby Daisy starts growing like a weed.

Promising review: "I love these. They're perfect to organize our little guy's clothes. They make it easy to know what sizes we have and what we need before he comes ." — Jennifer

Get them from Amazon for $9.99 (available in two colors).

46. DERMAdoctor Ultra Gentle Brightening Antiperspirant that works to reduce sweat and skin discoloration. This'll improve skintone, is non-irritant, and is sure to have you throwing your arms in the air because you just won't care!

This is quick-drying, dermatologist approved, and free of fragrance, dyes, and gluten. BTW this is not tested on animals!

Promising review: "It is really good and brightens the underarms in the long run, it is also great in reducing smell." —Armani

Get it from SkinStore for $30.

47. A bag of Dreams Aren't This Good tortilla chips cooked up specifically to be reheated in the oven, so you can have fresh, hot, restaurant-worthy chips and salsa at your kitchen counter.

Fair warning: these chips will ruin other tortilla chips for you. My husband and I eat chips and salsa constantly and these are the best we've had. Being able to warm them up totally changes the snacking game. Plus all of their salsa options are delicious. To heat, place in an oven or toaster oven at 350 degrees (on a sheet of foil) for a few minutes.

Get a three-pack from Dreams Aren't This Good for $24.99 (available in two pack sizes).

48. And finally, a birthdate candle with an aroma uniquely formulated to correspond to your birthday. Gift yourself this and 2021 is sure to smell like a breath of fresh air!

Promising review: "The candle is beyond my expectations, from the astrological and numerology readings down to the fragrance. To my amazement, it was aromatically in line with my taste; I couldn't believe it. It matched perfectly with my taste and personality; they certainly know their stuff! The candle is all-around perfect. I'm completely satisfied with my purchase." — Nury C.

Get it from Birthdate Candles for $38 (available in 365 birthday options).

When you use these products and realize you're better at everything than everyone:

Reviews in this post have been edited for length and clarity.

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NPTEL Assignment Answers and Solutions 2024 (July-Dec). Get Answers of Week 1 2 3 4 5 6 7 8 8 10 11 12 for all courses. This guide offers clear and accurate answers for your all assignments across various NPTEL courses

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Nptel assignment answers 2024 with solutions (july-dec), how to use this repo to see nptel assignment answers and solutions 2024.

If you're here to find answers for specific NPTEL courses, follow these steps:

Access the Course Folder:

• Navigate to the folder of the course you are interested in. Each course has its own folder named accordingly, such as cloud-computing or computer-architecture .

Locate the Weekly Assignment Files:

• Inside the course folder, you will find files named week-01.md , week-02.md , and so on up to week-12.md . These files contain the assignment answers for each respective week.

Select the Week File:

• Click on the file corresponding to the week you are interested in. For example, if you need answers for Week 3, open the week-03.md file.

Review the Answers:

• Each week-XX.md file provides detailed solutions and explanations for that week’s assignments. Review these files to find the information you need.

By following these steps, you can easily locate and use the assignment answers and solutions for the NPTEL courses provided in this repository. We hope this resource assists you in your studies!

List of Courses

Here's a list of courses currently available in this repository:

• Artificial Intelligence Search Methods for Problem Solving
• Cloud Computing
• Computer Architecture
• Cyber Security and Privacy
• Data Science for Engineers
• Data Structure and Algorithms Using Java
• Database Management System
• Deep Learning for Computer Vision
• Deep Learning IIT Ropar
• Digital Circuits
• Ethical Hacking
• Introduction to Industry 4.0 and Industrial IoT
• Introduction to Internet of Things
• Introduction to Machine Learning IIT KGP
• Introduction to Machine Learning
• Introduction to Operating Systems
• ML and Deep Learning Fundamentals and Applications
• Problem Solving Through Programming in C
• Programming DSA Using Python
• Programming in Java
• Programming in Modern C
• Python for Data Science
• Soft Skill Development
• Soft Skills
• Software Engineering
• Software Testing
• The Joy of Computation Using Python
• Theory of Computation

Note: This repository is intended for educational purposes only. Please use the provided answers as a guide to better understand the course material.

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🚀 About Progiez

Progiez is an online educational platform aimed at providing solutions to various online courses offered by NPTEL, Coursera, LinkedIn Learning, and more. Explore our resources for detailed answers and solutions to enhance your learning experience.

Disclaimer: This repository is intended for educational purposes only. All content is provided for reference and should not be submitted as your own work.

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