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What is Problem Solving?.
Quality Glossary Definition: Problem solving
Problem solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution; and implementing a solution.
- The problem-solving process
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The Problem-Solving Process
In order to effectively manage and run a successful organization, leadership must guide their employees and develop problem-solving techniques. Finding a suitable solution for issues can be accomplished by following the basic four-step problem-solving process and methodology outlined below.
1. Define the problem
Diagnose the situation so that your focus is on the problem, not just its symptoms. Helpful problem-solving techniques include using flowcharts to identify the expected steps of a process and cause-and-effect diagrams to define and analyze root causes .
The sections below help explain key problem-solving steps. These steps support the involvement of interested parties, the use of factual information, comparison of expectations to reality, and a focus on root causes of a problem. You should begin by:
- Reviewing and documenting how processes currently work (i.e., who does what, with what information, using what tools, communicating with what organizations and individuals, in what time frame, using what format).
- Evaluating the possible impact of new tools and revised policies in the development of your "what should be" model.
2. Generate alternative solutions
Postpone the selection of one solution until several problem-solving alternatives have been proposed. Considering multiple alternatives can significantly enhance the value of your ideal solution. Once you have decided on the "what should be" model, this target standard becomes the basis for developing a road map for investigating alternatives. Brainstorming and team problem-solving techniques are both useful tools in this stage of problem solving.
Many alternative solutions to the problem should be generated before final evaluation. A common mistake in problem solving is that alternatives are evaluated as they are proposed, so the first acceptable solution is chosen, even if it’s not the best fit. If we focus on trying to get the results we want, we miss the potential for learning something new that will allow for real improvement in the problem-solving process.
3. Evaluate and select an alternative
Skilled problem solvers use a series of considerations when selecting the best alternative. They consider the extent to which:
- A particular alternative will solve the problem without causing other unanticipated problems.
- All the individuals involved will accept the alternative.
- Implementation of the alternative is likely.
- The alternative fits within the organizational constraints.
4. Implement and follow up on the solution
Leaders may be called upon to direct others to implement the solution, "sell" the solution, or facilitate the implementation with the help of others. Involving others in the implementation is an effective way to gain buy-in and support and minimize resistance to subsequent changes.
Regardless of how the solution is rolled out, feedback channels should be built into the implementation. This allows for continuous monitoring and testing of actual events against expectations. Problem solving, and the techniques used to gain clarity, are most effective if the solution remains in place and is updated to respond to future changes.
You can also search articles , case studies , and publications for problem solving resources.
Innovative Business Management Using TRIZ
Introduction To 8D Problem Solving: Including Practical Applications and Examples
The Quality Toolbox
Root Cause Analysis: The Core of Problem Solving and Corrective Action
One Good Idea: Some Sage Advice ( Quality Progress ) The person with the problem just wants it to go away quickly, and the problem-solvers also want to resolve it in as little time as possible because they have other responsibilities. Whatever the urgency, effective problem-solvers have the self-discipline to develop a complete description of the problem.
Diagnostic Quality Problem Solving: A Conceptual Framework And Six Strategies ( Quality Management Journal ) This paper contributes a conceptual framework for the generic process of diagnosis in quality problem solving by identifying its activities and how they are related.
Weathering The Storm ( Quality Progress ) Even in the most contentious circumstances, this approach describes how to sustain customer-supplier relationships during high-stakes problem solving situations to actually enhance customer-supplier relationships.
The Right Questions ( Quality Progress ) All problem solving begins with a problem description. Make the most of problem solving by asking effective questions.
Solving the Problem ( Quality Progress ) Brush up on your problem-solving skills and address the primary issues with these seven methods.
Refreshing Louisville Metro’s Problem-Solving System ( Journal for Quality and Participation ) Organization-wide transformation can be tricky, especially when it comes to sustaining any progress made over time. In Louisville Metro, a government organization based in Kentucky, many strategies were used to enact and sustain meaningful transformation.
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Making the Connection In this exclusive QP webcast, Jack ReVelle, ASQ Fellow and author, shares how quality tools can be combined to create a powerful problem-solving force.
Adapted from The Executive Guide to Improvement and Change , ASQ Quality Press.
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How to Solve a Problem
Last Updated: April 3, 2023 References Approved
This article was co-authored by Rachel Clissold . Rachel Clissold is a Life Coach and Consultant in Sydney, Australia. With over six years of coaching experience and over 17 years of corporate training, Rachel specializes in helping business leaders move through internal roadblocks, gain more freedom and clarity, and optimize their company’s efficiency and productivity. Rachel uses a wide range of techniques including coaching, intuitive guidance, neuro-linguistic programming, and holistic biohacking to help clients overcome fear, break through limitations, and bring their epic visions to life. Rachel is an acclaimed Reiki Master Practitioner, Qualified practitioner in NLP, EFT, Hypnosis & Past Life Regression. She has created events with up to 500 people around Australia, United Kingdom, Bali, and Costa Rica. There are 12 references cited in this article, which can be found at the bottom of the page. wikiHow marks an article as reader-approved once it receives enough positive feedback. This article received 14 testimonials and 91% of readers who voted found it helpful, earning it our reader-approved status. This article has been viewed 1,283,233 times.
How you deal with challenges will often determine your success and happiness. If you’re stuck on how to solve a problem, try defining it and breaking it into smaller pieces. Choose whether to approach the problem logically or whether you should think about how the outcome might make you feel. Find ways to creatively approach your problems by working with other people and approaching the problem from a different perspective.
Approaching the Problem
- For example, if your room is constantly messy, the problem might not be that you’re a messy person. It might be that you lack containers or places to put your items in an organized way.
- Try to be as clear and thorough as possible when defining the problem. If it is a personal issue, be honest with yourself as to the causes of the problem. If it is a logistics problem, determine exactly where and when the problem occurs.
- Determine whether the problem is real or self-created. Do you need to solve this problem or is this about something you want? Putting things in perspective can help you navigate the problem-solving process.
- For example, you might have several problems to solve and need to decide which ones to tackle first. Solving one problem may ease tension or take stress off of another problem.
- Once you make a decision, don’t doubt yourself. Be willing to look forward from that point on without wondering what would have happened had you chosen something else.
- For example, if you need to turn in many assignments to pass a class, focus on how many you have to do and approach them one by one.
- Try to combine and solve problems together whenever possible. For example, if you're running out of time to study, try listening to a recorded lecture while walking to class or flip through note cards as you're waiting for dinner.
- For example, if you’re trying to pass a cumulative test, figure out what you already know and what you need to study for. Review everything you already know, then start learning more information from your notes, textbook, or other resources that may help you.
- Pay attention to know these scenarios make you feel.
- For example, if you have a deadline, you may skip cooking dinner or going to the gym so that you can give that time to your project.
- Cut down on unnecessary tasks whenever possible. For example, you might get your groceries delivered to you to save on shopping time. You can spend that time instead on other tasks.
Taking a Creative Approach
- If you’re making a complex decision, write down your alternatives. This way, you won’t forget any options and will be able to cross off any that aren’t plausible.
- For example, you might be hungry and need something to eat. Think about whether you want to cook food, get fast food, order takeout, or sit down at a restaurant.
- Problems like accepting the job across the country that offers good pay but takes you away from your family may require different ways of approach. Consider the logical solution, but also consider your thoughts, feelings, and the way the decision affects others.
- For example, if you’re buying a home and not sure how to make your final decision, talk to other homeowners about their thoughts or regrets about buying a home.
- For example, if you’re having financial difficulties, notice how your efforts are affecting the money coming in and the money you’re spending. If keeping a budget helps, keep with it. If using cash exclusively is a headache, try something else.
- Keep a journal where you record your progress, successes, and challenges. You can look at this for motivation when you are feeling discouraged.
Managing Your Emotions While Confronting Difficulties
- The first step is often the scariest. Try doing something small to start. For example, if you're trying to become more active, start going for daily walks.
- For example, if you’re overwhelmed by having a long to-do list, maybe the problems isn’t the list, but not saying “no” to things you can’t do.
- If you're feeling stressed, angry, or overwhelmed, you may be burned out. Make a list of things that cause stress or frustration. Try to cut down on these in the future. If you start feeling overwhelmed again, it may be a sign that you need to cut back.
- Find a therapist by calling your local mental health clinic or your insurance provider. You can also get a recommendation from a physician or friend.
Expert Q&A Did you know you can get expert answers for this article? Unlock expert answers by supporting wikiHow
Support wikiHow by unlocking this expert answer.
- If you start feeling overwhelmed or frustrated, take a breather. Realize that every problem has a solution, but sometimes you're so wrapped up in it that you can't see anything but the problem. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0
- Don't turn away from your problems. It will come back sooner or later and it will be more difficult to solve. Common sense can help to reduce the size of the problem. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0
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- ↑ https://hbr.org/2017/06/how-you-define-the-problem-determines-whether-you-solve-it
- ↑ https://www.cuesta.edu/student/resources/ssc/study_guides/critical_thinking/106_think_decisions.html
- ↑ https://au.reachout.com/articles/a-step-by-step-guide-to-problem-solving
- ↑ Rachel Clissold. Certified Life Coach. Expert Interview. 26 August 2020.
- ↑ https://serc.carleton.edu/geoethics/Decision-Making
- ↑ https://www.psychologytoday.com/blog/positive-psychology-in-the-classroom/201303/visualize-the-good-and-the-bad
- ↑ https://www.britannica.com/topic/operations-research/Resource-allocation
- ↑ https://www.niu.edu/citl/resources/guides/instructional-guide/brainstorming.shtml
- ↑ https://www.healthywa.wa.gov.au/Articles/N_R/Problem-solving
- ↑ https://www.collegetransfer.net/Home/ChangeSwitchTransfer/I-want-to/Earn-My-College-Degree/Overcoming-Obstacles
- ↑ https://psychcentral.com/lib/5-ways-to-solve-all-your-problems/
- ↑ https://www.apa.org/topics/psychotherapy/understanding
About This Article
To solve a problem, start by brainstorming and writing down any solutions you can think of. Then, go through your list of solutions and cross off any that aren't plausible. Once you know what realistic options you have, choose one of them that makes the most sense for your situation. If the solution is long or complex, try breaking it up into smaller, more manageable steps so you don't get overwhelmed. Then, focus on one step at a time until you've solved your problem. To learn how to manage your emotions when you're solving a particularly difficult problem, scroll down. Did this summary help you? Yes No
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Problem-Solving Strategies and Obstacles
Kendra Cherry, MS, is the author of the "Everything Psychology Book (2nd Edition)" and has written thousands of articles on diverse psychology topics. Kendra holds a Master of Science degree in education from Boise State University with a primary research interest in educational psychology and a Bachelor of Science in psychology from Idaho State University with additional coursework in substance use and case management.
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Sean is a fact-checker and researcher with experience in sociology, field research, and data analytics.
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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.
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How to Improve Your Problem-Solving Skills
In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:
- Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
- Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
- Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
- Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
- Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
- Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.
You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.
Sarathy V. Real world problem-solving . Front Hum Neurosci . 2018;12:261. doi:10.3389/fnhum.2018.00261
Dunbar K. Problem solving . A Companion to Cognitive Science . 2017. doi:10.1002/9781405164535.ch20
Stewart SL, Celebre A, Hirdes JP, Poss JW. Risk of suicide and self-harm in kids: The development of an algorithm to identify high-risk individuals within the children's mental health system . Child Psychiat Human Develop . 2020;51:913-924. doi:10.1007/s10578-020-00968-9
Rosenbusch H, Soldner F, Evans AM, Zeelenberg M. Supervised machine learning methods in psychology: A practical introduction with annotated R code . Soc Personal Psychol Compass . 2021;15(2):e12579. doi:10.1111/spc3.12579
Mishra S. Decision-making under risk: Integrating perspectives from biology, economics, and psychology . Personal Soc Psychol Rev . 2014;18(3):280-307. doi:10.1177/1088868314530517
Csikszentmihalyi M, Sawyer K. Creative insight: The social dimension of a solitary moment . In: The Systems Model of Creativity . 2015:73-98. doi:10.1007/978-94-017-9085-7_7
Chrysikou EG, Motyka K, Nigro C, Yang SI, Thompson-Schill SL. Functional fixedness in creative thinking tasks depends on stimulus modality . Psychol Aesthet Creat Arts . 2016;10(4):425‐435. doi:10.1037/aca0000050
Huang F, Tang S, Hu Z. Unconditional perseveration of the short-term mental set in chunk decomposition . Front Psychol . 2018;9:2568. doi:10.3389/fpsyg.2018.02568
National Alliance on Mental Illness. Warning signs and symptoms .
Mayer RE. Thinking, problem solving, cognition, 2nd ed .
Schooler JW, Ohlsson S, Brooks K. Thoughts beyond words: When language overshadows insight. J Experiment Psychol: General . 1993;122:166-183. doi:10.1037/0096-3445.2.166
By Kendra Cherry Kendra Cherry, MS, is the author of the "Everything Psychology Book (2nd Edition)" and has written thousands of articles on diverse psychology topics. Kendra holds a Master of Science degree in education from Boise State University with a primary research interest in educational psychology and a Bachelor of Science in psychology from Idaho State University with additional coursework in substance use and case management.
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How to solve problems using the design thinking process
The design thinking process is a problem-solving design methodology that helps you develop solutions in a human-focused way. Initially designed at Stanford’s d.school, the five stage design thinking method can help solve ambiguous questions, or more open-ended problems. Learn how these five steps can help your team create innovative solutions to complex problems.
As humans, we’re approached with problems every single day. But how often do we come up with solutions to everyday problems that put the needs of individual humans first?
This is how the design thinking process started.
What is the design thinking process?
The design thinking process is a problem-solving design methodology that helps you tackle complex problems by framing the issue in a human-centric way. The design thinking process works especially well for problems that are not clearly defined or have a more ambiguous goal.
One of the first individuals to write about design thinking was John E. Arnold, a mechanical engineering professor at Stanford. Arnold wrote about four major areas of design thinking in his book, “Creative Engineering” in 1959. His work was later taught at Stanford’s Hasso-Plattner Institute of Design (also known as d.school), a design institute that pioneered the design thinking process.
This eventually led Nobel Prize laureate Herbert Simon to outline one of the first iterations of the design thinking process in his 1969 book, “The Sciences of the Artificial.” While there are many different variations of design thinking, “The Sciences of the Artificial” is often credited as the basis.
Anatomy of Work Special Report: How to spot—and overcome—the most crucial enterprise challenges
Learn how enterprises can improve processes and productivity, no matter how complex your organization is. With fewer redundancies, leaders and their teams can hit goals faster.
![[Resource Card] AOW Blog Image](https://assets.asana.biz/transform/fdc408f5-063d-4ea7-8d73-cb3ec61704fc/Global-AOW23-Black-Hole?io=transform:fill,width:1680&format=webp "solution to solve problems")
A non-linear design thinking approach
Design thinking is not a linear process. It’s important to understand that each stage of the process can (and should) inform the other steps. For example, when you’re going through user testing, you may learn about a new problem that didn’t come up during any of the previous stages. You may learn more about your target personas during the final testing phase, or discover that your initial problem statement can actually help solve even more problems, so you need to redefine the statement to include those as well.
Why use the design thinking process
The design thinking process is not the most intuitive way to solve a problem, but the results that come from it are worth the effort. Here are a few other reasons why implementing the design thinking process for your team is worth it.
Focus on problem solving
As human beings, we often don’t go out of our way to find problems. Since there’s always an abundance of problems to solve, we’re used to solving problems as they occur. The design thinking process forces you to look at problems from many different points of view.
The design thinking process requires focusing on human needs and behaviors, and how to create a solution to match those needs. This focus on problem solving can help your design team come up with creative solutions for complex problems.
Encourages collaboration and teamwork
The design thinking process cannot happen in a silo. It requires many different viewpoints from designers, future customers, and other stakeholders . Brainstorming sessions and collaboration are the backbone of the design thinking process.
Foster innovation
The design thinking process focuses on finding creative solutions that cater to human needs. This means your team is looking to find creative solutions for hyper specific and complex problems. If they’re solving unique problems, then the solutions they’re creating must be equally unique.
The iterative process of the design thinking process means that the innovation doesn’t have to end—your team can continue to update the usability of your product to ensure that your target audience’s problems are effectively solved.
The 5 stages of design thinking
Currently, one of the more popular models of design thinking is the model proposed by the Hasso-Plattner Institute of Design (or d.school) at Stanford. The main reason for its popularity is because of the success this process had in successful companies like Google, Apple, Toyota, and Nike. Here are the five steps designated by the d.school model that have helped many companies succeed.
1. Empathize stage
The first stage of the design thinking process is to look at the problem you’re trying to solve in an empathetic manner. To get an accurate representation of how the problem affects people, actively look for people who encountered this problem previously. Asking them how they would have liked to have the issue resolved is a good place to start, especially because of the human-centric nature of the design thinking process.
Empathy is an incredibly important aspect of the design thinking process. The design thinking process requires the designers to put aside any assumptions and unconscious biases they may have about the situation and put themselves in someone else’s shoes.
For example, if your team is looking to fix the employee onboarding process at your company, you may interview recent new hires to see how their onboarding experience went. Another option is to have a more tenured team member go through the onboarding process so they can experience exactly what a new hire experiences.
2. Define stage
Sometimes a designer will encounter a situation when there’s a general issue, but not a specific problem that needs to be solved. One way to help designers clearly define and outline a problem is to create human-centric problem statements.
A problem statement helps frame a problem in a way that provides relevant context in an easy to comprehend way. The main goal of a problem statement is to guide designers working on possible solutions for this problem. A problem statement frames the problem in a way that easily highlights the gap between the current state of things and the end goal.
Tip: Problem statements are best framed as a need for a specific individual. The more specific you are with your problem statement, the better designers can create a human-centric solution to the problem.
Examples of good problem statements:
We need to decrease the number of clicks a potential customer takes to go through the sign-up process.
We need to decrease the new subscriber unsubscribe rate by 10%.
We need to increase the Android app adoption rate by 20%.
3. Ideate stage
This is the stage where designers create potential solutions to solve the problem outlined in the problem statement. Use brainstorming techniques with your team to identify the human-centric solution to the problem defined in step two.
Here are a few brainstorming strategies you can use with your team to come up with a solution:
Standard brainstorm session: Your team gathers together and verbally discusses different ideas out loud.
Brainwrite: Everyone writes their ideas down on a piece of paper or a sticky note and each team member puts their ideas up on the whiteboard.
Worst possible idea: The inverse of your end goal. Your team produces the most goofy idea so nobody will look silly. This takes out the rigidity of other brainstorming techniques. This technique also helps you identify areas that you can improve upon in your actual solution by looking at the worst parts of an absurd solution.
It’s important that you don’t discount any ideas during the ideation phase of brainstorming. You want to have as many potential solutions as possible, as new ideas can help trigger even better ideas. Sometimes the most creative solution to a problem is the combination of many different ideas put together.
4. Prototype stage
During the prototype phase, you and your team design a few different variations of inexpensive or scaled down versions of the potential solution to the problem. Having different versions of the prototype gives your team opportunities to test out the solution and make any refinements.
Prototypes are often tested by other designers, team members outside of the initial design department, and trusted customers or members of the target audience. Having multiple versions of the product gives your team the opportunity to tweak and refine the design before testing with real users. During this process, it’s important to document the testers using the end product. This will give you valuable information as to what parts of the solution are good, and which require more changes.
After testing different prototypes out with teasers, your team should have different solutions for how your product can be improved. The testing and prototyping phase is an iterative process—so much so that it’s possible that some design projects never end.
After designers take the time to test, reiterate, and redesign new products, they may find new problems, different solutions, and gain an overall better understanding of the end-user. The design thinking framework is flexible and non-linear, so it’s totally normal for the process itself to influence the end design.
Tips for incorporating the design thinking process into your team
If you want your team to start using the design thinking process, but you’re unsure of how to start, here are a few tips to help you out.
Start small: Similar to how you would test a prototype on a small group of people, you want to test out the design thinking process with a smaller team to see how your team functions. Give this test team some small projects to work on so you can see how this team reacts. If it works out, you can slowly start rolling this process out to other teams.
Incorporate cross-functional team members : The design thinking process works best when your team members collaborate and brainstorm together. Identify who your designer’s key stakeholders are and ensure they’re included in the small test team.
Organize work in a collaborative project management software : Keep important design project documents such as user research, wireframes, and brainstorms in a collaborative tool like Asana . This way, team members will have one central source of truth for anything relating to the project they’re working on.
Foster collaborative design thinking with Asana
The design thinking process works best when your team works collaboratively. You don’t want something as simple as miscommunication to hinder your projects. Instead, compile all of the information your team needs about a design project in one place with Asana.
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How to Solve Problems
- Laura Amico
To bring the best ideas forward, teams must build psychological safety.
Teams today aren’t just asked to execute tasks: They’re called upon to solve problems. You’d think that many brains working together would mean better solutions, but the reality is that too often problem-solving teams fall victim to inefficiency, conflict, and cautious conclusions. The two charts below will help your team think about how to collaborate better and come up with the best solutions for the thorniest challenges.
First, think of the last time you had to solve a problem. Maybe it was a big one: A major trade route is blocked and your product is time sensitive and must make it to market on time. Maybe it was a small one: A traffic jam on your way to work means you’re going to be late for your first meeting of the day. Whatever the size of the impact, in solving your problem you moved through five stages, according to “ Why Groups Struggle to Solve Problems Together ,” by Al Pittampalli.
Pittampalli finds that most of us, when working individually, move through these stages intuitively. It’s different when you’re working in a team, however. You need to stop and identify these different stages to make sure the group is aligned. For example, while one colleague might join a problem-solving discussion ready to evaluate assumptions (Stage 3), another might still be defining the problem (Stage 1). By defining each stage of your problem-solving explicitly, you increase the odds of your team coming to better solutions more smoothly.
This problem-solving technique gains extra power when applied to Alison Reynold’s and David Lewis’ research on problem-solving teams. In their article, “ The Two Traits of the Best Problem-Solving Teams ,” they find that highly effective teams typically have a pair of common features: They are cognitively diverse and they are psychologically safe. They also exhibit an array of characteristics associated with learning and confidence; these teammates tend to be curious, experimental, and nurturing, for example.
As you and your colleagues consider these ideas, think about the last problem you had to solve as a team. First, map out what you remember from each step of your problem-solving. Were all of you on the same page at each stage? What aspects of the problem did you consider — or might you have missed — as a result? What can you do differently the next time you have a problem to solve? Second, ask where your team sees themselves on the chart. What kinds of behaviors could your team adopt to help you move into that top-right quadrant?
- Laura Amico is a senior editor at Harvard Business Review.
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The 14 Worst Problems You Can Run Into In An Airport (& How To Solve Them)
Airports can be an awful place for travel problems, but the good news is, most are very easily fixable.
Read update
More Problems You Can Run Into In An Airport (& How To Solve Them)
Airports can be exciting, because it means travel, but they can also be stressful. Because of the nature of flying, there are a million things that can go wrong from check in to boarding and then, even at arrivals. Even the thought of these problems can cause anxiety, but there's no need to be nervous if you know exactly how you'd solve them if they did happen.
Just remember — every problem is fixable! That airline wants you to fly with them again and airport staff are there to help so if there's an issue, they want to solve it as much as you do. Well. Almost.
UPDATE: 2023/05/05 11:49 EST BY KHYATI DAND
Amidst missed connections, delayed flights, lost baggage, long layovers, and frenzied security checks, airports cause more chaos than perhaps any other place in the world. Luckily, with every problem comes a solution. This list was updated to help flyers prepare for some of the worst (and most common) problems they could run into at an airport and ways to deal with them.
14 Travel Sickness Can Hit Hard
Travel sickness is a very real and common possibility when flying, especially if the journey involves long layovers across different airports with varying timezones. Add to that lack of sleep, dehydration, and physical fatigue, and it's not all that surprising if you feel a little too worse for wear.
A good way to avoid falling sick at an airport mid-travel is investing in lounge access: warm showers, flat beds, and free-flowing beverages for rehydration in between flights can do wonders for the body. Most airports will have pharmacies with basic medications as well, but it's always a good idea to carry your own, especially if you're going to be seeing a lot of airports over multi-stop flights.
13 Things Can Get Stolen
Unfortunately, the chaotic atmosphere of an airport is ideal for theft. Many travelers have found phones and wallets missing while their attention was on safeguarding their passports. It's even possible for entire suitcases to be stolen.
Being organized is key because the more frazzled you are, the more likely you will be to leave things unattended. Pack light, keep your valuables close, and invest in a suitcase that's distinct. It's harder to steal a bright yellow bag that's covered in stickers than it is to nick an inconspicuous black suitcase from the luggage carousel. In case you notice something missing, rush to the nearest security personnel or airport official. The quicker you are, the higher the possibility of catching the thief.
Related: Anti-Theft Travel Gear: What To Know (& Buy) For Your Trip
12 You Could Be At The Wrong Airport And The Wrong Terminal
You'd be surprised to see just how many people misread the terminal of their flight or worse yet, get the entire airport wrong. Some destinations have multiple airports close to each other, and it's certainly possible to accidentally book a flight that's arriving or taking from a different airport.
Always double-check the name of the airport at the time of booking and once again the night before your flight. Oftentimes, a flight will have a certain terminal written on it at the time of booking but the carrier may have changed it to a different one later . It's also a good idea to sign up for alerts from your airline as these let flyers know of any last-minute terminal changes. It's best to double, triple, and quadruple-check the airport name and terminal number -- better safe than sorry!
11 Missing A Flight
There you have it, every traveler's nightmare: a missed flight . Missing a flight is by far the worst problem you could run into at an airport but luckily, it's also a very common one which means, there are plenty of ways to fix it.
It goes without saying that planning to reach the airport with plenty of time to spare is the best way to avoid a missed flight. In case you miss it anyway, reach out to an airline agent asap as they will usually help book you onto the next flight out. Additionally, don't wait till the very end to inform the airline that you're about to miss a flight. The sooner you foresee the delay and let them know, the more likely you are to get refunds and airfare concessions.
If you're someone that has a knack for cutting it a bit short, it may be worth investing in flights that have a flat-tire policy which essentially means that an airline will accommodate you on another flight free of cost under certain conditions.
10 You Can Get Lost
The main, obvious problem that can happen in the larger airports is that it's far too easy to get lost. Some airports have multiple terminals, with gates spanning in every direction, and finding your gate can often seem like a daunting task for those who are directionally challenged.
Stay calm and follow the signs — every airport is signposted. And if all else fails, stop someone who works at the airport and politely ask them to point you in the right direction.
9 Your Flight Can Be Delayed
Try to never choose a flight that gets you to your destination a second before you actually need to be there. Always allow yourself room on the other side, because flight delays are shockingly common, and it can be anywhere from twenty minutes to twelve hours.
If the delay is significant, you may be entitled to compensation and the airline should at least provide food vouchers. Stay calm and don't panic — you'll get there eventually.
Related: Here's What To Do If Your Flight Is Delayed (Or Canceled)
8 Or Canceled
If your flight is canceled, it's the airline's responsibility to get you there. They'll rebook you on the next available flight or find another route, so even though it may be tempting to fully panic when you see 'CANCELED' in bold red letters next to your flight number, don't! Some people's flights are canceled, and they end up getting to their destination quicker because the layover is shorter, or they end up on a direct flight. See — they can even work to your advantage.
7 Luggage Can Be Lost
Lost luggage is a huge pain, and there's nothing worse than the heart-wrenching feeling of realizing your suitcase hasn't come out on the carousel . More often than not though, luggage is delayed rather than lost. All you have to do is approach the luggage services desk, and they'll look up where it is and hopefully get it to you. Most airlines will even hand-deliver the luggage straight to your hotel or residential address, regardless of how far from the airport it is. Just make sure you speak up the moment you know that the suitcase hasn't arrived.
6 Security Lines Can Be Huge
Another moment of familiar panic for passengers: when you have an hour to make it through security, you arrive, and the line is huge.
There's an easy solution to this — don't worry, you aren't stuck waiting in a line that's going to make you miss your flight. Flag down a member of security and show them your boarding pass. If you're in any danger of missing your flight, they will move you to the front of the line and ensure you have time to make it to your gate. Of course, they can't do that if you stay silent, so speak up!
Related: 10 Tips To Make Airport Security A Breeze
5 Passport Control Can Be A Nightmare
On the arrivals side, passport control can be a nightmare . Like security, the lines can be long (and this time, you can only skip them if you have a short connection time). But more than that, the interview itself can be a little terrifying. Customs & Border Patrol (or the country's equivalent) can be short and to the point, since it's their job to be a law enforcement officer, not customer service. The questions they ask can seem invasive, and it might be tempting to get defensive since you just want to get out of the airport.
Stay calm and answer politely. Don't go into too much detail. You'll get out of there much faster.
4 Sometimes Technology Don't Work As It Should
Recently, kiosks have been introduced everywhere in airports — for passport control, for checking in, for everything. But technology is only reliable to a point and often, they don't work.
Allow yourself plenty of time and don't rely on kiosks speeding you through the airport. Be aware that you may have to approach an actual person, and account for the time that waiting in that line may take.
3 Not Every Airport Has Good Food
It's also not a good idea to rely on getting food in the airport , especially if you have a strict diet like vegan or gluten-free. Some airports have wide food choices, but some have barely any at all. Always make sure you pack a few protein bars in your bag so you have a quick on-the-go snack and prevent running into the problem of being hangry.
Just don't try to take fresh fruit or veg through security, as that's where you may have some issues.
Related: These U.S. Airports Have The Best Food So You Don't Need To Fly Hungry
2 Long Layovers Can Be Very Boring
Often, waiting in an airport can be due to a layover . Don't rely on the airport having entertainment, as most don't — make sure you have a book and that any electronics you intend to use are fully charged. Preparing in advance can save you a lot in this situation, because otherwise you might be forced to sit there for hours staring into space.
Also, research the airport! Some airports even have sleeping pods.
1 Transport Can Be Hard To Find
You may be relying on a shuttle at the other side, but sometimes, it doesn't show — or sometimes, you can't find it. Stay calm and ask for directions but if possible, always make sure you carry a little cash in the local currency in case worse comes to worst, and you have to jump in a taxi. Also make sure you have the address of where you're staying written down for this exact reason.
NEXT: 10 Overused Expressions We All Hear From People At The Airport
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Mixture Problems With Solutions
Mixture problems and their solutions are presented along with their solutions. Percentages are also used to solve these types of problems.
Problem 1: How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?
Solution to Problem 1: Let x be the quantity of the 20% alcohol solution to be added to the 40 liters of a 50% alcohol. Let y be the quantity of the final 30% solution. Hence x + 40 = y We shall now express mathematically that the quantity of alcohol in x liters plus the quantity of alcohol in the 40 liters is equal to the quantity of alcohol in y liters. But remember the alcohol is measured in percentage term. 20% x + 50% * 40 = 30% y Substitute y by x + 40 in the last equation to obtain. 20% x + 50% * 40 = 30% (x + 40) Change percentages into fractions. 20 x / 100 + 50 * 40 / 100= 30 x / 100 + 30 * 40 / 100 Multiply all terms by 100 to simplify. 20 x + 50 * 40 = 30 x + 30 * 40 Solve for x. x = 80 liters 80 liters of 20% alcohol is be added to 40 liters of a 50% alcohol solution to make a 30% solution.
Problem 2: John wants to make a 100 ml of 5% alcohol solution mixing a quantity of a 2% alcohol solution with a 7% alcohol solution. What are the quantities of each of the two solutions (2% and 7%) he has to use?
Solution to Problem 2: Let x and y be the quantities of the 2% and 7% alcohol solutions to be used to make 100 ml. Hence x + y = 100 We now write mathematically that the quantity of alcohol in x ml plus the quantity of alcohol in y ml is equal to the quantity of alcohol in 100 ml. 2% x + 7% y = 5% 100 The first equation gives y = 100 - x. Substitute in the last equation to obtain 2% x + 7% (100 - x) = 5% 100 Multiply by 100 and simplify 2 x + 700 - 7 x = 5 * 100 Solve for x x = 40 ml Substitute x by 40 in the first equation to find y y = 100 - x = 60 ml
Problem 3: Sterling Silver is 92.5% pure silver. How many grams of Sterling Silver must be mixed to a 90% Silver alloy to obtain a 500g of a 91% Silver alloy?
Solution to Problem 3: Let x and y be the weights, in grams, of sterling silver and of the 90% alloy to make the 500 grams at 91%. Hence x + y =500 The number of grams of pure silver in x plus the number of grams of pure silver in y is equal to the number of grams of pure silver in the 500 grams. The pure silver is given in percentage forms. Hence 92.5% x + 90% y = 91% 500 Substitute y by 500 - x in the last equation to write 92.5% x + 90% (500 - x) = 91% 500 Simplify and solve 92.5 x + 45000 - 90 x = 45500 x = 200 grams. 200 grams of Sterling Silver is needed to make the 91% alloy.
Problem 4: How many Kilograms of Pure water is to be added to 100 Kilograms of a 30% saline solution to make it a 10% saline solution.
Solution to Problem 4: Let x be the weights, in Kilograms, of pure water to be added. Let y be the weight, in Kilograms, of the 10% solution. Hence x + 100 = y Let us now express the fact that the amount of salt in the pure water (which 0) plus the amount of salt in the 30% solution is equal to the amount of salt in the final saline solution at 10%. 0 + 30% 100 = 10% y Substitute y by x + 100 in the last equation and solve. 30% 100 = 10% (x + 100) Solve for x. x = 200 Kilograms.
Problem 5: A 50 ml after-shave lotion at 30% alcohol is mixed with 30 ml of pure water. What is the percentage of alcohol in the new solution?
Solution to Problem 5: The amount of the final mixture is given by 50 ml + 30 ml = 80 ml The amount of alcohol is equal to the amount of alcohol in pure water ( which is 0) plus the amount of alcohol in the 30% solution. Let x be the percentage of alcohol in the final solution. Hence 0 + 30% 50 ml = x (80) Solve for x x = 0.1817 = 18.75%
Problem 6: You add x ml of a 25% alcohol solution to a 200 ml of a 10% alcohol solution to obtain another solution. Find the amount of alcohol in the final solution in terms of x. Find the ratio, in terms of x, of the alcohol in the final solution to the total amount of the solution. What do you think will happen if x is very large? Find x so that the final solution has a percentage of 15%.
Solution to Problem 6: Let us first find the amount of alcohol in the 10% solution of 200 ml. 200 * 10% = 20 ml The amount of alcohol in the x ml of 25% solution is given by 25% x = 0.25 x The total amount of alcohol in the final solution is given by 20 + 0.25 x The ratio of alcohol in the final solution to the total amount of the solution is given by [ ( 20 + 0.25 x ) / (x + 200)] If x becomes very large in the above formula for the ratio, then the ratio becomes close to 0.25 or 25% (The above function is a rational function and 0.25 is its horizontal asymptote). This means that if you increase the amount x of the 25% solution, this will dominate and the final solution will be very close to a 25% solution. To have a percentage of 15%, we need to have [ ( 20 + 0.25 x ) / (x + 200)] = 15% = 0.15 Solve the above equation for x 20 + 0.25 x = 0.15 * (x + 200) x = 100 ml
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How to master communication in problem solving
May 11, 2023 The path from problem to solution is not linear. In fast-moving, complex times, decision-makers can’t effectively act alone when it comes to solving complicated workplace problems; diverse perspectives and rigorous debate are crucial to determining the best steps to take. What’s missing in many companies is the use of “contributory dissent,” or the capabilities required to engage in healthy if divergent discussions about critical business problems, write Ben Fletcher , Chris Hartley , Rupert Hoskin , and Dana Maor in a recent article . Contributory dissent allows individuals and groups to air their differences in a way that moves the discussion toward a positive outcome and doesn’t undermine leadership or group cohesion. Check out these insights to learn how to establish cultures and structures where individuals and teams feel free to bring innovative—and often better—alternative solutions to the table, and dive into the best ways to master communication in problem solving.
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15 Most Common Life Problems — And How To Solve Every Single One Of Them
Problems are forever and we can't avoid them — but we can solve them..
By Tim Denning — Updated on May 10, 2023
All of our problems are the same. Problems are forever and we can’t avoid them.
You’ll wake up tomorrow and have problems with breakfast. You’ll jump on the train and read a problem in your email inbox. You’ll get to the office and get a problem smack bang in your pretty face!
But the typical problems we face can be solved .
RELATED: Why We *Need* Something To Look Forward To, According To Science
Here are the 15 most common problems in life and how to solve each one:
1. you didn’t reach your goal..
Just because you set a goal doesn’t mean you’re going to get it. Many of life’s toughest goals take lots of attempts. Some of the goals I missed are:
- Dream careers
- Girls I wanted to date
- Saving enough money to build a school in Laos
- Reaching 100k followers on LinkedIn
People who talk about success and personal development also don’t reach their goals. The best feeling about reaching a goal is the journey it took to get there. If all your goals were easy, then you’d feel nothing at the end of the process.
Solution: Take the goal you didn’t achieve and try a different approach.
Doing the same thing over and over to achieve your goal is the definition of insanity. Your heroes miss their goals too. What makes them stand out is that they don’t give up. The fun of goal-setting is knowing that you’ll fail.
2. Someone criticized you.
If you want to make a dent in this world, then the critics will come out of the closet. The bigger your aspirations are, the more you’ll be criticized. The number of critics you have is in direct proportion to your success.
I had an entire blog post written about me saying how stupid I was. It felt like crap on day one. By day seven I’d made peace with the criticism and kept writing.
Solution: You can’t please everybody that you meet in life. When you speak on a stage, for example, 25% of people will like you, 25% won’t know who you are and 50% of people will think you’re a jerk even though you’ve probably done nothing wrong.
Critics are not all bad. You can learn things about yourself from them too. The solution is to learn from criticism, not be afraid of it.
3. Your career got messed up.
Whether you’re an entrepreneur or a happy-go-lucky office worker, your career is going to get messed up at some point.
The definition of business is this: Moving from one problem to another and making money in the meantime to fuel your mission. Business is really just problem-solving.
- Redundancy could right-hook you in the face.
- The business you founded could go backward and even bankrupt.
- Your career skills could become outdated.
- You could get fired for making a mistake.
Your career is going to get messed up. Things you can never predict in your career are going to happen.
Solution: See career challenges for what they are: an opportunity to try something different.
If your career never got messed up, then you’d probably stay in your comfort zone for your entire life and never try something different. The solution is to see your career getting messed up as a chance to grow.
Getting made redundant could be the one reality that makes you want to create your own startup. Having a customer leave could decrease your workload and create space for clients who won’t drain your time and make you no money.
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4. You have financial troubles.
That crazy little thing called money will let you down at some point. I’ve personally been rich and poor multiple times.
Upon reflection, the time I’ve been the happiest has been when I’ve had the least amount of money. Countless studies have shown that money isn’t what your life’s about . As humans, we seek meaning, love, and our own version of happiness. Money won’t give you any of those human needs.
That doesn’t mean money doesn’t matter; it just means that it shouldn’t be your main focus or something you obsess over.
Solution: The solution to financial problems is to see them as a gift and choose a meaning for your life instead.
Lack of money is a gift. When you don’t have money, you become resourceful and creative at the same time. Lack of money helps you decide on what matters and what doesn’t.
If things get really bad, then you’ll likely prioritize feeding your family over buying another useless car that will never make you happy. You’ll take joy in the simple things in life.
5. You’re unhealthy.
Our health has become a real problem. We wonder why we feel tired, sick, and get headaches. We’ll all experience health challenges at some point in our life. How many health challenges we experience in our younger years will come down to food and exercise.
The strategies for being healthy haven’t changed. There’s no mystery around being healthy, it’s just that we’ve become lazy. Convenience powered by apps has overtaken our ability to do basic tasks and not binge-watch Netflix every night.
Solution: Take ownership.
Quit feeling sick and do something about it. Have some blood tests. Change your diet to be more plant-based. Drink more water . Get to the gym three times a week for 30 minutes. Stand up from your desk every now and then so you’re not sitting for the whole day and messing your spine/neck up.
Whatever you do, take ownership of your health and quit being ignorant.
6. A relationship ended.
There’s less than 1% of people who met "The One," lived happily ever after, and never experienced a breakup. Even that 1% will have that relationship end at some point when either side passes away.
For the majority of us who don’t strike gold the first time around, we’re going to have to deal with breakups and the trials and tribulations of romance.
- We’ll probably find ourselves in a toxic relationship for too long.
- We’ll probably get cheated on at least once.
- We’ll probably have our hearts smashed into a million pieces when we discover that someone ‘No longer loves us anymore.’
These are the realities of the human condition and our need to reproduce and keep our species alive.
Solution: Finding love is about understanding what love is not. You need relationships to end to find out what love really is.
All breakups suck in the beginning until you grow and move on. Then, the solution to this problem is to find yourself.
Once you find yourself, the heart will be ready for love again. How you move forward from there is up to you. You can try the good old fashion nightclub scene. You could go to Meetups. Or, you could start swiping left and right on a few dating apps.
Have your heart broken — just don’t let it stay that way.
7. You made yourself look like a jerk.
This one is an ugly truth for me. I’ve embarrassed myself more times than I’ve had protein and veggies for dinner. Here are a few just for laughs (and your entertainment):
- There was the time I tried to pretend I could be the Wolf of Wall Street and got laughed out of the interview due to not being able to explain derivatives.
- There was the time I thought this girl liked me and tried to hug her while we were walking only to have her hate my guts.
- There was the time I went out with friends and threw up on my friend’s couch after having a single shot of tequila.
- There was the time I did my first public speaking gig and messed up a speech about my own life which I’d rehearsed over 100 times.
We could talk for days about how I’ve embarrassed myself over the years. We could even compare epic fails to see whose are worse. This is not a game though. We’re all going to go into situations with the best of intentions or all the experience in the world and still screw up.
Solution: Embarrassing yourself is a sign of courage. Courage is what is found in leaders and those who are doers.
Embarrassing yourself is an acceptance that you might fail in the short term. Those who fail in the short term will eventually win in the long term with practice.
The opposite of embarrassing yourself is perfection. That’s a life where you think too highly of yourself and you spend your entire day trying to impress everybody to eventually impress nobody. Making an idiot of yourself is perfectly fine. What’s not fine is being perfect.
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8. Someone messed your stuff up.
Car, home, or insert other material possession that doesn’t matter — none of these material things that got messed up are joining you in the afterlife. You can’t bury the Bentley with you so you can drive around with your great, great, great grandpa and do burnouts in the afterlife.
The stuff that is going to get messed up doesn’t matter.
Solution: What matters is that you don’t get messed up. What matters is that you take care of yourself so you can take care of others.
Maybe when your junk gets messed up, you’ll realize that you didn’t need it in the first place.
9. You feel like your life has no meaning.
These moments where nothing makes sense are where you get to explore. We’re not born with a meaning for our life. Meaning comes from learning who we are and growing as a person. The meaning for your life when you’re 19 will probably change from when you’re 51 and have three grown-up kids.
The quickest way to destroy your life is to believe that life has no meaning. A lack of meaning leads to depression, carelessness, drug-taking, and even crime at an extreme level.
Solution: If you feel like your life has no meaning, then it’s time to experiment.
Standing still is not how you find the answer. Being intensely focused on one’s self only leads to more suffering. A short-term solution to this problem is to experiment with helping those who have nothing. Spend time with people who’d kill to be in your position and get some perspective.
I’ve found in my life that the greatest meaning for your life is normally tied to finding something you’d be happy to do for free that helps others.
10. You feel like you can’t go on.
We’ve all had those days. Those deep and sometimes dark thoughts can lead to a place you’ve never visited. Some failures in life hurt more than others. Some failures can’t be solved through a listicle post such as this one with a dose of inspiration.
If you truly feel like you can’t go on, there’s another way.
Solution: Seek real help.
These dark thoughts must be treated. and sometimes the best medicine is to seek professional help through counseling, or for an extreme case, by calling Lifeline .
While I’ve never had suicidal thoughts, personally, I have dealt with mental illness. There is a way to come out the other side, but you have to put aside your pride and seek help. Please don’t become another victim of suicide by doing nothing.
11. Every day feels the same.
You wake up. You eat. You go to work. You eat. You come home. You eat. You go to bed.
Life can feel the same if you do nothing. It’s up to you to create variety and shape your habits into something more than a fixed schedule that makes you feel bored. Days feel the same when there’s no purpose behind anything you’re doing.
Solution: You must find joy in the repetition.
You do that by taking those reps and making them mean something. Add some variety by breaking your comfort zone. Set a goal to do something wild during your day every so often.
- Travel to another country
- Talk to someone new
- Try learning a new skill
Even after trying something new, you have to get used to some level of repetition. Let that repetition become habits that serve something which can help others.
12. Your friends are screwing your life up.
Dump them. Divorce them. Delete their number.
Every relationship you have in your life is a choice. The people around us often hold us back . They fill our minds with limiting beliefs, stories, and goals that give us no sense of meaning.
Friends can kill our dreams or make us believe something we never thought was possible.
Solution: Everyone deserves a second chance. Start by telling your toxic friends how you feel.
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Give them a chance to change with the new you. If they refuse, take a break from them for a while. Ask yourself whether you want them in your life long-term.
"Fitting in" is what we’re taught to do. What I’d advise you to do is be you instead, and that will attract the right people into your life.
RELATED: How To Stop Living Your Life Based On Your Fears
13. You feel stressed.
About 77% of people in the United States alone experience regular stress.
I recently learned about the effects of stress . I had a cortisol test and the doctor found the levels to be twice the normal range. This stress led to brain fog, tiredness, and a lack of mental clarity.
Stress is also caused by what you let into your life. Having options can be a bad thing.
Solution: We don’t need more; we need less to destress:
- Declutter your home and office.
- Say no to more meetings.
- Say yes to invites from people that make you feel like saying “Hell yes!”
- Buy less material things.
- Have fewer people in your life.
- Listen to one podcast instead of many.
- Read fewer books instead of everyone that’s recommended on a podcast.
- Have fewer recurring subscriptions.
- Invest and save more money so you can stress less about unexpected bills.
- Take regular breaks (quarterly has worked for me).
14. A fear is standing in your way.
There are so many common fears — fear of spiders, flying, public speaking, dying, career change, heights, and maybe even a fear of expressing yourself.
Fear is a concept of the mind. Nothing is scary or not scary. Our mind makes that choice for us and provides meaning to everything. Fear can be overcome and that’s why we love stories of battling with fear. I’ve famously spoken about creating fear lists and then knocking them off one at a time.
Solution: Smash the fear into tiny little pieces.
Don’t avoid it. Don’t let it stand in your way any longer. Make a decision to overcome each fear you have and you’ll be unstoppable by the end.
Don’t let nerves trick you into thinking you’re fearful. We all get nerves, but we can still keep moving forward with nerves — I’ve even learned to use nerves to my advantage by using them as an extra energy source.
Nerves tell me I’m on the right track. I’ve overcome my fear of public speaking and my fear of flying — my fear of spiders remains, but I’m working on that one. Real fear can be overcome through deliberate practice.
15. You're dealing with the concept of death.
Last but not least, the old chestnut of death. Death is the one life problem we all have in common and can’t solve. Sorry for the bad news. Death is going to take us eventually and it will take people you love through your life too.
Solution: The solution to dealing with death is not to overcome it but to accept it.
Death can be our greatest motivator if we let it. Once you understand what death means in all of its darkness, you’ll understand life. You’ll see death not as a problem but as a fact. That fact will change the way you see everything going forward.
For me, it took several near-death experiences (almost being murdered and a cancer scare) to see death for what it is. Death is not an easy pill to swallow. No post like this is going to give you all the answers you’re probably wanting to know.
The only way I see of dealing with the reality of death is to go out there and live the best damn life you can, while you can! Use your life to do something that gives you meaning and then you’ll no longer see death as a problem when it comes upon you.
RELATED: 11 Little Habits Of The Strongest, Most Resilient People
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Tim Denning is a writer for Business Insider and CNBC whose work focuses on personal development and entrepreneurship.
This article was originally published at Medium . Reprinted with permission from the author.
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