Identify Goal
Define Problem
Define Problem
Gather Data
Define Causes
Identify Options
Clarify Problem
Generate Ideas
Evaluate Options
Generate Ideas
Choose the Best Solution
Implement Solution
Select Solution
Take Action
MacLeod offers her own problem solving procedure, which echoes the above steps:
“1. Recognize the Problem: State what you see. Sometimes the problem is covert. 2. Identify: Get the facts — What exactly happened? What is the issue? 3. and 4. Explore and Connect: Dig deeper and encourage group members to relate their similar experiences. Now you're getting more into the feelings and background [of the situation], not just the facts. 5. Possible Solutions: Consider and brainstorm ideas for resolution. 6. Implement: Choose a solution and try it out — this could be role play and/or a discussion of how the solution would be put in place. 7. Evaluate: Revisit to see if the solution was successful or not.”
Many of these problem solving techniques can be used in concert with one another, or multiple can be appropriate for any given problem. It’s less about facilitating a perfect CPS session, and more about encouraging team members to continually think outside the box and push beyond personal boundaries that inhibit their innovative thinking. So, try out several methods, find those that resonate best with your team, and continue adopting new techniques and adapting your processes along the way.
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5 steps (and 4 techniques) for effective problem solving.
Problem solving is the process of reviewing every element of an issue so you can get to a solution or fix it. Problem solving steps cover multiple aspects of a problem that you can bring together to find a solution. Whether that’s in a group collaboratively or independently, the process remains the same, but the approach and the steps can differ.
To find a problem solving approach that works for you, your team, or your company, you have to take into consideration the environment you’re in and the personalities around you.
Knowing the characters in the room will help you decide on the best approach to try and ultimately get to the best solution.
5 problem solving steps, 4 techniques to encourage problem solving, the bottom line.
No matter what the problem is, to solve it, you nearly always have to follow these problem solving steps. Missing any of these steps can cause the problem to either resurface or the solution to not be implemented correctly.
Once you know these steps, you can then get creative with the approach you take to find the solutions you need.
You must define and understand the problem before you start, whether you’re solving it independently or as a group. If you don’t have a single view of what the problem is, you could be fixing something that doesn’t need fixing, or you’ll fix the wrong problem.
Spend time elaborating on the problem, write it down, and discuss everything, so you’re clear on why the problem is occurring and who it is impacting.
Once you have clarity on the problem, you then need to start thinking about every possible solution . This is where you go big and broad, as you want to come up with as many alternative solutions as possible. Don’t just take the first idea; build out as many as you can through active listening, as the more you create, the more likely you’ll find a solution that has the best impact on the team.
Whichever solution you pick individually or as a team, make sure you think about the impact on others if you implement this solution. Ask questions like:
At this stage of problem solving, be prepared for feedback, and plan for this. When you roll out the solution, request feedback on the success of the change made.
Making a change shouldn’t be a one time action. Spend time reviewing the results of the change to make sure it’s made the required impact and met the desired outcomes.
Make changes where needed so you can further improve the solution implemented.
Each individual or team is going to have different needs and may need a different technique to encourage each of the problem solving steps. Try one of these to stimulate the process.
The 1-2-4-All is a good problem solving approach that can work no matter how large the group is. Everyone is involved, and you can generate a vast amount of ideas quickly.
Ideas and solutions are discussed and organized rapidly, and what is great about this approach is the attendees own their ideas, so when it comes to implementing the solutions, you don’t have more work to gain buy-in.
As a facilitator, you first need to present the group with a question explaining the problem or situation. For example, “What actions or ideas would you recommend to solve the company’s lack of quiet working areas?”
With the question clear for all to see, the group then spends 5 minutes to reflect on the question individually. They can jot down their thoughts and ideas on Post-Its.
Now ask the participants to find one or two other people to discuss their ideas and thoughts with. Ask the group to move around to find a partner so they can mix with new people.
Ask the pairs to spend 5 minutes discussing their shared ideas and thoughts.
Next, put the group into groups of two or three pairs to make groups of 4-6. Each group shouldn’t be larger than six as the chances of everyone being able to speak reduces.
Ask the group to discuss one interesting idea they’ve heard in previous rounds, and each group member shares one each.
The group then needs to pick their preferred solution to the problem. This doesn’t have to be voted on, just one that resonated most with the group.
Then ask for three actions that could be taken to implement this change.
Bring everyone back together as a group and ask open questions like “What is the one thing you discussed that stood out for you?” or “Is there something you now see differently following these discussions?”
By the end of the session, you’ll have multiple approaches to solve the problem, and the whole group will have contributed to the future solutions and improvements.
The Lightning Decision Jam is a great way to solve problems collaboratively and agree on one solution or experiment you want to try straight away. It encourages team decision making, but at the same time, the individual can get their ideas and feedback across. [1]
If, as a team, you have a particular area you want to improve upon, like the office environment, for example, this approach is perfect to incorporate in the problem solving steps.
The approach follows a simple loop.
Make a Note – Stick It on The Wall – Vote – Prioritize
Using sticky notes, the technique identifies major problems, encourages solutions, and opens the group up for discussion. It allows each team member to play an active role in identifying both problems and ways to solve them.
Mind mapping is a fantastic visual thinking tool that allows you to bring problems to life by building out the connections and visualizing the relationships that make up the problem.
You can use a mind map to quickly expand upon the problem and give yourself the full picture of the causes of the problem, as well as solutions [2] .
The goal of a mind map is to simplify the problem and link the causes and solutions to the problem.
To create a mind map, you must first create the central topic (level 1). In this case, that’s the problem.
Next, create the linked topics (level 2) that you place around and connect to the main central topic with a simple line.
If the central topic is “The client is always changing their mind at the last minute,” then you could have linked topics like:
Adding these linking topics allows you to start building out the main causes of the problem as you can begin to see the full picture of what you need to fix. Once you’re happy that you’ve covered the breadth of the problem and its issues, you can start to ideate on how you’re going to fix it with the problem solving steps.
Now, start adding subtopics (level 3) linking to each of the level 2 topics. This is where you can start to go big on solutions and ideas to help fix the problem.
For each of the linked topics (level 2), start to think about how you can prevent them, mitigate them, or improve them. As this is just ideas on paper, write down anything that comes to mind, even if you think the client will never agree to it!
The more you write down, the more ideas you’ll have until you find one or two that could solve the main problem.
Once you run out of ideas, take a step back and highlight your favorite solutions to take forward and implement.
The five why’s can sound a little controversial, and you shouldn’t try this without prepping the team beforehand.
Asking “why” is a great way to go deep into the root of the problem to make the individual or team really think about the cause. When a problem arises, we often have preconceived ideas about why this problem has occurred, which is usually based on our experiences or beliefs.
Start with describing the problem, and then the facilitator can ask “Why?” fives time or more until you get to the root of the problem. It’s tough at first to keep being asked why, but it’s also satisfying when you get to the root of the problem [3] .
As a facilitator, although the basic approach is to ask why, you need to be careful not to guide the participant down a single route.
To help with this, you can use a mind map with the problem at the center. Then ask a why question that will result in multiple secondary topics around the central problem. Having this visual representation of the problem helps you build out more useful why questions around it.
Once you get to the root of the problem, don’t forget to be clear in the actions to put a fix in place to resolve it.
Learn more about how to use the five why’s here .
To fix a problem, you must first be in a position where you fully understand it. There are many ways to misinterpret a problem, and the best way to understand them is through conversation with the team or individuals who are experiencing it.
Once you’re aligned, you can then begin to work on the solutions that will have the greatest impact through effective problem solving steps.
For the more significant or difficult problems to solve, it’s often advisable to break the solution up into smaller actions or improvements.
Trial these improvements in short iterations, and then continue the conversations to review and improve the solution. Implementing all of these steps will help you root out the problems and find useful solutions each time.
[1] | ^ | UX Planet: |
[2] | ^ | Focus: |
[3] | ^ | Expert Program Management: |
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Picture this, you're handling your daily tasks at work and your boss calls you in and says, "We have a problem."
Unfortunately, we don't live in a world in which problems are instantly resolved with the snap of our fingers. Knowing how to effectively solve problems is an important professional skill to hone. If you have a problem that needs to be solved, what is the right process to use to ensure you get the most effective solution?
In this article we'll break down the problem-solving process and how you can find the most effective solutions for complex problems.
Problem solving is the process of finding a resolution for a specific issue or conflict. There are many possible solutions for solving a problem, which is why it's important to go through a problem-solving process to find the best solution. You could use a flathead screwdriver to unscrew a Phillips head screw, but there is a better tool for the situation. Utilizing common problem-solving techniques helps you find the best solution to fit the needs of the specific situation, much like using the right tools.
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While it might be tempting to dive into a problem head first, take the time to move step by step. Here’s how you can effectively break down the problem-solving process with your team:
One of the easiest ways to identify a problem is to ask questions. A good place to start is to ask journalistic questions, like:
Who : Who is involved with this problem? Who caused the problem? Who is most affected by this issue?
What: What is happening? What is the extent of the issue? What does this problem prevent from moving forward?
Where: Where did this problem take place? Does this problem affect anything else in the immediate area?
When: When did this problem happen? When does this problem take effect? Is this an urgent issue that needs to be solved within a certain timeframe?
Why: Why is it happening? Why does it impact workflows?
How: How did this problem occur? How is it affecting workflows and team members from being productive?
Asking journalistic questions can help you define a strong problem statement so you can highlight the current situation objectively, and create a plan around that situation.
Here’s an example of how a design team uses journalistic questions to identify their problem:
Overarching problem: Design requests are being missed
Who: Design team, digital marketing team, web development team
What: Design requests are forgotten, lost, or being created ad hoc.
Where: Email requests, design request spreadsheet
When: Missed requests on January 20th, January 31st, February 4th, February 6th
How : Email request was lost in inbox and the intake spreadsheet was not updated correctly. The digital marketing team had to delay launching ads for a few days while design requests were bottlenecked. Designers had to work extra hours to ensure all requests were completed.
In this example, there are many different aspects of this problem that can be solved. Using journalistic questions can help you identify different issues and who you should involve in the process.
If at all possible, bring in a facilitator who doesn't have a major stake in the solution. Bringing an individual who has little-to-no stake in the matter can help keep your team on track and encourage good problem-solving skills.
Here are a few brainstorming techniques to encourage creative thinking:
Brainstorm alone before hand: Before you come together as a group, provide some context to your team on what exactly the issue is that you're brainstorming. This will give time for you and your teammates to have some ideas ready by the time you meet.
Say yes to everything (at first): When you first start brainstorming, don't say no to any ideas just yet—try to get as many ideas down as possible. Having as many ideas as possible ensures that you’ll get a variety of solutions. Save the trimming for the next step of the strategy.
Talk to team members one-on-one: Some people may be less comfortable sharing their ideas in a group setting. Discuss the issue with team members individually and encourage them to share their opinions without restrictions—you might find some more detailed insights than originally anticipated.
Break out of your routine: If you're used to brainstorming in a conference room or over Zoom calls, do something a little different! Take your brainstorming meeting to a coffee shop or have your Zoom call while you're taking a walk. Getting out of your routine can force your brain out of its usual rut and increase critical thinking.
After you brainstorm with team members to get their unique perspectives on a scenario, it's time to look at the different strategies and decide which option is the best solution for the problem at hand. When defining the solution, consider these main two questions: What is the desired outcome of this solution and who stands to benefit from this solution?
Set a deadline for when this decision needs to be made and update stakeholders accordingly. Sometimes there's too many people who need to make a decision. Use your best judgement based on the limitations provided to do great things fast.
To implement your solution, start by working with the individuals who are as closest to the problem. This can help those most affected by the problem get unblocked. Then move farther out to those who are less affected, and so on and so forth. Some solutions are simple enough that you don’t need to work through multiple teams.
After you prioritize implementation with the right teams, assign out the ongoing work that needs to be completed by the rest of the team. This can prevent people from becoming overburdened during the implementation plan . Once your solution is in place, schedule check-ins to see how the solution is working and course-correct if necessary.
There are a few ways to go about identifying problems (and solutions). Here are some strategies you can try, as well as common ways to apply them:
Trial and error problem solving doesn't usually require a whole team of people to solve. To use trial and error problem solving, identify the cause of the problem, and then rapidly test possible solutions to see if anything changes.
This problem-solving method is often used in tech support teams through troubleshooting.
The 5 whys problem-solving method helps get to the root cause of an issue. You start by asking once, “Why did this issue happen?” After answering the first why, ask again, “Why did that happen?” You'll do this five times until you can attribute the problem to a root cause.
This technique can help you dig in and find the human error that caused something to go wrong. More importantly, it also helps you and your team develop an actionable plan so that you can prevent the issue from happening again.
Here’s an example:
Problem: The email marketing campaign was accidentally sent to the wrong audience.
“Why did this happen?” Because the audience name was not updated in our email platform.
“Why were the audience names not changed?” Because the audience segment was not renamed after editing.
“Why was the audience segment not renamed?” Because everybody has an individual way of creating an audience segment.
“Why does everybody have an individual way of creating an audience segment?” Because there is no standardized process for creating audience segments.
“Why is there no standardized process for creating audience segments?” Because the team hasn't decided on a way to standardize the process as the team introduced new members.
In this example, we can see a few areas that could be optimized to prevent this mistake from happening again. When working through these questions, make sure that everyone who was involved in the situation is present so that you can co-create next steps to avoid the same problem.
A SWOT analysis can help you highlight the strengths and weaknesses of a specific solution. SWOT stands for:
Strength: Why is this specific solution a good fit for this problem?
Weaknesses: What are the weak points of this solution? Is there anything that you can do to strengthen those weaknesses?
Opportunities: What other benefits could arise from implementing this solution?
Threats: Is there anything about this decision that can detrimentally impact your team?
As you identify specific solutions, you can highlight the different strengths, weaknesses, opportunities, and threats of each solution.
This particular problem-solving strategy is good to use when you're narrowing down the answers and need to compare and contrast the differences between different solutions.
After you’ve worked through a tough problem, don't forget to celebrate how far you've come. Not only is this important for your team of problem solvers to see their work in action, but this can also help you become a more efficient, effective , and flexible team. The more problems you tackle together, the more you’ll achieve.
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Mckinsey approach to problem solving, a guide to the 7-step mckinsey problem solving process.
McKinsey and Company is recognized for its rigorous approach to problem solving. They train their consultants on their seven-step process that anyone can learn.
This resource guides you through that process, largely informed by the McKinsey Staff Paper 66. It also includes a PowerPoint Toolkit with slide templates of each step of the process that you can download and customize for your own use.
Overview of the mckinsey approach to problem solving, problem solving process, problem definition.
Structure the problem, hypothesis trees, issue trees, analyses and workplan, synthesize findings, craft recommendations, communicate, distinctiveness practices, harness the power of collaboration, sources and additional reading, request the mckinsey approach to problem solving.
Problem solving — finding the optimal solution to a given business opportunity or challenge — is the very heart of how consultants create client impact, and considered the most important skill for success at McKinsey.
The characteristic “McKinsey method” of problem solving is a structured, inductive approach that can be used to solve any problem. Using this standardized process saves us from reinventing the problem-solving wheel, and allows for greater focus on distinctiveness in the solution. Every new McKinsey associate must learn this method on his or her first day with the firm.
There are four fundamental disciplines of the McKinsey method:
A thorough understanding and crisp definition of the problem.
Structuring the problem, prioritizing the issues, planning analyses, conducting analyses, synthesizing findings, and developing recommendations.
Constructing alternative perspectives; identifying relationships; distilling the essence of an issue, analysis, or recommendation; and staying ahead of others in the problem-solving process.
Actively seeking out client, customer, and supplier perspectives, as well as internal and external expert insight and knowledge.
Once the problem has been defined, the problem-solving process proceeds with a series of steps:
Not all problems require strict adherence to the process. Some steps may be truncated, such as when specific knowledge or analogies from other industries make it possible to construct hypotheses and associated workplans earlier than their formal place in the process. Nonetheless, it remains important to be capable of executing every step in the basic process.
When confronted with a new and complex problem, this process establishes a path to defining and disaggregating the problem in a way that will allow the team to move to a solution. The process also ensures nothing is missed and concentrates efforts on the highest-impact areas. Adhering to the process gives the client clear steps to follow, building confidence, credibility, and long-term capability.
The most important step in your entire project is to first carefully define the problem. The problem definition will serve the guide all of the team’s work, so it is critical to ensure that all key stakeholders agree that it is the right problem to be solving.
The problem definition will serve the guide all of the team’s work, so it is critical to ensure that all key stakeholders agree that it is the right problem to be solving.
There are often dozens of issues that a team could focus on, and it is often not obvious how to define the problem.
In any real-life situation, there are many possible problem statements. Your choice of problem statement will serve to constrain the range of possible solutions.
Constraints can be a good thing (e.g., limit solutions to actions within the available budget.) And constraints can be a bad thing (e.g., eliminating the possibility of creative ideas.) So choose wisely.
The problem statement may ignore many issues to focus on the priority that should be addressed. The problem statement should be phrased as a question, such that the answer will be the solution.
A mother, a father, and their two teenage children have all arrived home on a Friday at 6 p.m. The family has not prepared dinner for Friday evening. The daughter has lacrosse practice on Saturday and an essay to write for English class due on Monday. The son has theatre rehearsal on both Saturday and Sunday and will need one parent to drive him to the high school both days, though he can get a ride home with a friend.
The family dog, a poodle, must be taken to the groomer on Saturday morning. The mother will need to spend time this weekend working on assignments for her finance class she is taking as part of her Executive MBA. The father plans to go on a 100-mile bike ride, which he can do either Saturday or Sunday. The family has two cars, but one is at the body shop. They are trying to save money to pay for an addition to their house.
The problem definition should not be vague, without clear measures of success. Rather, it should be a SMART definition:
Given one set of facts, it is possible to come up with many possible problem statements. The choice of problem statement constrains the range of possible solutions.
Before starting to solve the problem, the family first needs to agree on what problem they want to solve.
This is a helpful tool to use to clearly define the problem. There are often dozens of issues that a team could focus on, and it is often not obvious how to define the problem. In any real-life situation, there are many possible problem statements. Your choice of problem statement will serve to constrain the range of possible solutions.
In completing the Problem Statement Worksheet, you are prompted to define the key stakeholders.
As you become involved in the problem-solving process, you should expand the question of key stakeholders to include what the team wants from them and what they want from the team, their values and motivations (helpful and unhelpful), and the communications mechanisms that will be most effective for each of them.
Using the Stakeholder Analysis Worksheet allows you to comprehensively identify:
The two most helpful techniques for rigorously structuring any problem are hypothesis trees and issue trees. Each of these techniques disaggregates the primary question into a cascade of issues or hypotheses that, when addressed, will together answer the primary question.
A hypothesis tree might break down the same question into two or more hypotheses.
The aim at this stage is to structure the problem into discrete, mutually exclusive pieces that are small enough to yield to analysis and that, taken together, are collectively exhaustive.
Articulating the problem as hypotheses, rather than issues, is the preferred approach because it leads to a more focused analysis of the problem. Questions to ask include:
Quickly developing a powerful hypothesis tree enables us to develop solutions more rapidly that will have real impact. This can sometimes seem premature to clients, who might find the “solution” reached too quickly and want to see the analysis behind it.
Take care to explain the approach (most important, that a hypothesis is not an answer) and its benefits (that a good hypothesis is the basis of a proven means of successful problem solving and avoids “boiling the ocean”).
Problem Statement: How can Alpha increase EBITDA by $13M (to $50M) by 2025?
The hypotheses might be:
These hypotheses will be further disaggregated into subsidiary hypotheses at the next level of the tree.
Often, the team has insufficient knowledge to build a complete hypothesis tree at the start of an engagement. In these cases, it is best to begin by structuring the problem using an issue tree.
An issue tree is best set out as a series of open questions in sentence form. For example, “How can the client minimize its tax burden?” is more useful than “Tax.” Open questions – those that begin with what, how, or why– produce deeper insights than closed ones. In some cases, an issue tree can be sharpened by toggling between issue and hypothesis – working forward from an issue to identify the hypothesis, and back from the hypothesis to sharpen the relevant open question.
Once the problem has been structured, the next step is to prioritize the issues or hypotheses on which the team will focus its work. When prioritizing, it is common to use a two-by-two matrix – e.g., a matrix featuring “impact” and “ease of impact” as the two axes.
Applying some of these prioritization criteria will knock out portions of the issue tree altogether. Consider testing the issues against them all, albeit quickly, to help drive the prioritization process.
Once the criteria are defined, prioritizing should be straightforward: Simply map the issues to the framework and focus on those that score highest against the criteria.
As the team conducts analysis and learns more about the problem and the potential solution, make sure to revisit the prioritization matrix so as to remain focused on the highest-priority issues.
The issues might be:
Each of these issues is then further broken down into deeper insights to solutions.
If the prioritization has been carried out effectively, the team will have clarified the key issues or hypotheses that must be subjected to analysis. The aim of these analyses is to prove the hypotheses true or false, or to develop useful perspectives on each key issue. Now the task is to design an effective and efficient workplan for conducting the analyses.
Transforming the prioritized problem structure into a workplan involves two main tasks:
A good workplan will detail the following for each issue or hypothesis: analyses, end products, sources, and timing and responsibility. Developing the workplan takes time; doing it well requires working through the definition of each element of the workplan in a rigorous and methodical fashion.
It’s useful to match the workplan to three horizons:
The detail in the workplan will typically be greater for the near term (the next week) than for the long term (the study horizon), especially early in a new engagement when considerable ambiguity about the end state remains.
Here are three different templates for a workplan:
This is the most difficult element of the problem-solving process. After a period of being immersed in the details, it is crucial to step back and distinguish the important from the merely interesting. Distinctive problem solvers seek the essence of the story that will underpin a crisp recommendation for action.
Although synthesis appears, formally speaking, as the penultimate step in the process, it should happen throughout. Ideally, after you have made almost any analytical progress, you should attempt to articulate the “Day 1” or “Week 1” answer. Continue to synthesize as you go along. This will remind the team of the question you are trying to answer, assist prioritization, highlight the logical links of the emerging solution, and ensure that you have a story ready to articulate at all times during the study.
McKinsey’s primary tool for synthesizing is the pyramid principle. Essentially, this principle asserts that every synthesis should explain a single concept, per the “governing thought.” The supporting ideas in the synthesis form a thought hierarchy proceeding in a logical structure from the most detailed facts to the governing thought, ruthlessly excluding the interesting but irrelevant.
While this hierarchy can be laid out as a tree (like with issue and hypothesis trees), the best problem solvers capture it by creating dot-dash storylines — the Pyramid Structure for Grouping Arguments.
It is at this point that we address the client’s questions: “What do I do, and how do I do it?” This means not offering actionable recommendations, along with a plan and client commitment for implementation.
The essence of this step is to translate the overall solution into the actions required to deliver sustained impact. A pragmatic action plan should include:
Crucial questions to ask as you build recommendations for organizational change are:
Once the recommendations have been crafted in the problem-solving process, it’s vital to effectively communicate those findings and recommendations.
An executive summary is a great slide to use for this. See more on executive summary slides, including 30 templates, at our Ultimate Guide to Executive Summary Slides .
Great problem solvers identify unique disruptions and discontinuities, novel insights, and step-out opportunities that lead to truly distinctive impact. This is done by applying a number of practices throughout the problem-solving process to help develop these insights.
Identifying alternative ways of looking at the problem expands the range of possibilities, opens you up to innovative ideas, and allows you to formulate more powerful hypotheses. Questions that help here include:
Strong problem solvers discern connections and recognize patterns in two different ways:
Cutting through complexity to identify the heart of the problem and its solution is a critical skill.
Without getting ahead of the client, you cannot be distinctive. Paradoxically, to get ahead – and stay ahead – it is often necessary to step back from the problem to validate or revalidate the approach and the solution.
No matter how skilled, knowledgeable, or experienced you are, you will never create the most distinctive solution on your own. The best problem solvers know how to leverage the power of their team, clients, the Firm, and outside parties. Seeking the right expertise at the right time, and leveraging it in the right way, are ultimately how we bring distinctiveness to our work, how we maximize efficiency, and how we learn.
When solving a problem, it is important to ask, “Have I accessed all the sources of insight that are available?” Here are the sources you should consider:
The key here is to think open, not closed. Opening up to varied sources of data and perspectives furthers our mission to develop truly innovative and distinctive solutions for our clients.
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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.
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Last Updated: Aug 28, 2024
By Roger Meslar, BARBRI Sr. Director of MBE Testing and Assessments
During the Multistate Bar Exam (MBE), you’ll answer 200 multiple-choice questions over a total 6-hour timeframe – 100 questions in the 3-hour morning session and 100 in the 3-hour afternoon session. This means that you’ll have an average of 1.8 minutes to answer each MBE question. Getting through these questions quickly enough on the exam requires a repeatable methodology or approach.
Using this systematic approach, you’ll focus more on the problem to solve and less on the details that are potentially irrelevant. By coming to your own conclusion before comparing it to the answers available to you, you’ll also move more quickly through each question.
Some people think it might be better to skip the difficult questions and come back to them at the end. We advise you not to hold hard questions. At the end of the test, you’re tired and your critical thinking skills are at their lowest.
Go ahead and deal with them head-on. Using the systematic approach, mark your best guess to the answer in the booklet. When you’ve finished answering all the questions, you can go back and check those marked answers if you have the time.
When tackling the questions that require more time, you can actually use those questions as an opportunity to make up time. Take one minute and use the systematic approach to make your best guess and continue through the test. The correct answer will usually stick out as familiar to you.
Check out more U.S. bar exam study tips . BARBRI’s MBE success learning path, combined with knowing where you are on the bar exam curve before you sit for the actual MBE, help you study smarter, not harder.
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Rearrangement of single atoms by solving assignment problems via convolutional neural network.
1. introduction, 2. methodology, model formulation, 3. convolutional neural network model formulation, understand the data.
5. conclusions, author contributions, institutional review board statement, informed consent statement, data availability statement, conflicts of interest.
Click here to enlarge figure
Problem Size (Target Size) | Number of Datasets | Percentage of Overall Position Accuracy | Percentage of 98% Correct Arrangement | Percentage of 99% Correct Arrangement | Percentage of Defect-Free Arrangement |
---|---|---|---|---|---|
10 × 10 Grid (49 Atoms) | 200,000 | 99.63 | 99.10 | 98.44 | 87.85 |
13 × 13 Grid (81 Atoms) | 600,000 | 98.93 | 95.10 | 89.01 | 68.54 |
21 × 21 Grid (169 Atoms) | 1,000,000 | 97.24 | 87.80 | 59.04 | 4.45 |
Problem Size | Calculation Time per Dataset (Calculation Time 5000 Datasets) | % Time Saving (Time Reduction) | |
---|---|---|---|
Optimal Solution | CNN | ||
10 × 10 Grid | 0.0159 (79.73) s | 0.0031 (15.32) s | 80.50 (5.12 folds) |
13 × 13 Grid | 0.0898 (449.14) s | 0.0048 (24.38) s | 94.65 (18.71 folds) |
21 × 21 Grid | 1.289 (6445.9) s | 0.0061 (30.50) s | 99.53 (211.3 folds) |
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Rattanamongkhonkun, K.; Pongvuthithum, R.; Likasiri, C. Rearrangement of Single Atoms by Solving Assignment Problems via Convolutional Neural Network. Appl. Sci. 2024 , 14 , 7877. https://doi.org/10.3390/app14177877
Rattanamongkhonkun K, Pongvuthithum R, Likasiri C. Rearrangement of Single Atoms by Solving Assignment Problems via Convolutional Neural Network. Applied Sciences . 2024; 14(17):7877. https://doi.org/10.3390/app14177877
Rattanamongkhonkun, Kanya, Radom Pongvuthithum, and Chulin Likasiri. 2024. "Rearrangement of Single Atoms by Solving Assignment Problems via Convolutional Neural Network" Applied Sciences 14, no. 17: 7877. https://doi.org/10.3390/app14177877
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The C4DLab is running a week-long training program for faculty on Design Thinking and Problem-Based Learning, innovative problem-solving approaches. The training, aptly dubbed “Innovation Training” for revolutionary approach to solving real-world problems, is currently underway in the PhD room of the Department of Computing and Informatics.
The training has attracted participants from various faculties within the University of Nairobi and is set to conclude on Friday, September 6, 2024.
This training programme aligns with Afretech's Innovation and Entrepreneurship Pillar, headed by Dr. Sam Ruhiu, the primary facilitator of the workshop.
Dr. Ruhiu emphasized the need for a paradigm shift among university faculty, stressing the need to move beyond mere scholarly research results and translate them into practical innovations that address real-world needs. He highlighted the importance of a mental shift towards entrepreneurship, which involves creating products and services that meet consumer demands as a way of completing the innovation pipeline.
Historically, many valuable research projects by both faculty and students have stalled at the research results stage, failing to progress to innovation and entrepreneurship. This training aims to rectify this trend.
The morning session provided a foundation for Design Thinking, covering its historical development and case studies from renowned global academic institutions like Stanford, MIT and University of Colorado in the U.S., and Aalto in Finland.
The session also explored notable innovation failures, such as those by Thomas Edison (the inventor of the light bulb), AT&T, and Warner Annex. These failures were often attributed to a techno-centric focus rather than a user-needs-driven approach.
The training's goal is to equip educators with practical tools and strategies to foster creativity and critical thinking in the classroom. By enhancing faculty's ability to drive innovation, the training seeks to prepare students for future problem-solving challenges.
The specific objectives of the training include:
The second session, co-facilitated by Dr. Ruhiu, Mr. Peter Oketch and Ms. Caroline Jelagat, involved a number of team-building exercises where participants from different faculties worked together to construct a tower. The exercises demonstrated the importance of teamwork, a crucial aspect of Design Thinking.
The session concluded with a reflection time, during which participants considered the most challenging aspects of the task, individual roles, and the emergence of leadership within the group. Then there was Experience Design, where a two-member team designed a gift-giving experience for the partner in turn and each evaluated the experience through discovery questions.
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This paper proposes a modeling and solution approach for the integrated planning of the planting and harvesting of sucrose cane and energy-cane considering multiple harvesters. An integer linear bi-objective optimization model is proposed, which seeks to find a trade-off between the maximization of the production volumes of sucrose and fiber and the minimization of the operational costs. The model considers the technical constraints of the mill, such as the milling capacity and meeting the monthly demand. A MIP-heuristic based on relax-and-fix and fix-and-optimize strategies with exact decomposition is appropriately proposed to determine approximations to Pareto optimal solutions to this problem. These approximations are used as incumbents for a branch-and-bound tree to generate potentially Pareto optimal solutions. The results reveal that the MIP-heuristic efficiently solves the problem for real and semi-random instances, generating approximate solutions with a reduced error and a reasonable computational effort. Moreover, the different solutions quantify the trade-off between cost and production volume, opening up the possibility of increasing sucrose and fiber content or decreasing the costs of solutions found. Thus, the proposed bi-objective approach, the solution technique and the different Pareto optimal solutions obtained can assist mill managers in making better decisions in sugarcane production.
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A multiple objective methodology for sugarcane harvest management with varying maturation periods.
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The authors thank to Brazilian foundations: CNPq n \(^{\textrm{o}}\) 306518/2022-8, CNPq n \(^{\textrm{o}}\) 304218/2022-7, FAPESP 2021/03039-1,FAPESP 2022/12652-1, PROPE/PROPG/UNESP/ FUNDUNESP grant 12/2022, for the financial support and language services provided.
Gilmar Tolentino, Antônio Roberto Balbo, Sônia Cristina Poltroniere, Angelo Aliano Filho and Helenice de Oliveira Florentino have contributed equally to this work.
Department of Mathematics, State University of Sao Paulo, Bauru, São Paulo, 17033-360, Brazil
Gilmar Tolentino, Antônio Roberto Balbo & Sônia Cristina Poltroniere
Department of Mathematics, Universidade Tecnológica Federal do Paraná, Apucarana, Paraná, 86812-460, Brazil
Angelo Aliano Filho
Department of Bioestatistics, State University of Sao Paulo, Botucatu, São Paulo, 18618-690, Brazil
Helenice de Oliveira Florentino
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Problem-solving strategies can be enhanced with the application of creative techniques. You can use creativity to: Approach problems from different angles. Improve your problem-solving process. Spark creativity in your employees and peers. 6. Adaptability. Adaptability is the capacity to adjust to change. When a particular solution to an issue ...
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 ...
As to why this is the case, we need to consider the Asian learning-sociocultural context as a contributing factor. Asian students are more familiar with algebra problem-solving as opposed to non-algebra problem-solving strategies (Cai, Citation 2000; Ngu et al., Citation 2018). Thus, we reason that Asian students in this study, irrespective of ...
BARBRI'S systematic approach to MBE problem solving: First, cover the answer choices and read the call of the question so you can determine the subject being tested and the issue you are tasked to answer - without being distracted by the answer choices.
This paper aims to present an approach to address the atom rearrangement problem by developing Convolutional Neural Network (CNN) models. These models predict the coordinates for atom movements while ensuring collision-free transitions and filling all vacancies in the target array. The process begins with designing a cost function for the assignment problem that incorporates constraints to ...
The C4DLab is running a week-long training program for faculty on Design Thinking and Problem-Based Learning, innovative problem-solving approaches. The training, aptly dubbed "Innovation Training" for revolutionary approach to solving real-world problems, is currently underway in the PhD room of the Department of Computing and Informatics.
This paper proposes a modeling and solution approach for the integrated planning of the planting and harvesting of sucrose cane and energy-cane considering multiple harvesters. An integer linear bi-objective optimization model is proposed, which seeks to find a trade-off between the maximization of the production volumes of sucrose and fiber and the minimization of the operational costs. The ...