art of problem solving sample questions

The Art of Effective Problem Solving: A Step-by-Step Guide

Whether we realise it or not, problem solving skills are an important part of our daily lives. From resolving a minor annoyance at home to tackling complex business challenges at work, our ability to solve problems has a significant impact on our success and happiness. However, not everyone is naturally gifted at problem-solving, and even those who are can always improve their skills. In this blog post, we will go over the art of effective problem-solving step by step.

Problem Solving Methodologies

Methodology of 8D (Eight Discipline) Problem Solving:

A3 Problem Solving Method:

The A3 problem solving technique is a visual, team-based problem-solving approach that is frequently used in Lean Six Sigma projects. The A3 report is a one-page document that clearly and concisely outlines the problem, root cause analysis, and proposed solution.

Subsequently, in the Lean Six Sigma framework, the 8D and A3 problem solving methodologies are two popular approaches to problem solving. Both methodologies provide a structured, team-based problem-solving approach that guides individuals through a comprehensive and systematic process of identifying, analysing, and resolving problems in an effective and efficient manner.

Step 1 – Define the Problem

By repeatedly asking “ why ,” you’ll eventually get to the bottom of the problem. This is an important step in the problem-solving process because it ensures that you’re dealing with the root cause rather than just the symptoms.

Step 2 – Gather Information and Brainstorm Ideas

Gathering information and brainstorming ideas is the next step in effective problem solving. This entails researching the problem and relevant information, collaborating with others, and coming up with a variety of potential solutions. This increases your chances of finding the best solution to the problem.

Next, work with others to gather a variety of perspectives. Brainstorming with others can be an excellent way to come up with new and creative ideas. Encourage everyone to share their thoughts and ideas when working in a group, and make an effort to actively listen to what others have to say. Be open to new and unconventional ideas and resist the urge to dismiss them too quickly.

Once you’ve compiled a list of potential solutions, it’s time to assess them and select the best one. This is the next step in the problem-solving process, which we’ll go over in greater detail in the following section.

Step 3 – Evaluate Options and Choose the Best Solution

Once you’ve compiled a list of potential solutions, it’s time to assess them and select the best one. This is the third step in effective problem solving, and it entails weighing the advantages and disadvantages of each solution, considering their feasibility and practicability, and selecting the solution that is most likely to solve the problem effectively.

You’ll be able to tell which solutions are likely to succeed and which aren’t by assessing their feasibility and practicability.

Step 4 – Implement and Monitor the Solution

When you’ve decided on the best solution, it’s time to put it into action. The fourth and final step in effective problem solving is to put the solution into action, monitor its progress, and make any necessary adjustments.

Finally, make any necessary modifications to the solution. This could entail changing the solution, altering the plan of action, or delegating different tasks. Be willing to make changes if they will improve the solution or help it solve the problem more effectively.

You can increase your chances of success in problem solving by following these steps and considering factors such as the pros and cons of each solution, their feasibility and practicability, and making any necessary adjustments. Furthermore, keep in mind that problem solving is an iterative process, and there may be times when you need to go back to the beginning and restart. Maintain your adaptability and try new solutions until you find the one that works best for you.

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What’s The Best Approach to MBE Questions?

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.

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.
• If the call of the question isn’t specific enough, read the sentence above the call for more guidance and, if necessary, quickly scan the answer choices for subject-specific buzzwords.
• While still hiding the answer choices, use the facts –and the law associated with those facts–to formulate your own answer.
• Lastly, carefully read the answer choices provided to find the one that best fits the answer you arrived at using the steps above.

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.

Should I skip hard questions and come back?

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.

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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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26 Expert-Backed Problem Solving Examples – Interview Answers

Published: February 13, 2023

Interview Questions and Answers

Actionable advice from real experts:

Biron Clark

Former Recruiter

Contributor

Dr. Kyle Elliott

Career Coach

Hayley Jukes

Editor-in-Chief

Biron Clark , Former Recruiter

Kyle Elliott , Career Coach

Hayley Jukes , Editor

As a recruiter , I know employers like to hire people who can solve problems and work well under pressure.

 A job rarely goes 100% according to plan, so hiring managers are more likely to hire you if you seem like you can handle unexpected challenges while staying calm and logical.

But how do they measure this?

Hiring managers will ask you interview questions about your problem-solving skills, and they might also look for examples of problem-solving on your resume and cover letter. 

In this article, I’m going to share a list of problem-solving examples and sample interview answers to questions like, “Give an example of a time you used logic to solve a problem?” and “Describe a time when you had to solve a problem without managerial input. How did you handle it, and what was the result?”

• Problem-solving involves identifying, prioritizing, analyzing, and solving problems using a variety of skills like critical thinking, creativity, decision making, and communication.
• Describe the Situation, Task, Action, and Result ( STAR method ) when discussing your problem-solving experiences.
• Tailor your interview answer with the specific skills and qualifications outlined in the job description.
• Provide numerical data or metrics to demonstrate the tangible impact of your problem-solving efforts.

What are Problem Solving Skills? 

Problem-solving is the ability to identify a problem, prioritize based on gravity and urgency, analyze the root cause, gather relevant information, develop and evaluate viable solutions, decide on the most effective and logical solution, and plan and execute implementation. 

Problem-solving encompasses other skills that can be showcased in an interview response and your resume. Problem-solving skills examples include:

• Critical thinking
• Analytical skills
• Decision making
• Research skills
• Technical skills
• Communication skills
• Adaptability and flexibility

Why is Problem Solving Important in the Workplace?

Problem-solving is essential in the workplace because it directly impacts productivity and efficiency. Whenever you encounter a problem, tackling it head-on prevents minor issues from escalating into bigger ones that could disrupt the entire workflow. 

Beyond maintaining smooth operations, your ability to solve problems fosters innovation. It encourages you to think creatively, finding better ways to achieve goals, which keeps the business competitive and pushes the boundaries of what you can achieve. 

Effective problem-solving also contributes to a healthier work environment; it reduces stress by providing clear strategies for overcoming obstacles and builds confidence within teams. 

Examples of Problem-Solving in the Workplace

• Correcting a mistake at work, whether it was made by you or someone else
• Overcoming a delay at work through problem solving and communication
• Resolving an issue with a difficult or upset customer
• Overcoming issues related to a limited budget, and still delivering good work through the use of creative problem solving
• Overcoming a scheduling/staffing shortage in the department to still deliver excellent work
• Troubleshooting and resolving technical issues
• Handling and resolving a conflict with a coworker
• Solving any problems related to money, customer billing, accounting and bookkeeping, etc.
• Taking initiative when another team member overlooked or missed something important
• Taking initiative to meet with your superior to discuss a problem before it became potentially worse
• Solving a safety issue at work or reporting the issue to those who could solve it
• Using problem solving abilities to reduce/eliminate a company expense
• Finding a way to make the company more profitable through new service or product offerings, new pricing ideas, promotion and sale ideas, etc.
• Changing how a process, team, or task is organized to make it more efficient
• Using creative thinking to come up with a solution that the company hasn’t used before
• Performing research to collect data and information to find a new solution to a problem
• Boosting a company or team’s performance by improving some aspect of communication among employees
• Finding a new piece of data that can guide a company’s decisions or strategy better in a certain area

Problem-Solving Examples for Recent Grads/Entry-Level Job Seekers

• Coordinating work between team members in a class project
• Reassigning a missing team member’s work to other group members in a class project
• Adjusting your workflow on a project to accommodate a tight deadline
• Speaking to your professor to get help when you were struggling or unsure about a project
• Asking classmates, peers, or professors for help in an area of struggle
• Talking to your academic advisor to brainstorm solutions to a problem you were facing
• Researching solutions to an academic problem online, via Google or other methods
• Using problem solving and creative thinking to obtain an internship or other work opportunity during school after struggling at first

How To Answer “Tell Us About a Problem You Solved”

When you answer interview questions about problem-solving scenarios, or if you decide to demonstrate your problem-solving skills in a cover letter (which is a good idea any time the job description mentions problem-solving as a necessary skill), I recommend using the STAR method.

STAR stands for:

It’s a simple way of walking the listener or reader through the story in a way that will make sense to them. 

Start by briefly describing the general situation and the task at hand. After this, describe the course of action you chose and why. Ideally, show that you evaluated all the information you could given the time you had, and made a decision based on logic and fact. Finally, describe the positive result you achieved.

Note: Our sample answers below are structured following the STAR formula. Be sure to check them out!

EXPERT ADVICE

Dr. Kyle Elliott , MPA, CHES Tech & Interview Career Coach caffeinatedkyle.com

How can I communicate complex problem-solving experiences clearly and succinctly?

Before answering any interview question, it’s important to understand why the interviewer is asking the question in the first place.

When it comes to questions about your complex problem-solving experiences, for example, the interviewer likely wants to know about your leadership acumen, collaboration abilities, and communication skills, not the problem itself.

Therefore, your answer should be focused on highlighting how you excelled in each of these areas, not diving into the weeds of the problem itself, which is a common mistake less-experienced interviewees often make.

Tailoring Your Answer Based on the Skills Mentioned in the Job Description

As a recruiter, one of the top tips I can give you when responding to the prompt “Tell us about a problem you solved,” is to tailor your answer to the specific skills and qualifications outlined in the job description. 

Once you’ve pinpointed the skills and key competencies the employer is seeking, craft your response to highlight experiences where you successfully utilized or developed those particular abilities. 

For instance, if the job requires strong leadership skills, focus on a problem-solving scenario where you took charge and effectively guided a team toward resolution. 

By aligning your answer with the desired skills outlined in the job description, you demonstrate your suitability for the role and show the employer that you understand their needs.

Amanda Augustine expands on this by saying:

“Showcase the specific skills you used to solve the problem. Did it require critical thinking, analytical abilities, or strong collaboration? Highlight the relevant skills the employer is seeking.”  

Interview Answers to “Tell Me About a Time You Solved a Problem”

Now, let’s look at some sample interview answers to, “Give me an example of a time you used logic to solve a problem,” or “Tell me about a time you solved a problem,” since you’re likely to hear different versions of this interview question in all sorts of industries.

The example interview responses are structured using the STAR method and are categorized into the top 5 key problem-solving skills recruiters look for in a candidate.

1. Analytical Thinking

Situation: In my previous role as a data analyst , our team encountered a significant drop in website traffic.

Task: I was tasked with identifying the root cause of the decrease.

Action: I conducted a thorough analysis of website metrics, including traffic sources, user demographics, and page performance. Through my analysis, I discovered a technical issue with our website’s loading speed, causing users to bounce. 

Result: By optimizing server response time, compressing images, and minimizing redirects, we saw a 20% increase in traffic within two weeks.

2. Critical Thinking

Situation: During a project deadline crunch, our team encountered a major technical issue that threatened to derail our progress.

Task: My task was to assess the situation and devise a solution quickly.

Action: I immediately convened a meeting with the team to brainstorm potential solutions. Instead of panicking, I encouraged everyone to think outside the box and consider unconventional approaches. We analyzed the problem from different angles and weighed the pros and cons of each solution.

Result: By devising a workaround solution, we were able to meet the project deadline, avoiding potential delays that could have cost the company $100,000 in penalties for missing contractual obligations.

3. Decision Making

Situation: As a project manager , I was faced with a dilemma when two key team members had conflicting opinions on the project direction.

Task: My task was to make a decisive choice that would align with the project goals and maintain team cohesion.

Action: I scheduled a meeting with both team members to understand their perspectives in detail. I listened actively, asked probing questions, and encouraged open dialogue. After carefully weighing the pros and cons of each approach, I made a decision that incorporated elements from both viewpoints.

Result: The decision I made not only resolved the immediate conflict but also led to a stronger sense of collaboration within the team. By valuing input from all team members and making a well-informed decision, we were able to achieve our project objectives efficiently.

4. Communication (Teamwork)

Situation: During a cross-functional project, miscommunication between departments was causing delays and misunderstandings.

Task: My task was to improve communication channels and foster better teamwork among team members.

Action: I initiated regular cross-departmental meetings to ensure that everyone was on the same page regarding project goals and timelines. I also implemented a centralized communication platform where team members could share updates, ask questions, and collaborate more effectively.

Result: Streamlining workflows and improving communication channels led to a 30% reduction in project completion time, saving the company $25,000 in operational costs.

5. Persistence 

Situation: During a challenging sales quarter, I encountered numerous rejections and setbacks while trying to close a major client deal.

Task: My task was to persistently pursue the client and overcome obstacles to secure the deal.

Action: I maintained regular communication with the client, addressing their concerns and demonstrating the value proposition of our product. Despite facing multiple rejections, I remained persistent and resilient, adjusting my approach based on feedback and market dynamics.

Result: After months of perseverance, I successfully closed the deal with the client. By closing the major client deal, I exceeded quarterly sales targets by 25%, resulting in a revenue increase of $250,000 for the company.

Tips to Improve Your Problem-Solving Skills

Throughout your career, being able to showcase and effectively communicate your problem-solving skills gives you more leverage in achieving better jobs and earning more money .

So to improve your problem-solving skills, I recommend always analyzing a problem and situation before acting.

 When discussing problem-solving with employers, you never want to sound like you rush or make impulsive decisions. They want to see fact-based or data-based decisions when you solve problems.

Don’t just say you’re good at solving problems. Show it with specifics. How much did you boost efficiency? Did you save the company money? Adding numbers can really make your achievements stand out.

To get better at solving problems, analyze the outcomes of past solutions you came up with. You can recognize what works and what doesn’t.

Think about how you can improve researching and analyzing a situation, how you can get better at communicating, and deciding on the right people in the organization to talk to and “pull in” to help you if needed, etc.

Finally, practice staying calm even in stressful situations. Take a few minutes to walk outside if needed. Step away from your phone and computer to clear your head. A work problem is rarely so urgent that you cannot take five minutes to think (with the possible exception of safety problems), and you’ll get better outcomes if you solve problems by acting logically instead of rushing to react in a panic.

You can use all of the ideas above to describe your problem-solving skills when asked interview questions about the topic. If you say that you do the things above, employers will be impressed when they assess your problem-solving ability.

More Interview Resources

• 3 Answers to “How Do You Handle Stress?”
• How to Answer “How Do You Handle Conflict?” (Interview Question)
• Sample Answers to “Tell Me About a Time You Failed”

About the Author

Biron Clark is a former executive recruiter who has worked individually with hundreds of job seekers, reviewed thousands of resumes and LinkedIn profiles, and recruited for top venture-backed startups and Fortune 500 companies. He has been advising job seekers since 2012 to think differently in their job search and land high-paying, competitive positions. Follow on Twitter and LinkedIn .

Read more articles by Biron Clark

About the Contributor

Kyle Elliott , career coach and mental health advocate, transforms his side hustle into a notable practice, aiding Silicon Valley professionals in maximizing potential. Follow Kyle on LinkedIn .

About the Editor

Hayley Jukes is the Editor-in-Chief at CareerSidekick with five years of experience creating engaging articles, books, and transcripts for diverse platforms and audiences.

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Top 20 Problem Solving Interview Questions (Example Answers Included)

Mike Simpson 0 Comments

By Mike Simpson

When candidates prepare for interviews, they usually focus on highlighting their leadership, communication, teamwork, and similar crucial soft skills . However, not everyone gets ready for problem-solving interview questions. And that can be a big mistake.

Problem-solving is relevant to nearly any job on the planet. Yes, it’s more prevalent in certain industries, but it’s helpful almost everywhere.

Regardless of the role you want to land, you may be asked to provide problem-solving examples or describe how you would deal with specific situations. That’s why being ready to showcase your problem-solving skills is so vital.

If you aren’t sure who to tackle problem-solving questions, don’t worry, we have your back. Come with us as we explore this exciting part of the interview process, as well as some problem-solving interview questions and example answers.

What Is Problem-Solving?

When you’re trying to land a position, there’s a good chance you’ll face some problem-solving interview questions. But what exactly is problem-solving? And why is it so important to hiring managers?

Well, the good folks at Merriam-Webster define problem-solving as “the process or act of finding a solution to a problem.” While that may seem like common sense, there’s a critical part to that definition that should catch your eye.

What part is that? The word “process.”

In the end, problem-solving is an activity. It’s your ability to take appropriate steps to find answers, determine how to proceed, or otherwise overcome the challenge.

Being great at it usually means having a range of helpful problem-solving skills and traits. Research, diligence, patience, attention-to-detail , collaboration… they can all play a role. So can analytical thinking , creativity, and open-mindedness.

But why do hiring managers worry about your problem-solving skills? Well, mainly, because every job comes with its fair share of problems.

While problem-solving is relevant to scientific, technical, legal, medical, and a whole slew of other careers. It helps you overcome challenges and deal with the unexpected. It plays a role in troubleshooting and innovation. That’s why it matters to hiring managers.

How to Answer Problem-Solving Interview Questions

Okay, before we get to our examples, let’s take a quick second to talk about strategy. Knowing how to answer problem-solving interview questions is crucial. Why? Because the hiring manager might ask you something that you don’t anticipate.

Problem-solving interview questions are all about seeing how you think. As a result, they can be a bit… unconventional.

These aren’t your run-of-the-mill job interview questions . Instead, they are tricky behavioral interview questions . After all, the goal is to find out how you approach problem-solving, so most are going to feature scenarios, brainteasers, or something similar.

So, having a great strategy means knowing how to deal with behavioral questions. Luckily, there are a couple of tools that can help.

First, when it comes to the classic approach to behavioral interview questions, look no further than the STAR Method . With the STAR method, you learn how to turn your answers into captivating stories. This makes your responses tons more engaging, ensuring you keep the hiring manager’s attention from beginning to end.

Now, should you stop with the STAR Method? Of course not. If you want to take your answers to the next level, spend some time with the Tailoring Method , too.

With the Tailoring Method, it’s all about relevance. So, if you get a chance to choose an example that demonstrates your problem-solving skills, this is really the way to go.

We also wanted to let you know that we created an amazing free cheat sheet that will give you word-for-word answers for some of the toughest interview questions you are going to face in your upcoming interview. After all, hiring managers will often ask you more generalized interview questions!

Click below to get your free PDF now:

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Top 3 Problem-Solving-Based Interview Questions

Alright, here is what you’ve been waiting for: the problem-solving questions and sample answers.

While many questions in this category are job-specific, these tend to apply to nearly any job. That means there’s a good chance you’ll come across them at some point in your career, making them a great starting point when you’re practicing for an interview.

So, let’s dive in, shall we? Here’s a look at the top three problem-solving interview questions and example responses.

1. Can you tell me about a time when you had to solve a challenging problem?

In the land of problem-solving questions, this one might be your best-case scenario. It lets you choose your own problem-solving examples to highlight, putting you in complete control.

When you choose an example, go with one that is relevant to what you’ll face in the role. The closer the match, the better the answer is in the eyes of the hiring manager.

EXAMPLE ANSWER:

“While working as a mobile telecom support specialist for a large organization, we had to transition our MDM service from one vendor to another within 45 days. This personally physically handling 500 devices within the agency. Devices had to be gathered from the headquarters and satellite offices, which were located all across the state, something that was challenging even without the tight deadline. I approached the situation by identifying the location assignment of all personnel within the organization, enabling me to estimate transit times for receiving the devices. Next, I timed out how many devices I could personally update in a day. Together, this allowed me to create a general timeline. After that, I coordinated with each location, both expressing the urgency of adhering to deadlines and scheduling bulk shipping options. While there were occasional bouts of resistance, I worked with location leaders to calm concerns and facilitate action. While performing all of the updates was daunting, my approach to organizing the event made it a success. Ultimately, the entire transition was finished five days before the deadline, exceeding the expectations of many.”

2. Describe a time where you made a mistake. What did you do to fix it?

While this might not look like it’s based on problem-solving on the surface, it actually is. When you make a mistake, it creates a challenge, one you have to work your way through. At a minimum, it’s an opportunity to highlight problem-solving skills, even if you don’t address the topic directly.

When you choose an example, you want to go with a situation where the end was positive. However, the issue still has to be significant, causing something negative to happen in the moment that you, ideally, overcame.

“When I first began in a supervisory role, I had trouble setting down my individual contributor hat. I tried to keep up with my past duties while also taking on the responsibilities of my new role. As a result, I began rushing and introduced an error into the code of the software my team was updating. The error led to a memory leak. We became aware of the issue when the performance was hindered, though we didn’t immediately know the cause. I dove back into the code, reviewing recent changes, and, ultimately, determined the issue was a mistake on my end. When I made that discovery, I took several steps. First, I let my team know that the error was mine and let them know its nature. Second, I worked with my team to correct the issue, resolving the memory leak. Finally, I took this as a lesson about delegation. I began assigning work to my team more effectively, a move that allowed me to excel as a manager and help them thrive as contributors. It was a crucial learning moment, one that I have valued every day since.”

3. If you identify a potential risk in a project, what steps do you take to prevent it?

Yes, this is also a problem-solving question. The difference is, with this one, it’s not about fixing an issue; it’s about stopping it from happening. Still, you use problem-solving skills along the way, so it falls in this question category.

If you can, use an example of a moment when you mitigated risk in the past. If you haven’t had that opportunity, approach it theoretically, discussing the steps you would take to prevent an issue from developing.

“If I identify a potential risk in a project, my first step is to assess the various factors that could lead to a poor outcome. Prevention requires analysis. Ensuring I fully understand what can trigger the undesired event creates the right foundation, allowing me to figure out how to reduce the likelihood of those events occurring. Once I have the right level of understanding, I come up with a mitigation plan. Exactly what this includes varies depending on the nature of the issue, though it usually involves various steps and checks designed to monitor the project as it progresses to spot paths that may make the problem more likely to happen. I find this approach effective as it combines knowledge and ongoing vigilance. That way, if the project begins to head into risky territory, I can correct its trajectory.”

17 More Problem-Solving-Based Interview Questions

In the world of problem-solving questions, some apply to a wide range of jobs, while others are more niche. For example, customer service reps and IT helpdesk professionals both encounter challenges, but not usually the same kind.

As a result, some of the questions in this list may be more relevant to certain careers than others. However, they all give you insights into what this kind of question looks like, making them worth reviewing.

Here are 17 more problem-solving interview questions you might face off against during your job search:

• How would you describe your problem-solving skills?
• Can you tell me about a time when you had to use creativity to deal with an obstacle?
• Describe a time when you discovered an unmet customer need while assisting a customer and found a way to meet it.
• If you were faced with an upset customer, how would you diffuse the situation?
• Tell me about a time when you had to troubleshoot a complex issue.
• Imagine you were overseeing a project and needed a particular item. You have two choices of vendors: one that can deliver on time but would be over budget, and one that’s under budget but would deliver one week later than you need it. How do you figure out which approach to use?
• Your manager wants to upgrade a tool you regularly use for your job and wants your recommendation. How do you formulate one?
• A supplier has said that an item you need for a project isn’t going to be delivered as scheduled, something that would cause your project to fall behind schedule. What do you do to try and keep the timeline on target?
• Can you share an example of a moment where you encountered a unique problem you and your colleagues had never seen before? How did you figure out what to do?
• Imagine you were scheduled to give a presentation with a colleague, and your colleague called in sick right before it was set to begin. What would you do?
• If you are given two urgent tasks from different members of the leadership team, both with the same tight deadline, how do you choose which to tackle first?
• Tell me about a time you and a colleague didn’t see eye-to-eye. How did you decide what to do?
• Describe your troubleshooting process.
• Tell me about a time where there was a problem that you weren’t able to solve. What happened?
• In your opening, what skills or traits make a person an exceptional problem-solver?
• When you face a problem that requires action, do you usually jump in or take a moment to carefully assess the situation?
• When you encounter a new problem you’ve never seen before, what is the first step that you take?

Putting It All Together

At this point, you should have a solid idea of how to approach problem-solving interview questions. Use the tips above to your advantage. That way, you can thrive during your next interview.

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Co-Founder and CEO of TheInterviewGuys.com. Mike is a job interview and career expert and the head writer at TheInterviewGuys.com.

His advice and insights have been shared and featured by publications such as Forbes , Entrepreneur , CNBC and more as well as educational institutions such as the University of Michigan , Penn State , Northeastern and others.

Learn more about The Interview Guys on our About Us page .

About The Author

Mike simpson.

Co-Founder and CEO of TheInterviewGuys.com. Mike is a job interview and career expert and the head writer at TheInterviewGuys.com. His advice and insights have been shared and featured by publications such as Forbes , Entrepreneur , CNBC and more as well as educational institutions such as the University of Michigan , Penn State , Northeastern and others. Learn more about The Interview Guys on our About Us page .

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PRACTICE PLANS

Practice is on us this week! Use these plans to prepare your students to compete or to review math skills.

These plans cover a variety of math topics and skills, and are designed to cover 45-60 minutes of practice time.  

A special thank you to Taren Long, our 2020-2021 DoD STEM Ambassador!

Taren created many of the awesome Practice Plans below, based on her experience as longtime MATHCOUNTS coach.

We start with a short problem set so Mathletes can practice related skills that will be expanded upon throughout the practice plan.

The Problems

Next, a video introduces a common type of competition problem or a helpful problem-solving strategy with 2-3 example problems.

Piece It Together

Next, Mathletes solve a set of related problems to build on the strategies and skills they learned in the Warm-Up and problems video.

We'll end with a related activity, puzzle or game to give Mathletes a fun opportunity to apply their problem-solving skills creatively!

Addition and subtraction may sound easy for middle schoolers, but what if you are missing some digits? What if you want to maximize or minimize a result? This plan focuses on some common types of MATHCOUNTS problems in which Mathletes will need to apply number sense and logic to a variety of scenarios.

Download the Mathlete handout.

Download the coaches version with solutions.

Explore measures of central tendency, specifically mean and median, by solving common types of MATHCOUNTS problems related to sets of numbers. Use the extension at the end to develop a rule for finding the average of a sequence of numbers.

Mathletes are likely most comfortable working with numbers in base 10, but there are many other number systems to explore - other integer bases, fractional bases, and even negative bases. This plan introduces Mathletes to the basics of bases and how to convert from one to another. 

Explore combinatorics by looking at a common type of MATHCOUNTS counting problem – counting paths between two points. End with an extension that connects counting paths to another type of combinatoric problem.

This plan will help Mathletes to develop a strategic approach to counting the occurrences of a certain shape in a more complex figure made of multiple intersecting lines.

Mathletes will analyze frequency tables, histograms, stem-and-leaf plots and other visual representations to solve problems about sets of data. In the extension, Mathletes will analyze a set of data to draw their own conclusions.

An important formula to know, the difference of squares identity is derived geometrically in the video for this practice plan. Mathletes will then try to recognize the difference of squares structure in various expressions and use the identity to find the value.

Explore the formula d = rt by starting with unit conversion problems. Mathletes will solve for distance, rate and time by paying attention to the units given in the problem and using the appropriate equivalent version of the formula: d = rt , r = d / t or t = d / r .

Download Mathlete handout.

Download coach version with solutions.

Download The Problems PowerPoint.

Mathletes will apply divisibility rules of various integers to simplify computation, better understand number composition and aid in problem solving. In the extension, Mathletes can prove why each of these rules work!

Using the commutative, associative and distributive properties, Mathletes will arrange arithmetic problems in a different order that allows them to be solved more readily.

This plan will introduce Mathletes to The Fundamental Counting Principle – a faster method to determining the total number of possible outcomes of an event without listing them all out!

Mathletes will explore interior angles of various polygons and understand how to find the number of sides a polygon has using information about its interior angles.  

Training Today's Brightest Minds to Solve Tomorrow's Problems

Art of problem solving brings its problem-solving teaching methods to local academic centers, with one virtual campus and 15 locations in the us, and more being added every year., we challenge students.

More than test preparation, our rigorous math, science, and language arts classes inspire students to reach their full potential.

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Art of Problem Solving has been a leader in math education for high-performing students since 1993. We launched AoPS Academy in 2016 to bring our rigorous curriculum and expert instructors into classrooms around the United States. With campuses in 8 states (and growing!), our approach nurtures a love for complex problem solving, which is fully incorporated into all our math, science, and language arts courses. Most importantly, our students become part of a community of motivated learners that helps elevate them to new heights.

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Our family regularly talks about AoPS. We try to think about how our life would be different without you all. What if my daughter hadn't learned to love math? What if she never experienced being pushed to her limits? Overcoming failure? She wouldn't be who she is. And she is AWESOME! A very proud mom here. We are so fortunate that we found AoPS Academy. I credit AoPS for much of her confidence.

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AMC 12 Problems and Solutions/Tasks

• 2001 AMC 12
• 2002 AMC 12A
• 2002 AMC 12B
• 2003 AMC 12A
• 2003 AMC 12B
• 2004 AMC 12A
• 2005 AMC 12A
• 2005 AMC 12B
• 2006 AMC 12A
• 2006 AMC 12B
• Links to forum topics where each problem was discussed.
• PDF documents with all problems for each test.
• Lists of answers for each test.
• List of solutions
• PDF documents with solutions

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Top 50 DSA Practice Problems to Sharpen Your Skills

Mastering Data Structures and Algorithms (DSA) is crucial for every software developer, not just for cracking coding interviews but also for solving real-world problems efficiently. Practicing DSA problems regularly enhances problem-solving skills and prepares you for various scenarios. This article presents the top 50 DSA practice problems that cover a broad spectrum of essential data structures and algorithms. These problems are tailored to improve your analytical thinking and provide a deep understanding of fundamental concepts. Let’s dive into these challenges to boost your skills in DSA.

1. Find the Maximum Subarray Sum (Kadane’s Algorithm)

Given an array of integers, find the contiguous subarray with the maximum sum.

2. Two Sum Problem

Find two numbers in a given array that add up to a specific target number.

3. Merge Two Sorted Arrays

Given two sorted arrays, merge them into a single sorted array.

4. Rotate Array

Rotate an array to the right by a given number of steps.

5. Find the Duplicate Number in an Array

Identify the duplicate number in an array containing multiple elements where one number is repeated.

6. Find the Missing Number in an Array

Given an array of integers containing numbers from 1 to n, find the one missing number.

7. Longest Palindromic Substring

Find the longest substring in a given string that reads the same forwards and backwards.

8. Reverse a String

Reverse a given string using iterative and recursive methods.

9. Check if Two Strings are Anagrams

Determine if two strings are anagrams of each other by checking character frequencies.

10. Valid Parentheses Checker

Check if a given string containing only parentheses is valid by ensuring proper opening and closing.

11. Binary Tree Inorder Traversal

Implement an inorder traversal of a binary tree both recursively and iteratively.

12. Find the Lowest Common Ancestor in a Binary Search Tree

Given a binary search tree and two nodes, find their lowest common ancestor.

13. Binary Tree Level Order Traversal

Traverse a binary tree level by level from top to bottom.

14. Depth-First Search (DFS) on a Graph

Implement DFS to explore all nodes in a graph.

15. Breadth-First Search (BFS) on a Graph

Use BFS to traverse a graph starting from a specific node.

16. Find the Shortest Path in a Binary Maze

Determine the shortest path in a binary maze from a starting point to an endpoint using BFS.

17. Detect a Cycle in a Directed Graph (Kahn’s Algorithm)

Use Kahn’s Algorithm to detect cycles in a directed graph.

18. Longest Increasing Subsequence

Find the longest increasing subsequence in a given array of integers.

19. 0/1 Knapsack Problem

Solve the classic 0/1 knapsack problem using dynamic programming.

20. Fibonacci Sequence using Dynamic Programming

Implement the Fibonacci sequence calculation using dynamic programming for efficiency.

21. Minimum Coin Change Problem

Find the minimum number of coins required to make a given amount using a set of denominations.

22. Edit Distance Between Two Strings

Calculate the minimum number of edits (insertions, deletions, or substitutions) required to transform one string into another.

23. Reverse a Linked List

Reverse a singly linked list using iterative and recursive methods.

24. Detect a Cycle in a Linked List (Floyd’s Cycle Detection Algorithm)

Identify if a linked list has a cycle using the Tortoise and Hare method.

25. Merge Two Sorted Linked Lists

Merge two sorted linked lists into one sorted linked list.

26. Find the Intersection Point of Two Linked Lists

Find the node where two singly linked lists intersect.

27. Find the Middle of a Linked List

Locate the middle node of a linked list in one pass using the slow and fast pointer technique.

28. Implement a Stack using Queues

Use two queues to implement a stack data structure.

29. Implement a Queue using Stacks

Use two stacks to implement a queue data structure.

30. Design a Min Stack

Design a stack that supports push, pop, top, and retrieving the minimum element in constant time.

31. Find the Largest Rectangle in a Histogram

Given a histogram, find the largest rectangle that can be formed with consecutive bars.

32. Implement Binary Search

Implement binary search on a sorted array to find a target value.

33. Find a Peak Element in an Array

Identify a peak element in an array where the element is greater than its neighbors.

34. Implement Quick Sort

Sort an array using the quick sort algorithm.

35. Implement Merge Sort

Implement merge sort to sort an array efficiently.

36. Heap Sort Algorithm

Use heap data structure to sort an array using heap sort.

37. Find the Kth Largest Element in an Array

Find the kth largest element in an unsorted array using a heap.

38. Solve the N-Queens Problem

Place N queens on an N×N chessboard such that no two queens threaten each other.

39. Sudoku Solver using Backtracking

Solve a Sudoku puzzle using backtracking.

40. Generate Valid Parentheses Combinations

Generate all combinations of well-formed parentheses given a number of pairs.

41. Find All Permutations of a String

Generate all possible permutations of a given string.

42. Combination Sum Problem

Find all unique combinations in a set of candidate numbers where the chosen numbers sum to a target.

43. Word Search in a 2D Grid

Given a 2D grid of letters, check if a given word exists in the grid.

44. Topological Sort in a Directed Graph

Perform a topological sort on a directed acyclic graph (DAG).

45. Find the Diameter of a Binary Tree

Calculate the longest path between any two nodes in a binary tree.

46. Check if a Binary Tree is a Valid Binary Search Tree

Verify if a binary tree meets the conditions of a binary search tree (BST).

47. Convert Sorted Array to Binary Search Tree

Convert a sorted array into a balanced binary search tree.

48. Design a LRU Cache

Implement an LRU (Least Recently Used) cache data structure with O(1) operations.

49. Find the Median of Two Sorted Arrays

Find the median value of two sorted arrays combined.

50. Longest Common Subsequence

Find the longest subsequence common to two given strings.

Solving these DSA problems will make you prepared for interviews and will also help in improving your coding skills. The goals of some of the problems are as follows, every problem is a chance to develop problem-solving skills and learn more about various sorts of data structures and algorithms. Solving the following DSA practice problems are significant as they prepare a candidate to solve similar problems without stress.

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