Problem Solving and Analytical Skills
How to develop and demonstrate your problem-solving skillsWe all solve problems on a daily basis, in academic situations, at work and in our day-to-day lives.
Some of the problems that are typically faced by students include:
- Putting together an argument for an essay
- Debugging a computer program
- Dealing with an awkward customer when working part-time in a shop or restaurant
- Thinking about how you are going to manage your budget to keep you going until the end of term
- Working out why your printer won’t respond
- Developing a strategy to reach the next level of a computer game.
Any job will also bring problems to be faced. It is important to show to a recruiter that you have the right skills to resolve these problems, and the personal resilience to handle the challenges and pressure they may bring.You need to be able to:
|Problems can also be opportunities: they allow you to see things differently and to do things in a different way: perhaps to make a fresh start.|
- Evaluate information or situations
- Break them down into their key components
- Consider various ways of approaching and resolving them
- Decide on the most appropriate of these ways
Solving these problems involves both analytical and creative skills. Which particular skills are needed will vary, depending on the problem and your role in the organisation, but the following skills are key to problem-solving:
A large cosmetics company had a problem that some of the soap boxes coming off the production lines were empty. The problem was quickly isolated to the assembly line, which transported the packaged boxes of soap to the delivery department: some soap boxes went through the assembly line empty.
The management asked its engineers to solve the problem. They spent much time and money in devising an X-ray machine with high-res monitors manned by staff to watch all the boxes on the line to make sure they weren't empty.
A workman hearing about this, came up with another solution. He got a powerful industrial fan and pointed it at the assembly line. As each soap box passed the fan, the empty boxes were blown off the line. Moral: the simplest solution is usually the best!
Analytical and critical thinking skills help you to evaluate the problem and to make decisions. A logical and methodical approach is best in some circumstances: for example, you will need to be able to draw on your academic or subject knowledge to identify solutions of a practical or technical nature.
In other situations, using creativity or lateral thinking will be necessary to to come up with ideas for resolving the problem and find fresh approaches
Not everyone has these two types of skills in equal measure: for this reason, team working is often a key component in problem-solving. Further skills, such as communication, persuasion and negotiation, are important in finding solutions to problems involving people.
Whatever issue you are faced with, some steps are fundamental:
- Identify the problem
- Define the problem
- Examine the options
- Act on a plan
- Look at the consequences
This is the IDEAL model of problem-solving.
The final stage is to put the solution you have decided on into practice and check the results.
Developing your analytical and problem-solving skills
Most problem-solving skills are developed through everyday life and experience. However, the following interests and activities may be useful in demonstrating a high level of these skills - this may be particularly important when applying to employers in areas such as engineering, IT, operational research and some areas of finance.
- ‘Mind games’ such as cryptic crosswords, Sudoku, chess, bridge, etc;
- Computer games – the best of these can involve strategic planning, critical and statistical analysis and assessing the pros and cons of different courses of action;
- ‘Practical’ interests such as programming, computer repairs, car maintenance, or DIY;
- Working with sound or lighting equipment for a band, event or show;
- Academic study: evaluating different sources of information for essays, designing and constructing a ‘microshelter’ for an architecture project; setting up a lab experiment.
There are several stages to solving a problem:
1) Evaluating the problem
- Clarifying the nature of a problem
- Formulating questions
- Gathering information systematically
- Collating and organising data
- Condensing and summarising information
- Defining the desired objective
2) Managing the problem
- Using the information gathered effectively
- Breaking down a problem into smaller, more manageable, parts
- Using techniques such as brainstorming and lateral thinking to consider options
- Analysing these options in greater depth
- Identifying steps that can be taken to achieve the objective
- deciding between the possible options for what action to take
- deciding on further information to be gathered before taking action
- deciding on resources (time, funding, staff etc) to be allocated to this problem
- See our page on decision-making skills
4) Resolving the problem
- Implementing action
- Providing information to other stakeholders; delegating tasks
- Reviewing progress
5) Examining the results
- Monitoring the outcome of the action taken
- Reviewing the problem and problem-solving process to avoid similar situations in future
At any stage of this process, it may be necessary to return to an earlier stage – for example, if further problems arise or if a solution does not appear to be working as desired.
Problem-solving skills and graduate jobs: what do recruiters want?
Analytical ability, problem solving skills and using initiative are among the top ten skills for recruiters of graduates. They want people who will take the personal responsibility to make sure targets are met; who can see that there might be a better way of doing something and who are prepared to research and implement change; people who don’t panic or give up when things go wrong but who will seek a way around the problem.
These problems may be similar to academic problems (e.g. in scientific research) or may be more “practical” problems such as those involved in people management.
These skills can be asked for in a variety of ways. Many job ads will simply ask for candidates who “can take the initiative" or "have the ability to resolve problems"; others, however, may not make it so clear. You have to learn to interpret phrases like:
- “Someone keen to take responsibility and with the confidence to challenge established practices and come up with new ways of working…”
- “An enquiring mind and the ability to understand and solve complex challenges are necessary…”
- “We are looking for innovative minds and creative spirits ...”
- “We need ambitious graduates who will respond with enthusiasm to every issue they face…”
These quotes from employers’ job adverts on graduate websites are all asking for essentially the same two things:
- The ability to use your own initiative, to think for yourself, to be creative and pro-active.
- The ability to resolve problems, to think logically and/or laterally, to use ingenuity to overcome difficulties and to research and implement solutions.
These qualities help graduates to make a difference to their employer, whether that employer provides a service or manufactures a product.
How will they assess these skills?
Think of PROBLEMS as CHALLENGES
On application formsIf analytical or problem-solving skills are a key part of the job, there is likely to be a question on the application form which asks you to give evidence of your competency in these areas, such as:
- Describe a situation in which you analysed data and solved a complex problem;
- Describe a complex problem you have faced and the steps that you took to solve it;
- Describe a setback in your life and say what you did to overcome it. What lessons did you learn from this?
- Describe a time when you demonstrated creativity in solving a difficult problem;
- Describe a time when you provided a new or different solution to a problem;
- Give me a specific example of a time when you used good judgment and logic in solving a problem;
- Describe a difficult problem that you have solved. State how you decided which were the critical issues, say what you did and what your solution was. What other approaches could you have taken?
- Give an example of a problem you have solved that required analysis. What methods did you use and what conclusions did you reach?
When answering these questions, cover the process you used to solve the problem rather than just outlining the problem itself. Give examples of how you used initiative/creativity, or made effective use of resources, in solving the problem. It is also useful to say what you learned from this process, especially if the problem was not resolved to your complete satisfaction.
Employers may follow up on your answers to these questions at interview: see below.
There is further information about competency-based questions such as this at www.kent.ac.uk/careers/compet/skillquest.htm
Evidence you could give to an employer to convince them that you have problem-solving skills
- Analysing data from a project or experiment
- Working as a “troubleshooter” on a computer helpdesk
- Advising a client at the Kent Law Clinic
- Implementing a new filing system in an office job
- Acting as a student rep
- Dealing with staff problems or unexpected staff shortages in a part-time job
- Coping with living on a limited student budget
Putting the evidence onto an application form
Give an example of a time when you have successfully resolved a complex problem:
1: Describe a situation from the last five years when you demonstrated effective use the skill you have chosen:
In the sixth form, I took part with two friends in a “Robot Challenge” competition. The brief was to design and build a robot that could perform a dance routine synchronised with a music soundtrack.
2: What action did you have to take?
My responsibility was to control the movement of the robot through the sensors and actuators. This was a complex task because of the number of movements that the robot was required to execute and the different stimuli to which it had to respond. In addition, the robot proved particularly sensitive to changes in light levels and I needed to experiment with a number of adaptations to discover the optimum balance between responsiveness and reliability.
3: What was the result of your action?
Our team achieved second place in the local competition and progressed to the regional final, where we came fifth out of 25 teams.
Through psychometric tests
A study in the Personality and Social Psychology Bulletin suggests you are more likely to succeed if you solve a difficult problem on another person’s behalf rather than for yourself. One of the problems was:
A prisoner was attempting to escape from a tower. He found a rope in his cell that was half as long enough to permit him to reach the ground safely. He divided the rope in half, tied the two parts together, and escaped. How could he have done this?
Students were asked to think of either themselves or a stranger stuck in the tower. 66% of the students who imagined a stranger in the tower, found the solution compared with 48% of those who envisaged themselves in the tower. THe authors said if we imagine that our problems belong to someone else, we might find better solutions. The solution, by the way is to split the rope lengthwise.
The most common of these tests involve verbal and numerical reasoning: you may also encounter diagrammatic reasoning and critical thinking tests. They may be administered online at an early stage of the selection process, or at first interview or assessment centres. There is a great deal of information about these tests at www.kent.ac.uk/careers/psychotests.htm
Further questioning on the answers given on your application form
If your application form has included competency-based questions such as the ones above, you can expect the employer to ask for more detail about the problem or the situation and the way that you went about finding a solution. Be prepared to be asked about alternative ways in which you might have gone about tackling this problem and what you would have done if things hadn’t worked out.
Competency-based questions ask you about actions that you have taken in the past: hypothetical questions ask you about the course of action you might take in the event of some fictional situation, often work-related.
- "How would you deal with a staff member who persistently arrives late and takes regular, unauthorised, breaks from work for a cigarette?”
- "You are working on the till in a retail store when a customer’s credit card is refused. The cardholder is a regular customer who is trying to buy a present for their mother’s birthday the following day. How would you deal with this situation?"
- "Your manager regularly leaves you in charge of a small office in his absence. The other staff regularly complain to you about the way he runs things, and how irritated they are by his interference in their day-to-day work - what do you do?"
- "You work in a company that manufactures meat pies and pasties. Sales have been falling for several years and you are asked to come up with ideas to revive the company”
There is usually no right or wrong answer to these questions: the interviewers are seeking to assess your logical thinking and common sense. You may need to ask questions to clarify the situation and gather more information. You can expect your answers to be challenged, the interviewers asking questions such as:
- “Yes, but what if …?”
- “Have you thought about ….?”
- “Why would you do that …?”
This doesn’t mean that there is anything wrong with the answer you have given – just that the interviewers are trying to find out how you have arrived at your solution to the problem. They may also be testing you out to see how you cope with pressure and how well you can argue a point.
Although the situation is hypothetical, if you have been faced with any similar situation in real life you can use this, and the way that you handled it then, to support your answer.
For further information on handling hypothetical questions, see www.kent.ac.uk/careers/intervw.htm#Hypothetical
These are most commonly asked at interviews for science, engineering and IT posts. They may relate to your previous relevant work experience or to a student project, or may relate to hypothetical situations as in the examples below:
- “The scenario was that we were in charge of lighting a theatre. We were given different conditions as to what type of problem could be caused by various faults in the lighting plan and who this problem would affect e.g. lighting technician, stage manager or director. There was only ever one problem with the lighting plan.
It got harder as different conditions were added to the original ones and you had to take more and more information into consideration, such as: certain lights need to always be turned on first; some lights need to be warmed up in the breaks; different lights create different effects”
- “I was asked to suggest a route to synthesise ethylene glycol – one of the company’s products” (Chemistry graduate interviewed by petrochemicals company)
- “If I were organising a national cancer screening campaign, what standards/ precautions/ feasibility/ practicality checks would I do before implementing the scheme?” (Medical physicist)
- “They asked technical questions mainly to work out my thought process on problem solving, there was no correct answer as long as they were logical and eventually you had to come to a point where you gave up and admitted defeat!”
(Graduate interviewed for IT support post with NHS trust)
It's not that I'm so smart, it's just that I stay with problems longer.
Albert EinsteinLeaders are problem solvers by talent and temperament, and by choice.
Harlan ClevelandProblems are only opportunities in work clothes.
Henri KaiserDifficulties are opportunities to better things; they are stepping-stones to greater experience.... When one door closes, another always opens.
Brian AdamsEvery exit is an entry somewhere else.
Tom StoppardThere are no foolish questions and no man becomes a fool until he has stopped asking questions.
Saul SteinbergThe most serious mistakes are not being made as a result of wrong answers. The truly dangerous thing is asking the wrong questions.
Peter DruckerIt is better to know some of the questions than all of the answers.
James ThurberThe mere formulation of a problem is far more often essential than its solution.
Albert EinsteinFor every failure, there's an alternative course of action. You just have to find it. When you come to a roadblock, take a detour.
Mary Kay Ash
When life gives you a lemon, make lemonade.If you really want something you can figure out how to make it happen.
CherThe creation of a thousand forests is in one acorn.
Ralph Waldo EmersonWhether you believe you can, or whether you believe you can't, you're absolutely right.
Henry FordNever doubt that a small group of thoughtful, committed citizens can change the world. Indeed it's the only thing that ever has.
Margaret MeadIt is easier to tone down a wild idea than to think up a new one.
Alex OsborneThe best way to get a good idea is to get a lot of ideas.
Linus PaulingEven if you are on the right track, you will get run over if you just stand there.
Will RogersThe human mind is like a parachute - it functions better when it's open.
Cole's RulesThe man with a new idea is a crank - until the idea succeeds.
Mark TwainMartin Luther King said "I have a dream", not "I have a plan.
See our science interviews page for more on technical questions.
Ethical questionsThese are particularly common in interviews for medicine and law. Some typical examples may include:
- Should all class C drugs be legalised?
- Should doctors be authorised to remove organs from a dead person without obtaining consent from their relatives?
- A patient urgently requires a bone marrow transplant but the only suitable donor is her brother, who has severe physical and mental disabilities. Can this brother donate?
- Should conjoined twins be separated even if it is almost certain that one of them will die in the process?
- Since the victims in rape cases have anonymity, should the same anonymity be granted to the accused?
Again, there is often no right or wrong answer, although you should be aware of the legal and regulatory framework behind these questions. You will be expected to put both sides of the argument before giving your opinion and can expect to be challenged and asked to justify your opinion.
Case study interviewsThis type of interview is often used for graduate positions in management consultancy and investment banking.
Case questions are business problems designed not only to test your logical and analytical thinking skills, ability to solve problems but also to make you think on your feet. Often there are no right answers to these types of questions, but they give the selector an idea of how you think, your reasoning skills, how you react under pressure and your common sense.
The problems may be brief (sometimes seemingly bizarre) “estimation” or “brain teaser” questions such as the following:
- How many cars are there in the EU?
- How many laptops will be purchased in the UK in 2020?
- Why are manhole covers round?
Alternatively, you may be asked questions related to the issues facing real-life clients:
- A manufacturer of umbrellas, based in the west of Ireland, wants to expand into mainland Europe. What issues should they consider? What risks might they face?
- A parcel delivery company plans to offer a new service where customers can hand a package directly to one of the company's drivers instead of taking it to a depot. What issues need to be thought about?
These business problems are similar to those put forward for group discussions at assessment centres (see below) – the difference is that you have to tackle these on your own!
For further information on case interviews, with examples of the questions and problems set at them, see www.kent.ac.uk/careers/interviews/CaseInterviews.htm
Through group tasks and discussions at assessment centresAlmost all assessment centres will involve a strong element of group work. These tasks may involve the group sitting around a table discussing a problem or may (as in the final two examples) be more active and practical:
- “We were asked to come up with a business proposal for building a computer network between an imaginary group of islands, to be presented to the islands government”
- Candidates for a place at medical school were given background information on ten patients and asked to select five of them who would receive a kidney transplant
- “We were provided with information on four sites that were possible locations for the construction of a nuclear power station. This information included material on the environment, the local economy, transport links and the estimated costs of construction. We had to select one and recommend it to the Secretary of State for Energy, giving the reasons for our decision.”
- “We were given a task involving Lego bricks - we had to work out how many bricks we wanted to use to build the tallest tower possible at the lowest cost”
- “A large part of the Army Officer selection process takes place outdoors – the teams of candidates have to negotiate an obstacle course using ladders, ropes, poles and planks”
The decision reached by the group is likely to be less important than the way in which the group works together to reach its decision – these tasks aim to test your teamworking and negotiation, as well as your problem-solving, skills.
There is more information about assessment centres, including examples of business games, case studies and “balloon debates” at www.kent.ac.uk/careers/applicn.htm#Selection
- There are five adjoining houses in a row in different colours: blue, green, red, white and yellow.
- In each house lives a person of different nationality: British, Indonesian, German, American and Dutch.
- Each person drinks a different beverage: grape juice, coffee, milk, tea and water.
- Each person has a different job: journalist, postman, magician, astronaut and actuary.
- Each person keeps a different pet: tiger, zebra, parrot, shark and aardvark.
- The British person lives in a red house.
- The Dutch person keeps an aardvark.
- The Indonesian drinks tea.
- The green house is on the left of the white, next to it.
- The owner of the green house drinks coffee.
- The journalist rears parrots.
- The owner of the yellow house is an actuary.
- The person living in the house in the centre drinks milk.
- The American lives in the first house.
- The astronaut lives next to the person who owns a tiger.
- The man who keeps a zebra lives next to the actuary.
- The postman drinks grape juice.
- The German is a magician.
- The American lives next to the blue house.
- The astronaut has a neighbour who drinks water.
Who owns the shark? (see the bottom of the page for the answer)
Further Information and Help
- Decision-making www.kent.ac.uk/careers/sk/decisionmaking.htm
- Lateral thinking www.kent.ac.uk/careers/sk/lateral.htm
- All kinds of practice numerical and verbal reasoning tests, with links to many more sites, at www.kent.ac.uk/careers/psychotests.htm
- Test of analytical reasoning skills www.queendom.com/tests/access_page/index.htm?idRegTest=2840
- Initiative and problem-solving www.careers.brad.ac.uk/student/skills/ipsolving.php
- www.businessballs.com/games.htm - puzzles, lateral thinking puzzles, trick questions, number puzzles, logic puzzles and word games
- How to Solve the Times Crossword – help from the BBC www.bbc.co.uk/dna/h2g2/A563690
A final thought …
"For every complex problem, there is a solution that is simple, neat, and wrong"
Solution to the logic puzzle
Some say that the above problem (in a slightly different version) was invented by Einstein and others say Lewis Carroll although no one really knows. Supposedly, Einstein also said that 98% of people couldn't solve it, which is unlikely!
The answer is that the German owns the shark and the full solution is given below:
This puzzle is also known as the Zebra Puzzle and you will find help on how to solve it in Wikipedia here
Last fully updated 2010