Problem Solving and Analytical Skills


How to develop and demonstrate your problem-solving skills

We 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:Angry man on computer


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.


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-define-examine-act-look-IDEAL


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.

There are several stages to solving a problem:problem solving

1) Evaluating the problem

2) Managing the problem

3) Decision-making

4) Resolving the problem

5) Examining the results


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

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:


These quotes from employers’ job adverts on graduate websites are all asking for essentially the same two things:

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 danger = opportunityCHALLENGES

In Chinese the character for danger and opportunity is the same. Well maybe not but it sounds good!

On application forms

If 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:


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

Evidence you could give to an employer to convince them that you have problem-solving skills

Examples could come from your course, extra-curricular activities such as student societies, school, work or work experience, year-in-industry placements, travel or other sources.

EXAMPLES: labyrinth

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


At interview

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. 

Hypothetical questions

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.


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:

Needle Stack

The only thing harder than looking for a needle in a hay stack is looking for a needle in a needle stack!


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

Technical questions

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:

See our science interviews page for more on technical questions.

Ethical questions

These are particularly common in interviews for medicine and law. Some typical examples may include:


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 interviews

This 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:


Alternatively, you may be asked questions related to the issues facing real-life clients:


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



Through group tasks and discussions at assessment centres

Almost 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:


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

A logic puzzle to test your problem solving skills


Who owns the shark? (see the bottom of the page for the answer)

Further Information and Help

A final thought …

"For every complex problem, there is a solution that is simple, neat, and wrong"
(H.L. Mencken)

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:

Yellow House


























This puzzle is also known as the Zebra Puzzle and you will find help on how to solve it in Wikipedia here


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 Last fully updated 2013