A problem is defined as the difference between how things are and how they should be, and the relevant knowledge needed to produce a good solution

This article will tell you how do define a problem and what you need to understand in order to have good problem model.

Heikki Immonen, Karelia University of Applied Sciences

In problem solving, everything starts with a good problem definition.

Navigation in a strange city is a helpful metaphor to understand it better. If a route in a strange city is the solution, then your starting location and target location define the problem, and the map represents your knowledge about the problem i.e. a problem model.

The problem definition for Apollo 13 engineers at NASA had three components

Apollo 13 is 1995 movie based on an actual human space flight mission that took place in 1970. The goal of the mission was to reach the surface of the moon, but this did not happen as technical problems forced the spacecraft to only loop around the moon and head back to Earth.

One of the major technical problems on their way back was related to modifying a system that removes carbon dioxide from the breathing air. A scene from the movie dramatizes how the problem was defined for the engineers (Howard, 1995)

Current state of the mission was that carbon dioxide levels where rising to toxic levels

The scene begins with acknowledgement of the current situation. In this case the mission control gets data that the carbon dioxide levels are rising dangerously.

’We’re already up to eight on the gauges. Anything over 15 and you get impaired judgement, blackouts, the beginnings of brain asphyxia”, an engineer report.

In other words, the current state captures how things are right now (carbon dioxide at 8) and how they will develop if nothing is done (over 15, resulting in all kinds of problems and finally death).

Goal state is to have carbon dioxide levels not rising to toxic levels so that astronaut can return safely

The goal state is not explicitly mentioned in this scene, but it is famously stated earlier in the movie (though according to Wikipedia, it was not ever said during the actual mission):

Failure is not an option!

In other words, everybody wants to prevent the carbon dioxide levels from rising to dangerous level as they want that astronauts return to Earth safely. This is the defined goal state.

Knowledge of filter problem, available tools and materials, and spacecraft details are highly relevant bits of knowledge engineers need

Final component of the problem definition, captured in the scene, comprises all the relevant knowledge, i.e., problem model, engineers have and can acquire that helps them produce a solution that works. This includes all the knowledge they have about the spacecraft and equipment and materials inside the vehicle.

To help themselves to get a better grasp of reality, the engineers pour all the equipment and material that the astronauts also have inside the spacecraft to a conference room table. One of the engineers then recaps already a more specific and detailed problem definition, while holding two carbon dioxide filter components in his hands:

We got to find a way to make this to fit in to the hole for this using nothing but that”, he says and points to the materials and tools on the table.

Current state defines what is happening now or is going to happen in the future

Understanding how the reality is, is key to a successful innovation. Current state is a model of reality that describes what is happening now and what is going to happen in the future. Current state is like your current location in a strange city. If you get it wrong, you have hard time reaching your goal because the route you have planned, i.e., the solution, will take you to a wrong place.

Many young innovators start with only a vague implicit knowledge of what the current state is. They invest all their energy in thinking about their solution. It is only when the first trial of the idea reveals gap in their knowledge, they are pulled in to the harsh reality. Many give up, some persist and start updating their understanding of the current state. After a while they are correctly able to define their location.

When defining current state focus on what is happening or will happen, not simply what is

The problem with map metaphor I used above, is that it can give you a too inanimate model of what the current state and innovation is about. Instead, expand your thinking and try to see the current state as representing a process or a series of actions. Focus on what is happening, not simply what is. This means that you don’t want to improve a product, but you want to improve what it does for your customers.

Also, the current state can expand to the future, as the likely future happenings are also part of the current state. Global warming is a good example of this. If nothing is done differently from how things are now, the climate will keep on getting warmer and warmer. Very bad habits are another example. If there is no intervention, ill health and premature death will likely follow.

Goal state, made possible by a solution, defines what should happen instead or shouldn’t happen in the first place

Goal state defines a new reality that is different from the current state. This sounds easy, but if all you have experienced is the current state, you have trouble envisioning a different way. Travelling, stories, benchmarking are all examples of actions that allow you to see how things could be. These actions seem to be programmed in to our DNA, too. Think of adventure and youth.

In terms of our map metaphor, goal state is your target location in the strange city you are in. Without a goal, you are wondering randomly, or simply staying where you are. A goal helps you push farther than via random wondering. The route you choose is the solution.

Gap between the current state and the goal state is the problem

What is a problem? Given the framework we are using, a problem is the gap between the current state and the goal state. Neither of them alone defines a problem. You need to have both.

The problem emerges, when in a strange city, you know where you are, and have defined where you want to go. The problem for you is then how to get from where you are to where you want to go. Now it is easy to understand that if you change your target location the problem becomes something very different. Likewise, two people might have the same target location, but they are currently located on different parts of the city. Thus, both of them face a different problem.

What the goal state should be is defined by (certain) stakeholder(s)

One thing that is important to understand, is that a goal state is something people decide. Because it is a deviation from the natural course of things, it will happen, only if humans change something.  The people who have a say on what the goal should be, are called stakeholders. For a business, a key stakeholder is the customer.

When you are navigating in a strange city, it is you and the people you are with who decide where you want to go. If you forget to hear everybody’s opinion, your destination will not likely make everybody happy.

Stakeholder is a person or group who is affected by or has other interest in the solution

Formal definitions of a stakeholder are typically something like the one used by Dori (2016): “Stakeholder is an individual, an organization, or a group of people that has an interest in, or might be affect by a system”. Here in a system refers to the solution to be developed.

This is a broad definition, and it means that in the beginning of a problem-solving process it is good to stop and think and study who the stakeholders are. You should then go a step deeper, and understand the different roles and interests each stakeholder has.

Beneficiary, customer, user and supplier are different types of stakeholders (Dori, 2016) recognized in systems engineering.

Problem model allows the design of a successful solution.

Problem model comprises all the relevant knowledge that you need or should have to solve the problem successfully. As you are trying to get from your current location to your goal, a map would be a key piece of your problem model. Other information, too, such as available money, different forms of transportation the city has available and current traffic conditions also belong to the problem model.

If you have a good map and correct information about transportation options, you are able to device a plan to reach the goal with great certainty. This plan is the solution. It is only the unexpected, such as a road being blocked, that can force you to re-think your plan.

Often, we leave the problem solving to experts, like taxi-drivers or doctors, who already have accurate problem models available for them.  One advantage they have, is that they already know many of the things that should be included in the problem model.

  • Former NASA astronaut and engineer and founder of the Epic Challenge program Dr. Charles Camarda emphasizes the importance of this initial problem immersion, that helps you develop an accurate model of what is going on (Camarda & de Weck, 2013).

Clarity and specificity is key step in acquiring more and problem relevant knowledge

One key aspect of a good problem model is clarity and specificity. The clearer you are about where you are or where you want to be, the easier it is to know what you need to know.

For example, if you want that your next family vacation is better than the previous one, you might want to be more specific about what you mean by “better” and “vacation”. For example, you could define “better” as something your spouse, kids, and you all like and enjoy while also not being too costly. And “vacation” you could decompose in to three components: travelling, accommodation, and activities.

Seek to understand why the current state is happening

Key step in developing a solution, and change the way things are, is to understand the related cause and effect relationships. If you know what “causes” result in bad “effects”, you can start thinking how to prevent those causes from happening

Let’s say you sometimes miss a bus, which causes you to arrive late to your appointment. You can study the causes of missing the bus. You then might discover that on those occasions you left your home too late, because you had to search for your keys or your phone. This is valuable information, and you can use this knowledge to prevent you from being late.

It is like pinpointing more precisely you location on the map.

  • When Dr. Camarda and his colleagues studied the causes of the Columbia shuttle accident, they where able to determine that the damage caused by the superheated air on an already damaged wing leading edge when shuttle was re-entering the atmosphere was the cause of destruction of the shuttle, but could be prevented with repaired done while on orbit (Camarda &de Weck, 2013)

Solutions work only when a cause-and-effect mechanism is harnessed, even though the mechanism is not always understood

Cause-and-effect relationships are not beneficial only when you are trying to understand why the current state is as it is. They are also very valuable when you are formulating your solution. To do this, you can compare the current state and goal state and be really specific about the difference between the two states. Then ask what cause and effect relationships govern that difference.

For example, the key difference between your location and your goal are is the distance between these two points or your physical location. This gives you a clue to think about phenomena that helps you close a distance, i.e., to move.

If the main issue with your mornings is that you don’t remember where you put your keys or phone, you should think how memory works, and use this knowledge to change something in a way that you don’t forget.  

  • Focusing on the transformation your solution should enable helps you to be more creative and solution neutral (de Weck, 2015)

Circumstances are things that affect the success of possible solutions.

Your problem model should also contain information and knowledge about circumstances that affect the success of different solutions. If it is raining, it can affect your preferred route to your destination.

A space engineer, working to design a food growing system for Mars, has to take in to account many circumstances that would not be important in the case of Earth. Things like extreme cold temperatures and very thin atmosphere.

Resources are available things with and from which solution are build and/or are consumed by the operation of a solution.

Finally, remember to factor in the resource you have available or can easily get access to. As all solution are devised from resources, the resource you have limit what you can do. Available budget, time and skills are common limiting resources. Questions like: Do you have money for a taxi?, are you in a hurry?, do you speak the same language as the taxi driver? are all linked to your available consumable and non-consumable resources.

Sometimes the most innovative solutions are based on new ways to use existing resources.

About this article

The writing of this article was supported by the INnoVations of REgional Sustainability: European UniversiTy Alliance project. . This project is funded by the Erasmus+ Program.

The content of this article represents the views of the author only and is his sole responsibility. The European Commission and the Agency do not accept any responsibility for use that may be made of the information it contains.


Camarda, C. J., de Weck, O., & Do, S. (2013, June). Innovative Conceptual Engineering Design (ICED): Creativity and Innovation in a CDIO-Like Curriculum. In Proceedings of the 9th International CDIO Conference.

de Weck, O. L. (2015). Fundamentals of systems engineering. Session 4: System Architecture, Concept Generation. Lecture notes. Accessible from

Howard. R. (1995). Apollo 13 (1995) – Square Peg in a Round Hole Scene (7/11) | Movieclips, available at:–J4_VQ

Wikipedia (2022). Failure Is Not an Option, retrieved 15 June 2022