How to solve problems

Key message: A problem is solved by a method. A method is the way to a goal. To solve a complex problem you need systems thinking.


How to solve problems - The steps of problem solving -


I have a problem when I am dissatisfied with a current situation, but at the moment I am not able to achieve a desired target situation (the goal). It may be that I do not know what the goal looks like or the means to achieve the goal are unknown or an obstacle must be overcome on the way to the goal (e.g. the required means may be known but not available). So a problem has four main elements: the initial situation, the obstacle, the goal (the target situation) and the method to achieve the goal.


"A problem occurs when a problem solver has a goal but initially does not know how to achieve the goal. This definition has three parts: (1) the current state - the problems begins in a given state; (2) the goal state - the problem solver wants the problem to be in a different state, and problem solving is required to transform the problem from the current (or given) state into the goal state, and (3) obstacles - the problem solver does not know the correct solution and an effective solution method is not obvious to the problem solver." (, 24.01.20)


In order to solve a problem, three main steps must always be carried out:

  1. analyze (understand) the problem (the unsatisfactory situation, the obstacle and the goal)
  2. generate several alternative solution ideas (methods)
  3. make a decision (select a method).

(Lindemann, U.(2009). Methodische Entwicklung technischer Produkte. Heidelberg: Springer, S. 46, my translation)


"If I had an hour to solve a problem I'd spend 55 minutes thinking about the problem and 5 minutes thinking about solutions." (Albert Einstein)


"A problem properly stated is half solved." (John Dewey)


How to understand situations? How to understand systems?

A situation describes the relations between several elements (persons or things) at a point in time. (I cannot imagine a situation that consists of only one element.) So a situation is a system at a certain point in time. When I analyze a situation, it means that I am analyzing a system.


A system is a set of interrelated elements. The viewer can decide where to place the system boundary, but the boundary should make sense.


How to analyze systems, how to analyze situations -


When we say: “I want to analyze this system (situation)” then we really mean: “I want to understand this system.” Why is it not possible to understand a system just by analyzing it? Because “A whole is greater than the sum of its parts.” Not only the individual elements of a system must be examined, but also their relationships to one another. Analysis breaks a system down into its constituent elements (into its parts). Synthesis combines the relations between the elements to come to an understanding of the whole.


Watch this video: (15.02.20). In contrast to the video I believe that analysis and synthesis belong together and that it is impossible to understand a system without doing both.


"Analysis and synthesis, as scientific methods, always go hand in hand; they complement one another. Every synthesis is built upon the results of a preceding analysis, and every analysis requires a subsequent synthesis in order to verify and correct its results." ( , 26.02.20, page 1)


In another video the authors say that 3 cups on a table are not a system because they exist independently from each other. I also don't agree. I analyze: there are three cups on the table. Their function is to take up liquid. I synthesize: I can invite two friends to drink a coffee with me (or I can do somthing else with the cups). (, 15.02.20)


"In very general terms, a system is any (circumscribed) object which consists of a number of "parts" or "components" which, in some way or another, work together in order to produce an overall effect or behavior. ... We can only concede to the obvious: that just about everything in the world would seem to be some sort of "system". ( , 26.02.20, page 6)


Three cups on a table are a simple system. Complex systems have many elements and many relations exist between them (high interconnectivity). In addition complex systems may be intransparent (some information about the system is missing) and they may be dynamic (the system changes over time). Complex systems are much harder to understand than simple systems.


When we break down a complex system to its constituent elements we get a large amount of them. Therefore it makes sense to arrange the elements in groups. The groups can be seen as subsystems of the whole system. The continuation of this approach results in a hierarchical representation showing the structure of the system. Only if all elements are equal, they cannot be categorized.


how to understand systems, develop systems, design systems, system analysis, sytem synthesis  -


The figure above shows the hierarchical structure of a complex system (the structure of a system is the arrangement of its elements). The figure gives us an overview of the system elements and also a first indication of their relationship to each other, because we can see which elements belong together. Non-fiction books are systems of statements and their table of contents shows the hierarchical arrangement of these statements. Therefore the table of contents of a book is an example for the figure above.


"Only the knowledge of the elements and their structural arrangement enables understanding of systems and explains the statement that the whole is more than the sum of the parts." (Daenzer, W. F. (1976) Systems Engineering: Leitfaden zur methodischen Durchführung umfangreicher Planungsvorhaben. Peter Hanstein Verlag, Köln, page 12, my translation)


Some psychologists do situation research because they want to predict the behavior of a person in a special situation:


"... considering the situation the person is currently in can enhance behavioral prediction. ... [To assess situational information, we need to measure the physical cues of the situation and the perceiver’s interpretation of the situation’s characteristics.]

Elements that are physically present and constitute the situation are referred to as situation cues ... Cues give the answer to five simple W-questions. Who is with you? Which objects are around you? What is happening? Where are you? When is this happening? ... Listing and quantifying all cues ... in a situation would take a tremendous amount of time and effort, if it could even be achieved.

... assessing situations via their perceived characteristics requires that perceivers rate situations on these characteristics. ... For example, most people would agree that sitting in a café and enjoying a drink with friends is more pleasant than cleaning one’s house. Of course, some people may hold a different view on this, which needs to be explicitly considered when seeking to assess the situation in its completeness." (Horstmann, K. T., Rauthmann, J. F., & Sherman, R. A. (2017). The measurement of situational influences. In V. Zeigler-Hill and T. K. Shackelford (eds.), The SAGE Handbook of Personality and Individual Differences, page 2-9)


This means: To understand a situation, we first need to identify the main elements the cues (see above the figure "Situation Analysis"). Between the main elements exist relations. These relations are governed by rules and have characteristics. Therefore in a second step we must examine these rules and characteristics.


We need imagination to understand the relations between the elements of a situation because we need to put ourselves in the position of the elements. In the position of an element we can ask ourselves:

What are my characteristics?  How do I influence the other elements of the situation? Which rules apply to me? How have I developed over time? How will I develop in the future? 


When we have analyzed all the main elements in this way, we understand the situation and can synthesize "the whole". However, sometimes it is a good idea to start with "the whole" and then proceed with an analysis. What we should start with depends on the knowledge about the system that is available to us.


"... the choice of a suitable method for the study of a given system depends, to a large extent, on the type of knowledge that is empirically accessicble to us ..." ( , 26.02.20, page 7)


The study of a system can start with an investigation of "the whole" as a functioning unit or with an investigation of its parts (its elements):


"We regard a system as a primary unit [a functioning unit] when we treat it as a black box and ask about its overall behavior - i.e. what it does or accomplishes. For example, we may submit our black box to various inputs and observe the resulting outputs.
As a set of parts or components (which somehow work together to produce the system's overall behavior) we can examine the system's construction - i.e. its internal structure and processes. ... and the specific relationships between its parts ..." ( , 26.02.20, page 6)


Sometimes it is useful to start an analysis and a synthesis at the same time. For example, when the police are looking for a serial killer, they investigate all the crime evidence (the elements) and hire a profiler to describe the killer's criminal profile ("the whole").


"The whole is more than the sum of its parts." So what is "the whole"?

There are many different types of systems and you can look at each system from different angles. "The whole" of a system is the most useful for the viewer of the system. It is the answer to the main question the viewer poses to the system. Therefore "the whole" of a system depends on the observer.


If we put all the parts of a car in a box, then we have the sum of its parts. If we assemble all of these parts, we have a functional unit (the car) as "the whole".
The main question to the system is here: "Can I use it as means of transport?" As means of transport the parts in the box are useless.


Here are some examples for "the whole":

"The whole" as knowledge/conclusion: The "whole" is the conclusion which is drawn from the examination of a system. The police analyze a crime because they want to know the offender. Another police department analyses the same crime from a different angle because they want to know how such crimes can be prevented.

"The Whole" as a function: A customer says to a product developer: "Please develop me a product with these main functions."

"The whole" as a key message: Every text has a key message (Literature often has a moral.)

"The whole" as the main characteristic: Two people talk about a car. The first says, "This is a nice car." The other says, "This car uses a lot of gas." They look at the car from different angles.

"The wole" as the main rule: You organize a meeting. The last meeting was very controversial. For the coming meeting you set the rule: everyone respects the other's point of view. (In this text here I synthesize the main rules for solving problems.)

"The whole" as an idea: A scientist sees that many people have the same problem. He has an idea to solve this problem and starts a research project.



People who don't distinguish between analyzing and synthesizing don't understand the importance of synthesis. They draw conclusions, but they don't take into account that "the whole is more than the sum of its parts". They do not consider the multiple relationships between the elements of a complex system. Therefore they draw simple conclusions that are often wrong.

How to analyze and set a goal?

"A goal is the object or aim of an action ... usually within a specified time limit." (Locke, E.A. & Latham, G.P. (2002). Building a Practically Useful Theory of Goal Setting and Task Motivation: A 35-Year Odyssey, American Psychologist, 57, page 705)


Definition:  A goal is a desired future result toward which effort is directed. (For the sake of simplicity, I do not distinguish between goal, objective, aim and target.)


A desired future result toward which no effort is directed is a whish, not a goal. A goal (the desired future result) can be broadly determined or specific. If someone has the goal to become rich, he can make a great effort to reach that goal although it is not precisely defined. When several people work together to achieve a goal, it is advisable to define that goal precisely.


A goal is not an isolated goal value, but it is a situation. A situation is a system at a point in time. Just as there are simple and complex systems, there are simple and complex goals. "I want to go to the kitchen and drink a glas of water." This is a simple goal and the answer to the question "Have you achieved your goal?" can normally be yes or no. For a complex goal, the question cannot be answered with a simple yes or no, because in a complex goal situation there are always several elements that are related to the goal. Here is an example:


A student sets himself the goal to get a very good grade in an exam. He prepares day and night for the exam for 7 weeks. He reaches his goal and gets a very good grade in the exam. Unfortunately, his girlfriend is annoyed with him because he hasn't spent any time with her and she separates from him. In addition, he learned too hard and he is sick for 4 weeks after the exam. He should have considered his goal as a goal situation. A complex goal should be set in a comprehensive way: a very good grade without annoying the girlfriend and damaging the health.


The prerequisite to anticipate the goal situation is that we understand the current unsatisfactory situation. The main question is: Why is this situation unsatisfactory? A superficial answer to this question would not be sufficient to set a goal for the solution of a complex problem. An unsatisfactory situation has deficiencies. Deficiencies represent opportunities for improvement. For example, if the growth of a business is 3% and 5% would be possible, then 3% growth is a deficiency.


To understand an unsatisfactory situation, we first need to identify the main elements responsible for the deficiencies. In a second step we must examine the rules and characteristics causing these deficiencies. Then we understand what is positive and negative about the current situation. It is important to understand both because when we improve the negative, we must not damage the positive.


"In the field of user experience understanding negative experiences and the conditions in which they arise may prove very important in order to further develop products iteratively based on the user experience evaluations."

(Timo Partala, Aleksi Kallinen, Understanding the most satisfying and unsatisfying user experiences: Emotions, psychological needs, and context, Interacting with Computers, Volume 24, Issue 1, January 2012, page 26)


"It is good engineering practice to state the problem in terms of the top-level function that the system must perform. However, it is better to state the problem in terms of the deficiency that must be ameliorated. This stimulates consideration of more alternative designs." (, 22.08.20, page 3)


The whole process of goal setting looks like this:


The problem solving process - goal setting - goal-oriented requirements -


"Typically, the current system under consideration is analyzed in its organizational, operational and technical setting; problems [deficiencies] are pointed out and opportunities are identified; highlevel goals are then identified and refined to address such problems and meet the opportunities; requirements are then elaborated to meet those goals. ... Goals may be formulated at different levels of abstraction, ranging from high-level, strategic concerns ... to low-level [specific concerns]" (A. van Lamsweerde, Goal-Oriented Requirements Engineering: A Guided Tour, Proceedings of the 5th IEEE International Symposium on Requirements Engineering, IEEE Computer Society, 2001, page 249, 250)


Specific goals can be called requirements (in software and systems engineering) or SMART goals (specific, measurable, achievable, relevant and time-bound). A goal is a desired future result toward which effort is directed. A requirement is a capability, a function or a property of a desired result.


"I think in terms of three levels of requirements ... At the top are the business requirements, representing the high-level objectives ... The second level addresses the user requirements, which describe the tasks that users must be able to perform using the new product. [The third level are specific functional requirements.]" (K. E.Wiegers. Karl Wiegers describes 10 requirements traps to avoid. Software Testing and Quality Engineering, 2(1), 2000, page 1-2)


There is another aspect that plays a role in setting a goal. We normally want to achieve our goals at a certain point in time with as little effort as possible. So what would be the perfect goal? A goal would be perfect if it satisfies all aspects of the goal situation as well as possible and if it can be achieved at a certain point in time with as little effort as possible. The following figure shows the dependence of the quality of the result on the effort. It shows that it is impossible to achieve a perfect result. So setting a perfect goal is pointless. Goals and requirements must match the available budget and schedule.


How to set a goal? How to set an optimal goal? -


The optimal goal for a complex problem always lies within an optimal range.


"... there is no single optimal solution to complex systems problems. Most system designs have several performance and cost criteria. Systems Engineering creates a set of alternative designs that satisfies these performance and cost criteria to varying degrees. Moving from one alternative to another will usually improve at least one criterion and worsen at least one criterion (i.e., there will be trade-offs). None of the feasible alternatives is likely to optimize all the criteria (Szidarovszky, Gershon, and Duckstein, 1986)." (, 22.08.20, page 3)

So far we do not know the solution of the problem. We do not know which method to apply to reach the goal. Different methods result in different goal situations (goal systems). Therefore all goals and requirements are still uncertain.


"... if a project applies a rigid development approach and fails to recognise uncertainty and the need for evolution, it can actually drive additional costs into a project. A common reason for project problems is insufficient management of changing requirements during all stages of the project life." (Nolan, A., Abrahao, S., Clements, P. and Pickard, A. 2011. Managing Requirements Uncertainty in Engine Control Systems Development. Proceedings of the 19th International Requirements Engineering Conference. IEEE, page 259)


Nevertheless, at this stage we are making a list of possible goals and requirements and we prioritize them. This list will help us to decide what is the right method to solve the problem.


"One characteristic of excellent requirements is that they are explicitly prioritized. When customer expectations are high, timelines are short, and resources are limited, you want to make sure the product contains the most essential functions. ... A common approach to prioritization is to group requirements into three priority categories. Essential [must have] ... Conditional [should have] ... Optional [nice to have] ... Keep the prioritization as simple as possible to help you make the necessary development choices." (K. Wiegers, “First things first: prioritizing requirements,” Software Development, vol. 7, no. 9, pp. 48–53, 1999.)

Even if the goals and requirements are still uncertain, we need them to be able to assess the result quality. The figure above can be interpreted in two ways:

  1. We compare two possible goal systems and find that System 2 gives us a better result quality.
  2. We compare the current system 1 with the goal system 2 and see that the desired result quality is significantly higher than the current one.

Example: A pizzeria buys a new oven. With this new oven (system 2) more and better pizzas can be baked than with the old oven (system 1).


How to generate alternative solutions?

"We shall use the term intelligence to mean the ability of an organism to solve ... problems ..." (Bingham, W. V. (1937). Aptitudes and aptitude testing. New York: Harper and Brothers.)


Intelligent people are creative and can generate solutions for a problem. So what is creativity?


"Unfortunately, most creativity research does not include an explicit definition; this lack of definition patially accounts for the often-conflicting research on the topic ..." (Plucker, J.A. & Makel, M.C. (2010). Assessment of Creativity. In J.Kaufman (Ed.) Cambridge Handbook of Creativity. New York: Cambridge University Press, page 48)


It seems to be a problem to define creativity. Sir Ken Robinson says:


"Creativity is about producing something new." ( , 21.09.20)


We analyze: Someone is producing something new. We have a system with the two elements "someone" and "something new".


 ... to be continued


How to solve the climate change problem?

LEARN-STUDY-WORK is not a political website. Therefore this is just an example how to apply the first and the second step of the problems solving process shown in the image above.


First step: Understand (analyze and sythesize) the unsatisfactory situation, the obstacle and the goal.


The climate of our world changes. This is an unsatisfactory situation because as a result glaciers and sea ice melt, the sea level rises, more flooding and droughts occur, hurricanes and other storms become stronger, species become extinct and some diseases can spread due to migration.


The goal is to stop the climate change by reducing the amount of CO2 and other greenhouse gases in the atmosphere.


Unfortunately this is not easy to do because there are two obstacles:

1. To stop the climate change, many people would have to change their lifestyles considerably but not enough people agree.

2. To stop the climate change without changing the lifestyle would cost a huge amount of money but not enough countries are able or agree to invest this amount of money.


Second step: After the analysis of the situation, the obstacles and the goal I think of several solutions to overcome the obstacles and to achieve the goal. I list all conceivable strategies (a strategie is a long-term plan):


How to solve the climate change problem? -


*) "Use economic power" means buying green products and services and investing in "green" business.


Everyone must decide for himself which of these alternative strategies is effective and is in line with his values.