problem solving trial and error

Trial and Error

Trial and Error is a fundamental method of problem-solving, which involves attempting different solutions until the correct one is found. As a strategy frequently used in multiple fields, including psychology, science, and computer programming, its significance is profound and multifaceted.

Understanding the term

To fully appreciate the trial and error method’s value, let’s delve into its characteristics, process, and theoretical underpinnings.

Characteristics of the Trial and Error Method

The trial and error method is defined by two key elements: making attempts (trials) and learning from failures (errors). The process continues until a solution is found.

The Trial and Error Process

The process of trial and error consists of generating possible solutions, applying them, assessing their effectiveness, and revising the approach based on the results.

Theoretical Background

Trial and error has roots in behavioral psychology, where it’s often associated with Edward Thorndike’s Law of Effect. This law suggests that responses followed by satisfaction will be repeated, while those followed by discomfort will be discontinued.

Trial and Error in Everyday Life

The application of the trial and error method is ubiquitous, extending from our daily activities to complex scientific research.

Learning New Skills

When we learn to ride a bicycle, cook a new dish, or play a musical instrument, we use trial and error to master the skills.

Technological Advancements

In the tech industry, trial and error play a crucial role in software development and debugging, hardware design, and algorithm optimization.

Advantages and Disadvantages

The trial and error method, despite its universal application, comes with its pros and cons.

H3: Advantages

Trial and error encourages creativity and fosters resilience. It allows for the discovery of all possible solutions and can lead to unexpected yet effective outcomes.

H3: Disadvantages

However, trial and error can be time-consuming and resource-intensive. It may not be feasible when there’s a need for immediate solutions or when the risks of failure are high.

To better illustrate the concept of trial and error, let’s consider a couple of examples.

Example 1: Learning to Code

When learning to code, students often write a program, run it to see if it works, and if it doesn’t, they debug and modify their code. This is an example of trial and error.

Example 2: Medicinal Drug Discovery

In medicinal chemistry, scientists often synthesize and test numerous compounds before finding one that effectively treats a disease. This process embodies the trial and error method.

Enhancing the Trial and Error Process

While trial and error inherently involve some degree of uncertainty, some strategies can enhance its efficiency.

Learn from Each Attempt

Each trial, whether successful or unsuccessful, provides valuable information. Reflecting on each attempt can improve future trials and hasten the problem-solving process.

Embrace Failure

Viewing errors as learning opportunities rather than failures can foster resilience and creativity, essential traits for effective problem-solving.

In essence, trial and error is an indispensable problem-solving strategy that encourages creativity, resilience, and comprehensive solution discovery. By understanding its characteristics, benefits, and limitations, we can harness its potential more effectively in various domains of life. Remember, each trial brings you one step closer to a solution, and each error is a stepping stone to success.

Leadership & Flow

Global Research Program and Network

What is ‘trial and error’?

Trial and error is not a method of finding the best solution, nor a method of finding all solutions. It is a problem-solving technique that is used simply to find a solution.

‘ So, you screwed up? ’ – How many times have you heard this criticism when you failed? What this question often implies is that you are a loser , someone who lost its reputation or having difficulty managing a situation or a relationship. Hidden, this question sends the message: ‘You are not good enough’ .

No wonder, that it is inherently coded in us to fear failure and be ashamed when we fail. Even though every one fails sometimes in life, as failure is part of a learning process we cannot avoid. If we look deep inside, everybody would agree, that the failures that make us stronger and unique.

Studies show that the most successful people failed a lot. When testing concepts, ideas, solving new problems in the real world one cannot avoid making mistakes, or fall flat sometimes. Successful managers, leaders, and entrepreneurs all understand the importance of failure, indeed they are mastered in failing but:

• they have learned to move on; and
• learned from their mistakes, in other words, they truly understand the meaning of trial and error.

To me, failure and self-development come hand in hand. It is not a question if: ‘ Will you fail or not?’ , but rather ‘ What level of risk you take?’ when you fail . Successful managers and leaders suggest testing concepts, ideas in a low-risk environment to minimize risk associated with failure.

So, why not to use this ‘formula’ in teaching management and leadership?

Computer games and online simulations, such as FLIGBY offer to test and master leadership and management skills in a safe, low-risk environment and allows to experiment.

By playing FLIGBY the players can face with some of their lacking abilities, management or leadership skills. It is almost certain that they will fail someway or another as leaders/managers while playing the Game. Odd it might be, but true that failing in the Game motivates the player to play more in order to test and try out other alternative management and leadership styles and skills in order to succeed.

This is how FLIGBY unconsciously teaches new management and leadership skills and styles, teaches to accept failure as part of a learning process, and master in people management skills.

After all our whole life is based on ‘ trail and error’ , but no one can take away the experience we collect through truly experiencing life, including the mistakes we make!

(The author of this entry is Esztella Fazekas , member of the Leadership & Flow Research Team)

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means-ends analysis

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means-ends analysis , heuristic , or trial-and-error, problem-solving strategy in which an end goal is identified and then fulfilled via the generation of subgoals and action plans that help overcome obstacles encountered along the way. Solving a problem with means-ends analysis typically begins by examining the end goal and breaking it down into subgoals. Actions needed to achieve each subgoal are then developed. In some cases, subgoals are further broken down into sub-subgoals. When all of the subgoals have been achieved (or obstacles eliminated), the end goal has been met.

The idea of problem solving by means-ends analysis was introduced in 1972 by American computer scientists Allen Newell and Herbert A. Simon in their book Human Problem Solving . They developed the theory in the late 1950s and early ’60s while generating a computer model capable of simulating human problem solving, working with John Clifford Shaw, a scientist and computer expert at the RAND Corporation , where beginning in 1950 Newell also worked as a researcher. The scientists called their model the General Problem Solver (GPS). GPS would recursively apply heuristic techniques in solving a given problem and conduct a means-ends assessment after each subproblem was solved to determine whether it was closer to the intended solution. Through this process, GPS could find solutions to mathematical theorems, logical proofs, word problems, and a wide variety of other well-defined problems. (Newell and Simon received the 1975 Turing Award for their research pertaining to human cognition and artificial intelligence .)

Means-ends analysis is unique among problem-solving algorithms in that it emphasizes the generation of subgoals that directly contribute to reaching the end goal. The subgoals are not necessarily of the same type. In other approaches, namely divide-and-conquer, subproblems are created that are then solved recursively and are finally combined to solve the end problem; with divide-and-conquer, the subproblems are always of the same type.

An example of the process of carrying out means-ends analysis can be illustrated by using the end goal of having a well-designed, well-functioning website. Possible subgoals and sub-subgoals include:

technical setup, such as choosing a web hosting service, registering a domain name , and setting up the hosting environment and linking the domain;

design, involving the creation of a layout for the homepage, the creation of landing pages and interior pages, the selection of a colour scheme and typography, and the design of menus, buttons, and other interactive elements;

coding, with a need to learn coding languages and the coding and implementation of interactive elements;

content development, such as writing content and gathering images and videos;

testing browser compatibility, with testing of the website on different browsers and on different devices; and

testing and debugging to make sure the website functions properly, test interactive elements, and fix formatting issues, bugs, or inconsistencies.

Means-ends analysis is frequently used in artificial intelligence (AI) systems. As a goal-based problem-solving technique, it plays a significant role in creating AI systems that exhibit humanlike behaviour, because the algorithmic steps involved in the analysis simulate aspects of human cognition and problem-solving skills. AI systems also use means-ends analysis for limiting searches in programs by evaluating the difference between the current state of a problem and the goal state, while using a combination of backward and forward search techniques.

Businesses and organizations use means-ends analysis for planning, project management, and transformation projects. In project management, for example, means-end analysis can be used to break down complex projects into subprojects and then to track the progress of those subprojects. It is used in transformation projects to implement changes to business processes by splitting new processes into subprocesses.

Research has been conducted on applying means-ends analysis to product marketing campaigns for brand persuasion purposes. For example, in the 1990s, researchers applied means-ends analysis to study how consumers link a product’s attributes with the consequences (benefits) of using the product and how the attributes and consequences align with personal values. Such studies supported the effectiveness of means-ends analysis in brand persuasion. Later research confirmed the effectiveness of means-ends analysis and its suitability for a wide range of marketing applications and suggested the development of additional methodologies for analyzing observations.

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Trial and error

Imagine that you wake up in the morning, turn on your computer to do some study, and then discover your Wi-Fi isn’t working. First, you run a diagnostic test on your computer, but it doesn’t uncover anything. Next, you restart your computer, and still no luck. Lastly, you reboot your modem router, and… success!

The process you have just used is called trial and error, and it can be used to solve small problems like the one you had with your Wi-Fi. It can also be a powerful method in controlled situations for scientific breakthroughs, inventions, and developing new products. The idea is that you keep trying different approaches until you find one that works. The benefit of trial and error is that it allows you to test certain ideas (or hypotheses) to see if they are an effective solution to a problem. You can then take what you’ve learnt from your trials (and errors) and use it to make adjustments and to guide your next moves.

The downsides are that it can take time to conduct these trials, and this technique can’t be used in all situations. In some cases, a simple error could lead to disaster. For example, if you work as a bomb disposal expert and you need to disarm an explosive, cutting wires until you find the right one probably wouldn’t be a good idea!

• Can you think of another example of a situation in which it would not be a good idea to use trial and error?
• What about a situation in which trial and error would be a good strategy to use?

Answer the following questions to identify in which situations trial and error would be a good problem-solving technique to use.

Key Transferable Skills Copyright © 2024 by RMIT University Library is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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40 problem-solving techniques and processes

All teams and organizations encounter challenges. Approaching those challenges without a structured problem solving process can end up making things worse.

Proven problem solving techniques such as those outlined below can guide your group through a process of identifying problems and challenges , ideating on possible solutions , and then evaluating and implementing the most suitable .

In this post, you'll find problem-solving tools you can use to develop effective solutions. You'll also find some tips for facilitating the problem solving process and solving complex problems.

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What is problem solving?

Problem solving is a process of finding and implementing a solution to a challenge or obstacle. In most contexts, this means going through a problem solving process that begins with identifying the issue, exploring its root causes, ideating and refining possible solutions before implementing and measuring the impact of that solution.

For simple or small problems, it can be tempting to skip straight to implementing what you believe is the right solution. The danger with this approach is that without exploring the true causes of the issue, it might just occur again or your chosen solution may cause other issues.

Particularly in the world of work, good problem solving means using data to back up each step of the process, bringing in new perspectives and effectively measuring the impact of your solution.

Effective problem solving can help ensure that your team or organization is well positioned to overcome challenges, be resilient to change and create innovation. In my experience, problem solving is a combination of skillset, mindset and process, and it’s especially vital for leaders to cultivate this skill.

What is the seven step problem solving process?

A problem solving process is a step-by-step framework from going from discovering a problem all the way through to implementing a solution.

With practice, this framework can become intuitive, and innovative companies tend to have a consistent and ongoing ability to discover and tackle challenges when they come up.

You might see everything from a four step problem solving process through to seven steps. While all these processes cover roughly the same ground, I’ve found a seven step problem solving process is helpful for making all key steps legible.

We’ll outline that process here and then follow with techniques you can use to explore and work on that step of the problem solving process with a group.

The seven-step problem solving process is:

1. Problem identification 

The first stage of any problem solving process is to identify the problem(s) you need to solve. This often looks like using group discussions and activities to help a group surface and effectively articulate the challenges they’re facing and wish to resolve.

Be sure to align with your team on the exact definition and nature of the problem you’re solving. An effective process is one where everyone is pulling in the same direction – ensure clarity and alignment now to help avoid misunderstandings later.

2. Problem analysis and refinement

The process of problem analysis means ensuring that the problem you are seeking to solve is  the   right problem . Choosing the right problem to solve means you are on the right path to creating the right solution.

At this stage, you may look deeper at the problem you identified to try and discover the root cause at the level of people or process. You may also spend some time sourcing data, consulting relevant parties and creating and refining a problem statement.

Problem refinement means adjusting scope or focus of the problem you will be aiming to solve based on what comes up during your analysis. As you analyze data sources, you might discover that the root cause means you need to adjust your problem statement. Alternatively, you might find that your original problem statement is too big to be meaningful approached within your current project.

Remember that the goal of any problem refinement is to help set the stage for effective solution development and deployment. Set the right focus and get buy-in from your team here and you’ll be well positioned to move forward with confidence.

3. Solution generation

Once your group has nailed down the particulars of the problem you wish to solve, you want to encourage a free flow of ideas connecting to solving that problem. This can take the form of problem solving games that encourage creative thinking or techniquess designed to produce working prototypes of possible solutions. 

The key to ensuring the success of this stage of the problem solving process is to encourage quick, creative thinking and create an open space where all ideas are considered. The best solutions can often come from unlikely places and by using problem solving techniques that celebrate invention, you might come up with solution gold. 

4. Solution development

No solution is perfect right out of the gate. It’s important to discuss and develop the solutions your group has come up with over the course of following the previous problem solving steps in order to arrive at the best possible solution. Problem solving games used in this stage involve lots of critical thinking, measuring potential effort and impact, and looking at possible solutions analytically. 

During this stage, you will often ask your team to iterate and improve upon your front-running solutions and develop them further. Remember that problem solving strategies always benefit from a multitude of voices and opinions, and not to let ego get involved when it comes to choosing which solutions to develop and take further.

Finding the best solution is the goal of all problem solving workshops and here is the place to ensure that your solution is well thought out, sufficiently robust and fit for purpose. 

5. Decision making and planning

Nearly there! Once you’ve got a set of possible, you’ll need to make a decision on which to implement. This can be a consensus-based group decision or it might be for a leader or major stakeholder to decide. You’ll find a set of effective decision making methods below.

Once your group has reached consensus and selected a solution, there are some additional actions that also need to be decided upon. You’ll want to work on allocating ownership of the project, figure out who will do what, how the success of the solution will be measured and decide the next course of action.

Set clear accountabilities, actions, timeframes, and follow-ups for your chosen solution. Make these decisions and set clear next-steps in the problem solving workshop so that everyone is aligned and you can move forward effectively as a group. 

Ensuring that you plan for the roll-out of a solution is one of the most important problem solving steps. Without adequate planning or oversight, it can prove impossible to measure success or iterate further if the problem was not solved. 

6. Solution implementation 

This is what we were waiting for! All problem solving processes have the end goal of implementing an effective and impactful solution that your group has confidence in.

Project management and communication skills are key here – your solution may need to adjust when out in the wild or you might discover new challenges along the way. For some solutions, you might also implement a test with a small group and monitor results before rolling it out to an entire company.

You should have a clear owner for your solution who will oversee the plans you made together and help ensure they’re put into place. This person will often coordinate the implementation team and set-up processes to measure the efficacy of your solution too.

7. Solution evaluation 

So you and your team developed a great solution to a problem and have a gut feeling it’s been solved. Work done, right? Wrong. All problem solving strategies benefit from evaluation, consideration, and feedback.

You might find that the solution does not work for everyone, might create new problems, or is potentially so successful that you will want to roll it out to larger teams or as part of other initiatives. 

None of that is possible without taking the time to evaluate the success of the solution you developed in your problem solving model and adjust if necessary.

Remember that the problem solving process is often iterative and it can be common to not solve complex issues on the first try. Even when this is the case, you and your team will have generated learning that will be important for future problem solving workshops or in other parts of the organization. 

It’s also worth underlining how important record keeping is throughout the problem solving process. If a solution didn’t work, you need to have the data and records to see why that was the case. If you go back to the drawing board, notes from the previous workshop can help save time.

What does an effective problem solving process look like?

Every effective problem solving process begins with an agenda . In our experience, a well-structured problem solving workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

The format of a workshop ensures that you can get buy-in from your group, encourage free-thinking and solution exploration before making a decision on what to implement following the session.

This Design Sprint 2.0 template is an effective problem solving process from top agency AJ&Smart. It’s a great format for the entire problem solving process, with four-days of workshops designed to surface issues, explore solutions and even test a solution.

Check it for an example of how you might structure and run a problem solving process and feel free to copy and adjust it your needs!

For a shorter process you can run in a single afternoon, this remote problem solving agenda will guide you effectively in just a couple of hours.

Whatever the length of your workshop, by using SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Complete problem-solving methods

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

The Six Thinking Hats   #creative thinking   #meeting facilitation   #problem solving   #issue resolution   #idea generation   #conflict resolution   The Six Thinking Hats are used by individuals and groups to separate out conflicting styles of thinking. They enable and encourage a group of people to think constructively together in exploring and implementing change, rather than using argument to fight over who is right and who is wrong.

Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on. 

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages. 

Lightning Decision Jam (LDJ)   #action   #decision making   #problem solving   #issue analysis   #innovation   #design   #remote-friendly   It doesn’t matter where you work and what your job role is, if you work with other people together as a team, you will always encounter the same challenges: Unclear goals and miscommunication that cause busy work and overtime Unstructured meetings that leave attendants tired, confused and without clear outcomes. Frustration builds up because internal challenges to productivity are not addressed Sudden changes in priorities lead to a loss of focus and momentum Muddled compromise takes the place of clear decision- making, leaving everybody to come up with their own interpretation. In short, a lack of structure leads to a waste of time and effort, projects that drag on for too long and frustrated, burnt out teams. AJ&Smart has worked with some of the most innovative, productive companies in the world. What sets their teams apart from others is not better tools, bigger talent or more beautiful offices. The secret sauce to becoming a more productive, more creative and happier team is simple: Replace all open discussion or brainstorming with a structured process that leads to more ideas, clearer decisions and better outcomes. When a good process provides guardrails and a clear path to follow, it becomes easier to come up with ideas, make decisions and solve problems. This is why AJ&Smart created Lightning Decision Jam (LDJ). It’s a simple and short, but powerful group exercise that can be run either in-person, in the same room, or remotely with distributed teams.

Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design. 

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition   #problem solving   #idea generation   #creativity   #online   #remote-friendly   A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

The 5 Whys 

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges. 

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results. 

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys   #hyperisland   #innovation   This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold. 

World Cafe   #hyperisland   #innovation   #issue analysis   World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD)   #idea generation   #liberating structures   #action   #issue analysis   #remote-friendly   DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology   #action plan   #idea generation   #problem solving   #issue analysis   #large group   #online   #remote-friendly   Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around. 

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish. 

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis   #problem solving   ##root cause analysis   #decision making   #online facilitation   A process to help identify and understand the origins of problems, issues or observations.

Problem Tree 

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them. 

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree   #define intentions   #create   #design   #issue analysis   A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward. 

SWOT analysis   #gamestorming   #problem solving   #action   #meeting facilitation   The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results. 

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause. 

Agreement-Certainty Matrix   #issue analysis   #liberating structures   #problem solving   You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic .  A problem is simple when it can be solved reliably with practices that are easy to duplicate.  It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably.  A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail.  Chaotic is when the context is too turbulent to identify a path forward.  A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.”  The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process. 

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID   #gamestorming   #project planning   #issue analysis   #problem solving   When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!   

Speed Boat   #gamestorming   #problem solving   #action   Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How   #idea generation   #issue analysis   #problem solving   #online   #creative thinking   #remote-friendly   A questioning method for generating, explaining, investigating ideas.

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed. 

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.  

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It!   #gamestorming   #problem solving   #action   Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills. 

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO! 

LEGO Challenge   #hyperisland   #team   A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems. 

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken. 

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What?   #issue analysis   #innovation   #liberating structures   You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

Journalists  

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists   #vision   #big picture   #issue analysis   #remote-friendly   This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for brainstorming solutions

Now you have the context and background of the problem you are trying to solving, now comes the time to start ideating and thinking about how you’ll solve the issue.

Here, you’ll want to encourage creative, free thinking and speed. Get as many ideas out as possible and explore different perspectives so you have the raw material for the next step.

Looking at a problem from a new angle can be one of the most effective ways of creating an effective solution. TRIZ is a problem-solving tool that asks the group to consider what they must not do in order to solve a challenge.

By reversing the discussion, new topics and taboo subjects often emerge, allowing the group to think more deeply and create ideas that confront the status quo in a safe and meaningful way. If you’re working on a problem that you’ve tried to solve before, TRIZ is a great problem-solving method to help your team get unblocked.

Making Space with TRIZ   #issue analysis   #liberating structures   #issue resolution   You can clear space for innovation by helping a group let go of what it knows (but rarely admits) limits its success and by inviting creative destruction. TRIZ makes it possible to challenge sacred cows safely and encourages heretical thinking. The question “What must we stop doing to make progress on our deepest purpose?” induces seriously fun yet very courageous conversations. Since laughter often erupts, issues that are otherwise taboo get a chance to be aired and confronted. With creative destruction come opportunities for renewal as local action and innovation rush in to fill the vacuum. Whoosh!

Mindspin  

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly. 

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation. 

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex. 

MindSpin   #teampedia   #idea generation   #problem solving   #action   A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed. 

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable. 

The Creativity Dice   #creativity   #problem solving   #thiagi   #issue analysis   Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

Idea and Concept Development

Brainstorming without structure can quickly become chaotic or frustrating. In a problem-solving context, having an ideation framework to follow can help ensure your team is both creative and disciplined.

In this method, you’ll find an idea generation process that encourages your group to brainstorm effectively before developing their ideas and begin clustering them together. By using concepts such as Yes and…, more is more and postponing judgement, you can create the ideal conditions for brainstorming with ease.

Idea & Concept Development   #hyperisland   #innovation   #idea generation   Ideation and Concept Development is a process for groups to work creatively and collaboratively to generate creative ideas. It’s a general approach that can be adapted and customized to suit many different scenarios. It includes basic principles for idea generation and several steps for groups to work with. It also includes steps for idea selection and development.

Problem-solving techniques for developing and refining solutions 

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to develop and refine your ideas in order to bring them closer to a solution that actually solves the problem.

Use these problem-solving techniques when you want to help your team think through their ideas and refine them as part of your problem solving process.

Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result. 

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution. 

Improved Solutions   #creativity   #thiagi   #problem solving   #action   #team   You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged. 

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch   #design sprint   #innovation   #idea generation   #remote-friendly   The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper,  Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

Ensuring that everyone in a group is able to contribute to a discussion is vital during any problem solving process. Not only does this ensure all bases are covered, but its then easier to get buy-in and accountability when people have been able to contribute to the process.

1-2-4-All is a tried and tested facilitation technique where participants are asked to first brainstorm on a topic on their own. Next, they discuss and share ideas in a pair before moving into a small group. Those groups are then asked to present the best idea from their discussion to the rest of the team.

This method can be used in many different contexts effectively, though I find it particularly shines in the idea development stage of the process. Giving each participant time to concretize their ideas and develop them in progressively larger groups can create a great space for both innovation and psychological safety.

1-2-4-All   #idea generation   #liberating structures   #issue analysis   With this facilitation technique you can immediately include everyone regardless of how large the group is. You can generate better ideas and more of them faster than ever before. You can tap the know-how and imagination that is distributed widely in places not known in advance. Open, generative conversation unfolds. Ideas and solutions are sifted in rapid fashion. Most importantly, participants own the ideas, so follow-up and implementation is simplified. No buy-in strategies needed! Simple and elegant!

15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change. 

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.   

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change. 

15% Solutions   #action   #liberating structures   #remote-friendly   You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference.  15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change.  With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

Problem-solving techniques for making decisions and planning

After your group is happy with the possible solutions you’ve developed, now comes the time to choose which to implement. There’s more than one way to make a decision and the best option is often dependant on the needs and set-up of your group.

Sometimes, it’s the case that you’ll want to vote as a group on what is likely to be the most impactful solution. Other times, it might be down to a decision maker or major stakeholder to make the final decision. Whatever your process, here’s some techniques you can use to help you make a decision during your problem solving process.

How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process. 

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud. 

How-Now-Wow Matrix   #gamestorming   #idea generation   #remote-friendly   When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice. 

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them. 

Impact and Effort Matrix   #gamestorming   #decision making   #action   #remote-friendly   In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action? 

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus. 

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively. 

Dotmocracy   #action   #decision making   #group prioritization   #hyperisland   #remote-friendly   Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

Straddling the gap between decision making and planning, MoSCoW is a simple and effective method that allows a group team to easily prioritize a set of possible options.

Use this method in a problem solving process by collecting and summarizing all your possible solutions and then categorize them into 4 sections: “Must have”, “Should have”, “Could have”, or “Would like but won‘t get”.

This method is particularly useful when its less about choosing one possible solution and more about prioritorizing which to do first and which may not fit in the scope of your project. In my experience, complex challenges often require multiple small fixes, and this method can be a great way to move from a pile of things you’d all like to do to a structured plan.

MoSCoW   #define intentions   #create   #design   #action   #remote-friendly   MoSCoW is a method that allows the team to prioritize the different features that they will work on. Features are then categorized into “Must have”, “Should have”, “Could have”, or “Would like but won‘t get”. To be used at the beginning of a timeslot (for example during Sprint planning) and when planning is needed.

When it comes to managing the rollout of a solution, clarity and accountability are key factors in ensuring the success of the project. The RAACI chart is a simple but effective model for setting roles and responsibilities as part of a planning session.

Start by listing each person involved in the project and put them into the following groups in order to make it clear who is responsible for what during the rollout of your solution.

• Responsibility  (Which person and/or team will be taking action?)
• Authority  (At what “point” must the responsible person check in before going further?)
• Accountability  (Who must the responsible person check in with?)
• Consultation  (Who must be consulted by the responsible person before decisions are made?)
• Information  (Who must be informed of decisions, once made?)

Ensure this information is easily accessible and use it to inform who does what and who is looped into discussions and kept up to date.

RAACI   #roles and responsibility   #teamwork   #project management   Clarifying roles and responsibilities, levels of autonomy/latitude in decision making, and levels of engagement among diverse stakeholders.

Problem-solving warm-up activities

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process. Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute. 

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out   #team   #opening   #closing   #hyperisland   #remote-friendly   Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

Doodling Together  

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start. 

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems. 

Doodling Together   #collaboration   #creativity   #teamwork   #fun   #team   #visual methods   #energiser   #icebreaker   #remote-friendly   Create wild, weird and often funny postcards together & establish a group’s creative confidence.

Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team! 

Show and Tell   #gamestorming   #action   #opening   #meeting facilitation   Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible. 

Constellations   #trust   #connection   #opening   #coaching   #patterns   #system   Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic. 

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree   #thiagi   #opening   #perspectives   #remote-friendly   With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Closing activities for a problem-solving process

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round. 

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them. 

One breath feedback   #closing   #feedback   #action   This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

Who What When Matrix 

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward. 

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved. 

Who/What/When Matrix   #gamestorming   #action   #project planning   With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out! 

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised. 

Response Cards   #debriefing   #closing   #structured sharing   #questions and answers   #thiagi   #action   It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Tips for effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.  

Try different approaches  

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally 

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Create psychologically safe spaces for discussion

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner.

It can be tough for people to stand up and contribute if the problems or challenges are emotive or personal in nature. Try and create a psychologically safe space for these kinds of discussions and where possible, create regular opportunities for challenges to be brought up organically.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator 

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

Save time and effort creating an effective problem solving process

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks  to build your agenda. When you make changes or update your agenda, your session  timing   adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore  how to use SessionLab  to design effective problem solving workshops or  watch this five minute video  to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you! 

James Smart is Head of Content at SessionLab. He’s also a creative facilitator who has run workshops and designed courses for establishments like the National Centre for Writing, UK. He especially enjoys working with young people and empowering others in their creative practice.

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

Your list of techniques for problem solving can be helpfully extended by adding TRIZ to the list of techniques. TRIZ has 40 problem solving techniques derived from methods inventros and patent holders used to get new patents. About 10-12 are general approaches. many organization sponsor classes in TRIZ that are used to solve business problems or general organiztational problems. You can take a look at TRIZ and dwonload a free internet booklet to see if you feel it shound be included per your selection process.

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4 Main problem-solving strategies

In Psychology, you get to read about a ton of therapies. It’s mind-boggling how different theorists have looked at human nature differently and have come up with different, often somewhat contradictory, theoretical approaches.

Yet, you can’t deny the kernel of truth that’s there in all of them. All therapies, despite being different, have one thing in common- they all aim to solve people’s problems. They all aim to equip people with problem-solving strategies to help them deal with their life problems.

Problem-solving is really at the core of everything we do. Throughout our lives, we’re constantly trying to solve one problem or another. When we can’t, all sorts of psychological problems take hold. Getting good at solving problems is a fundamental life skill.

Problem-solving stages

What problem-solving does is take you from an initial state (A) where a problem exists to a final or goal state (B), where the problem no longer exists.

To move from A to B, you need to perform some actions called operators. Engaging in the right operators moves you from A to B. So, the stages of problem-solving are:

• Initial state

The problem itself can either be well-defined or ill-defined. A well-defined problem is one where you can clearly see where you are (A), where you want to go (B), and what you need to do to get there (engaging the right operators).

For example, feeling hungry and wanting to eat can be seen as a problem, albeit a simple one for many. Your initial state is hunger (A) and your final state is satisfaction or no hunger (B). Going to the kitchen and finding something to eat is using the right operator.

In contrast, ill-defined or complex problems are those where one or more of the three problem solving stages aren’t clear. For example, if your goal is to bring about world peace, what is it exactly that you want to do?

It’s been rightly said that a problem well-defined is a problem half-solved. Whenever you face an ill-defined problem, the first thing you need to do is get clear about all the three stages.

Often, people will have a decent idea of where they are (A) and where they want to be (B). What they usually get stuck on is finding the right operators.

Initial theory in problem-solving

When people first attempt to solve a problem, i.e. when they first engage their operators, they often have an initial theory of solving the problem. As I mentioned in my article on overcoming challenges for complex problems, this initial theory is often wrong.

But, at the time, it’s usually the result of the best information the individual can gather about the problem. When this initial theory fails, the problem-solver gets more data, and he refines the theory. Eventually, he finds an actual theory i.e. a theory that works. This finally allows him to engage the right operators to move from A to B.

Problem-solving strategies

These are operators that a problem solver tries to move from A to B. There are several problem-solving strategies but the main ones are:

• Trial and error

1. Algorithms

When you follow a step-by-step procedure to solve a problem or reach a goal, you’re using an algorithm. If you follow the steps exactly, you’re guaranteed to find the solution. The drawback of this strategy is that it can get cumbersome and time-consuming for large problems.

Say I hand you a 200-page book and ask you to read out to me what’s written on page 100. If you start from page 1 and keep turning the pages, you’ll eventually reach page 100. There’s no question about it. But the process is time-consuming. So instead you use what’s called a heuristic.

2. Heuristics

Heuristics are rules of thumb that people use to simplify problems. They’re often based on memories from past experiences. They cut down the number of steps needed to solve a problem, but they don’t always guarantee a solution. Heuristics save us time and effort if they work.

You know that page 100 lies in the middle of the book. Instead of starting from page one, you try to open the book in the middle. Of course, you may not hit page 100, but you can get really close with just a couple of tries.

If you open page 90, for instance, you can then algorithmically move from 90 to 100. Thus, you can use a combination of heuristics and algorithms to solve the problem. In real life, we often solve problems like this.

When police are looking for suspects in an investigation, they try to narrow down the problem similarly. Knowing the suspect is 6 feet tall isn’t enough, as there could be thousands of people out there with that height.

Knowing the suspect is 6 feet tall, male, wears glasses, and has blond hair narrows down the problem significantly.

3. Trial and error

When you have an initial theory to solve a problem, you try it out. If you fail, you refine or change your theory and try again. This is the trial-and-error process of solving problems. Behavioral and cognitive trial and error often go hand in hand, but for many problems, we start with behavioural trial and error until we’re forced to think.

Say you’re in a maze, trying to find your way out. You try one route without giving it much thought and you find it leads to nowhere. Then you try another route and fail again. This is behavioural trial and error because you aren’t putting any thought into your trials. You’re just throwing things at the wall to see what sticks.

This isn’t an ideal strategy but can be useful in situations where it’s impossible to get any information about the problem without doing some trials.

Then, when you have enough information about the problem, you shuffle that information in your mind to find a solution. This is cognitive trial and error or analytical thinking. Behavioral trial and error can take a lot of time, so using cognitive trial and error as much as possible is advisable. You got to sharpen your axe before you cut the tree.

When solving complex problems, people get frustrated after having tried several operators that didn’t work. They abandon their problem and go on with their routine activities. Suddenly, they get a flash of insight that makes them confident they can now solve the problem.

I’ve done an entire article on the underlying mechanics of insight . Long story short, when you take a step back from your problem, it helps you see things in a new light. You make use of associations that were previously unavailable to you.

You get more puzzle pieces to work with and this increases the odds of you finding a path from A to B, i.e. finding operators that work.

Pilot problem-solving

No matter what problem-solving strategy you employ, it’s all about finding out what works. Your actual theory tells you what operators will take you from A to B. Complex problems don’t reveal their actual theories easily solely because they are complex.

Therefore, the first step to solving a complex problem is getting as clear as you can about what you’re trying to accomplish- collecting as much information as you can about the problem.

This gives you enough raw materials to formulate an initial theory. We want our initial theory to be as close to an actual theory as possible. This saves time and resources.

Solving a complex problem can mean investing a lot of resources. Therefore, it is recommended you verify your initial theory if you can. I call this pilot problem-solving.

Before businesses invest in making a product, they sometimes distribute free versions to a small sample of potential customers to ensure their target audience will be receptive to the product.

Before making a series of TV episodes, TV show producers often release pilot episodes to figure out whether the show can take off.

Before conducting a large study, researchers do a pilot study to survey a small sample of the population to determine if the study is worth carrying out.

The same ‘testing the waters’ approach needs to be applied to solving any complex problem you might be facing. Is your problem worth investing a lot of resources in? In management, we’re constantly taught about Return On Investment (ROI). The ROI should justify the investment.

If the answer is yes, go ahead and formulate your initial theory based on extensive research. Find a way to verify your initial theory. You need this reassurance that you’re going in the right direction, especially for complex problems that take a long time to solve.

Getting your causal thinking right

Problem solving boils down to getting your causal thinking right. Finding solutions is all about finding out what works, i.e. finding operators that take you from A to B. To succeed, you need to be confident in your initial theory (If I do X and Y, they’ll lead me to B). You need to be sure that doing X and Y will lead you to B- doing X and Y will cause B.

All obstacles to problem-solving or goal-accomplishing are rooted in faulty causal thinking leading to not engaging the right operators. When your causal thinking is on point, you’ll have no problem engaging the right operators.

As you can imagine, for complex problems, getting our causal thinking right isn’t easy. That’s why we need to formulate an initial theory and refine it over time.

I like to think of problem-solving as the ability to project the present into the past or into the future. When you’re solving problems, you’re basically looking at your present situation and asking yourself two questions:

“What caused this?” (Projecting present into the past)

“What will this cause?” (Projecting present into the future)

The first question is more relevant to problem-solving and the second to goal-accomplishing.

If you find yourself in a mess , you need to answer the “What caused this?” question correctly. For the operators you’re currently engaging to reach your goal, ask yourself, “What will this cause?” If you think they cannot cause B, it’s time to refine your initial theory.

Hi, I’m Hanan Parvez (MA Psychology). I’ve published over 500 articles and authored one book. My work has been featured in Forbes , Business Insider , Reader’s Digest , and Entrepreneur .

7.3 Problem-Solving

Learning objectives.

By the end of this section, you will be able to:

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving

   People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.

PROBLEM-SOLVING STRATEGIES

   When people are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them (table below). For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

   Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.

Additional Problem Solving Strategies :

• Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
• Analogy – is using a solution that solves a similar problem.
• Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
• Divide and conquer – breaking down large complex problems into smaller more manageable problems.
• Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
• Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
• Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
• Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
• Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
• Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
• Reduction – adapting the problem to be as similar problems where a solution exists.
• Research – using existing knowledge or solutions to similar problems to solve the problem.
• Root cause analysis – trying to identify the cause of the problem.

The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.

One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :

Missionary-Cannibal Problem

Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.

Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.

The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:

• 1. Only one disk can be moved at a time.
• 2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
• 3. No disc may be placed on top of a smaller disk.

  Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.

Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.

The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.

As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage  (1990) suggesting that while collecting data for what would later be his book  The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.

While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as  insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).

While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.

Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground.  Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).

Solving puzzles.

   Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

   Here is another popular type of puzzle (figure below) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

   Take a look at the “Puzzling Scales” logic puzzle below (figure below). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

What steps did you take to solve this puzzle? You can read the solution at the end of this section.

Pitfalls to problem solving.

   Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

   Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in the table below.

Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.

   Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

References:

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology

Review Questions:

1. A specific formula for solving a problem is called ________.

a. an algorithm

b. a heuristic

c. a mental set

d. trial and error

2. Solving the Tower of Hanoi problem tends to utilize a  ________ strategy of problem solving.

a. divide and conquer

b. means-end analysis

d. experiment

3. A mental shortcut in the form of a general problem-solving framework is called ________.

4. Which type of bias involves becoming fixated on a single trait of a problem?

a. anchoring bias

b. confirmation bias

c. representative bias

d. availability bias

5. Which type of bias involves relying on a false stereotype to make a decision?

6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.

a. social adjustment

b. student load payment options

c. emotional learning

d. insight learning

7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.

a. functional fixedness

c. working memory

Critical Thinking Questions:

1. What is functional fixedness and how can overcoming it help you solve problems?

2. How does an algorithm save you time and energy when solving a problem?

Personal Application Question:

1. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

anchoring bias

availability heuristic

confirmation bias

functional fixedness

hindsight bias

problem-solving strategy

representative bias

trial and error

working backwards

Answers to Exercises

algorithm:  problem-solving strategy characterized by a specific set of instructions

anchoring bias:  faulty heuristic in which you fixate on a single aspect of a problem to find a solution

availability heuristic:  faulty heuristic in which you make a decision based on information readily available to you

confirmation bias:  faulty heuristic in which you focus on information that confirms your beliefs

functional fixedness:  inability to see an object as useful for any other use other than the one for which it was intended

heuristic:  mental shortcut that saves time when solving a problem

hindsight bias:  belief that the event just experienced was predictable, even though it really wasn’t

mental set:  continually using an old solution to a problem without results

problem-solving strategy:  method for solving problems

representative bias:  faulty heuristic in which you stereotype someone or something without a valid basis for your judgment

trial and error:  problem-solving strategy in which multiple solutions are attempted until the correct one is found

working backwards:  heuristic in which you begin to solve a problem by focusing on the end result

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Thinking and Intelligence

Problem Solving

OpenStaxCollege

[latexpage]

Learning Objectives

By the end of this section, you will be able to:

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving

People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

PROBLEM-SOLVING STRATEGIES

When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them ( [link] ). For example, a well-known strategy is trial and error . The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below ( [link] ) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

Here is another popular type of puzzle ( [link] ) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Take a look at the “Puzzling Scales” logic puzzle below ( [link] ). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

PITFALLS TO PROBLEM SOLVING

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

Check out this Apollo 13 scene where the group of NASA engineers are given the task of overcoming functional fixedness.

Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in [link] .

Please visit this site to see a clever music video that a high school teacher made to explain these and other cognitive biases to his AP psychology students.

Were you able to determine how many marbles are needed to balance the scales in [link] ? You need nine. Were you able to solve the problems in [link] and [link] ? Here are the answers ( [link] ).

Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

Review Questions

A specific formula for solving a problem is called ________.

• an algorithm
• a heuristic
• a mental set
• trial and error

A mental shortcut in the form of a general problem-solving framework is called ________.

Which type of bias involves becoming fixated on a single trait of a problem?

• anchoring bias
• confirmation bias
• representative bias
• availability bias

Which type of bias involves relying on a false stereotype to make a decision?

Critical Thinking Questions

What is functional fixedness and how can overcoming it help you solve problems?

Functional fixedness occurs when you cannot see a use for an object other than the use for which it was intended. For example, if you need something to hold up a tarp in the rain, but only have a pitchfork, you must overcome your expectation that a pitchfork can only be used for garden chores before you realize that you could stick it in the ground and drape the tarp on top of it to hold it up.

How does an algorithm save you time and energy when solving a problem?

An algorithm is a proven formula for achieving a desired outcome. It saves time because if you follow it exactly, you will solve the problem without having to figure out how to solve the problem. It is a bit like not reinventing the wheel.

Personal Application Question

Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

Problem Solving Copyright © 2014 by OpenStaxCollege is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

The Use of Trial and Error To Solve Problems

Some complex problems can be solved by a technique that is called trial and error. Trial and error is typically good for problems where you have multiple chances to get the correct solution. However, this is not a good technique for problems that don’t give you multiple chances to find a solution.

An example of situations where you wouldn’t want to use trial and error are diffusing a bomb or performing an operation on a patient. In these situations, making an error can lead to disaster. Trial and error is used best when it is applied to situations that give your large amounts of time and safety to come up with a solution. In addition to this, trial and error is also a great way to gain knowledge. Basically, a person that uses the trial and error method will try to a method to see if it is a good solution. If it is not a good solution, they try another option. If the method works, the person using it has acquired the correct solution to a problem. However, there are some situations where there are too many options, and it is not feasible for a person to go through all of them to find out which one works the best. In this event, a person will want to use the option that has the best possible chances of succeeding. If this doesn’t work, they can try the next best option until they find a good solution. There are a number of important factors that makes trial and error a good tool to use for solving problems. The purpose of trial and error is not to find out why a problem was solved. It is primarily used to solve the problem. While this may be good in some fields, it may not work so well in others. For example, while trial and error may be excellent in finding solutions to mechanical or engineering problems, it may not be good for certain fields which ask "why" a solution works. Trial and error is primarily good for fields where the solution is the most important factor. This is often the case in math courses which are taught in high school or college. Most math teachers place an emphasis on using trial and error to find a solution to problems, and many of them don’t spend a whole lot of time explaining "why" a solution works. One reason for this is because most math teachers have time constraints. However, some students who take advanced math classes in college may learn more about why certain solutions work. Another good aspect of the trial and error method is that it does not try to use a solution as a way of solving more than one problem. Trial and error is primarily used to find a single solution to a single problem. Trial and error is not a method of finding the best solution, nor is it a method of finding all solutions. It is a problem solving technique that is simply used to find a solution. One of the most powerful advantages to this technique is that it does not require you to have a lot of knowledge. However, it may require you to have large amounts of patience. Trial and error is typically used to discover new drugs, and it also plays an important role in the scientific method as well. Some also feel that organic evolution is a form of trial and error, because random mutations will occur until they are successful.

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• Trial and error

Trial and error explained

Trial and error is a fundamental method of problem-solving [1] characterized by repeated, varied attempts which are continued until success, [2] or until the practicer stops trying.

According to W.H. Thorpe , the term was devised by C. Lloyd Morgan (1852–1936) after trying out similar phrases "trial and failure" and "trial and practice". [3] Under Morgan's Canon , animal behaviour should be explained in the simplest possible way. Where behavior seems to imply higher mental processes, it might be explained by trial-and-error learning. An example is a skillful way in which his terrier Tony opened the garden gate, easily misunderstood as an insightful act by someone seeing the final behavior. Lloyd Morgan, however, had watched and recorded the series of approximations by which the dog had gradually learned the response, and could demonstrate that no insight was required to explain it.

Edward Lee Thorndike was the initiator of the theory of trial and error learning based on the findings he showed how to manage a trial-and-error experiment in the laboratory. In his famous experiment, a cat was placed in a series of puzzle boxes in order to study the law of effect in learning. [4] He plotted to learn curves which recorded the timing for each trial. Thorndike's key observation was that learning was promoted by positive results, which was later refined and extended by B. F. Skinner 's operant conditioning .

Trial and error is also a method of problem solving, repair , tuning, or obtaining knowledge . In the field of computer science , the method is called generate and test ( Brute force ) . In elementary algebra, when solving equations, it is guess and check .

This approach can be seen as one of the two basic approaches to problem-solving, contrasted with an approach using insight and theory . However, there are intermediate methods which for example, use theory to guide the method, an approach known as guided empiricism .

This way of thinking has become a mainstay of Karl Popper 's critical rationalism .

Methodology

The trial and error approach is used most successfully with simple problems and in games, and it is often the last resort when no apparent rule applies. This does not mean that the approach is inherently careless, for an individual can be methodical in manipulating the variables in an attempt to sort through possibilities that could result in success. Nevertheless, this method is often used by people who have little knowledge in the problem area. The trial-and-error approach has been studied from its natural computational point of view [5]

Simplest applications

Ashby (1960, section 11/5) offers three simple strategies for dealing with the same basic exercise-problem, which have very different efficiencies. Suppose a collection of 1000 on/off switches have to be set to a particular combination by random-based testing, where each test is expected to take one second. [This is also discussed in Traill (1978–2006, section C1.2]. The strategies are:

• the perfectionist all-or-nothing method, with no attempt at holding partial successes. This would be expected to take more than 10^301 seconds, [i.e., 2^1000 seconds, or 3·5×(10^291) centuries]
• a serial-test of switches, holding on to the partial successes (assuming that these are manifest), which would take 500 seconds on average
• parallel-but-individual testing of all switches simultaneously, which would take only one second

Note the tacit assumption here that no intelligence or insight is brought to bear on the problem. However, the existence of different available strategies allows us to consider a separate ("superior") domain of processing — a "meta-level" above the mechanics of switch handling — where the various available strategies can be randomly chosen. Once again this is "trial and error", but of a different type.

Hierarchies

Ashby's book develops this "meta-level" idea, and extends it into a whole recursive sequence of levels, successively above each other in a systematic hierarchy. On this basis, he argues that human intelligence emerges from such organization: relying heavily on trial-and-error (at least initially at each new stage), but emerging with what we would call "intelligence" at the end of it all. Thus presumably the topmost level of the hierarchy (at any stage) will still depend on simple trial-and-error.

Traill (1978–2006) suggests that this Ashby-hierarchy probably coincides with Piaget 's well-known theory of developmental stages. [This work also discusses Ashby's 1000-switch example; see §C1.2]. After all, it is part of Piagetian doctrine that children learn first by actively doing in a more-or-less random way, and then hopefully learn from the consequences — which all has a certain resemblance to Ashby's random "trial-and-error".

Application

Traill (2008, espec. Table "S" on p.31 ) follows Jerne and Popper in seeing this strategy as probably underlying all knowledge-gathering systems — at least in their initial phase .

Four such systems are identified:

• Natural selection which "educates" the DNA of the species,
• The brain of the individual (just discussed);
• The "brain" of society-as-such (including the publicly held body of science); and
• The adaptive immune system .

Trial and error has a number of features:

• solution-oriented: trial and error makes no attempt to discover why a solution works, merely that it is a solution.
• problem-specific: trial and error makes no attempt to generalize a solution to other problems.
• non-optimal: trial and error is generally an attempt to find a solution, not all solutions, and not the best solution.
• needs little knowledge: trials and error can proceed where there is little or no knowledge of the subject.

It is possible to use trial and error to find all solutions or the best solution, when a testably finite number of possible solutions exist. To find all solutions, one simply makes a note and continues, rather than ending the process, when a solution is found, until all solutions have been tried. To find the best solution, one finds all solutions by the method just described and then comparatively evaluates them based upon some predefined set of criteria, the existence of which is a condition for the possibility of finding a best solution. (Also, when only one solution can exist, as in assembling a jigsaw puzzle, then any solution found is the only solution and so is necessarily the best.)

Trial and error has traditionally been the main method of finding new drugs, such as antibiotics . Chemist s simply try chemicals at random until they find one with the desired effect. In a more sophisticated version, chemists select a narrow range of chemicals it is thought may have some effect using a technique called structure–activity relationship . (The latter case can be alternatively considered as a changing of the problem rather than of the solution strategy: instead of "What chemical will work well as an antibiotic?" the problem in the sophisticated approach is "Which, if any, of the chemicals in this narrow range will work well as an antibiotic?") The method is used widely in many disciplines, such as polymer technology to find new polymer types or families.

Trial and error is also commonly seen in player responses to video games - when faced with an obstacle or boss , players often form a number of strategies to surpass the obstacle or defeat the boss, with each strategy being carried out before the player either succeeds or quits the game.

Sports team s also make use of trial and error to qualify for and/or progress through the playoffs and win the championship , attempting different strategies, plays, lineups and formations in hopes of defeating each and every opponent along the way to victory. This is especially crucial in playoff series in which multiple wins are required to advance, where a team that loses a game will have the opportunity to try new tactics to find a way to win, if they are not eliminated yet.

The scientific method can be regarded as containing an element of trial and error in its formulation and testing of hypotheses. Also compare genetic algorithm s, simulated annealing and reinforcement learning – all varieties for search which apply the basic idea of trial and error.

Biological evolution can be considered as a form of trial and error. [6] Random mutations and sexual genetic variations can be viewed as trials and poor reproductive fitness, or lack of improved fitness, as the error. Thus after a long time 'knowledge' of well-adapted genomes accumulates simply by virtue of them being able to reproduce.

Bogosort , a conceptual sorting algorithm (that is extremely inefficient and impractical), can be viewed as a trial and error approach to sorting a list. However, typical simple examples of bogosort do not track which orders of the list have been tried and may try the same order any number of times, which violates one of the basic principles of trial and error. Trial and error is actually more efficient and practical than bogosort; unlike bogosort, it is guaranteed to halt in finite time on a finite list, and might even be a reasonable way to sort extremely short lists under some conditions.

Jumping spider s of the genus Portia use trial and error to find new tactics against unfamiliar prey or in unusual situations, and remember the new tactics. [7] Tests show that Portia fimbriata and Portia labiata can use trial and error in an artificial environment, where the spider's objective is to cross a miniature lagoon that is too wide for a simple jump, and must either jump then swim or only swim. [8] [9]

• Ariadne's thread (logic)
• Brute-force attack
• Brute-force search
• Dictionary attack
• Genetic algorithm
• Learning curve
• Margin of error
• Regula falsi

Further reading

• Ashby, W. R. (1960: Second Edition). Design for a Brain . Chapman & Hall: London.
• Traill, R.R. (1978–2006). Molecular explanation for intelligence… , Brunel University Thesis , HDL.handle.net
• Traill, R.R. (2008). Thinking by Molecule, Synapse, or both? — From Piaget’s Schema, to the Selecting/Editing of ncRNA . Ondwelle: Melbourne. Ondwelle.com — or French version Ondwelle.com.
• Zippelius, R. (1991). Die experimentierende Methode im Recht (Trial and error in Jurisprudence), Academy of Science, Mainz,

Notes and References

• Campbell . Donald T. . Blind variation and selective retention in creative thoughts as in other knowledge processes . Psychological Review . November 1960 . 67 . 6 . 380–400 . 10.1037/h0040373 . 13690223 . Campbell.
• Concise Oxford Dictionary p1489
• Thorpe W.H. The origins and rise of ethology. Hutchinson, London & Praeger, New York. p26.
• Thorndike E.L. 1898. Animal intelligence: an experimental study of the association processes in animals. Psychological Monographs #8.
• https://arxiv.org/abs/1205.1183 X. Bei, N. Chen, S. Zhang, On the Complexity of Trial and Error, STOC 2013
• Wright. Serwall. The roles of mutation, inbreeding, crossbreeding and selection in evolution . Proceedings of the Sixth International Congress on Genetics. 1932. 6. Volume 1. 365. 17 March 2014.
• Harland, D.P. . Jackson, R.R. . amp . 2000 . "Eight-legged cats" and how they see - a review of recent research on jumping spiders (Araneae: Salticidae) . Cimbebasia . 16 . 231–240 . 5 May 2011 . dead . https://web.archive.org/web/20060928164131/http://www.cogs.susx.ac.uk/ccnr/Papers/Downloads/Harland_Cimb2000.pdf . 28 September 2006.
• Jackson . Robert R. . Fiona R. Cross . Chris M. Carter . Geographic Variation in a Spider's Ability to Solve a Confinement Problem by Trial and Error . International Journal of Comparative Psychology . 2006 . 19 . 3 . 282–296 . 10.46867/IJCP.2006.19.03.06 . 8 June 2011. free.
• Jackson . Robert R. . Chris M. Carter . Michael S. Tarsitano . Trial-and-error solving of a confinement problem by a jumping spider, Portia fimbriata . Behaviour . 2001 . 138 . 10 . 1215–1234 . 4535886. Koninklijke Brill . Leiden. 0005-7959 . 10.1163/15685390152822184.

This article is licensed under the GNU Free Documentation License . It uses material from the Wikipedia article " Trial and error ".

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Solving Engineering Problems | Trial-And-Error vs Math

By Bruce Bartlett  5-28-2018

The job of an engineer is to solve problems. Bruce Bartlett looks at two approaches to solving engineering problems – math vs trial-and-error.

As engineers, our task is to create solutions that solve problems. For example, design a sound system to minimize feedback or determine the sonic effect of an object placed next to a microphone.

Two problem-solving methods are trial-and-error and prediction using mathematics. With trial-and-error, you come up with a solution intuitively, try it out, and see what happens. It’s cut-and-try. It’s repeated varied attempts that you continue until you reach success. Alternatively, you predict a result using math equations, or using the known properties of an object. Then test your prediction with real-world measurements.

Trial-and-error doesn’t necessarily produce the best result, but it’s often good enough.

Photo 1: Solving Engineering Problems – Trial and Error Method

The physical properties and geometry of objects create the mathematical laws of physics. Sometimes, using trial-and-error methods we can let the laws of physics do the heavy lifting of complex math to produce a desired result. In other words, reality produces the same result that you would get with the correct math equations.

With trial and error, you do an experiment – change one variable in a system – and measure the results. Instead of using math to calculate and predict the results of that experiment, you let nature’s laws “calculate” or form the result as an analog computer would. Nature “does the math” perfectly when it produces a result of an experiment.

Sometimes nature is too complex mathematically for us to predict a result using our limited knowledge of what’s going on physically. For example, how does a small object or an open slit next to a mic capsule affect its frequency response? If you tried to predict it with math, you’d need to know about fluid dynamics, geometry, the exact shape of the bump or slit, resonance, effect of obstacles of various shapes on sound waves (diffraction), etc.

But if you just create an object or slit, and measure the result (the delta or change in frequency response), nature “worked out the math” for you, effortlessly and precisely. Sometimes, cut-and-try gives usable results much faster than calculations.

If you want, you could come up with equations and try to match them to the data that nature has already “calculated” for you.

An Empirical Approach

Here’s an example. Suppose you have a P.A. system, and you want to create the loudest sound without feedback. You place a mic and speaker in certain locations relative to the sound source. You turn up the volume until feedback just starts. Then change one variable. For example, increase the distance of the loudspeaker from the mic. If the feedback stops, you can turn up the volume a little until feedback just starts again. From what you just learned, you can write an equation: Loudness before feedback is proportional to the distance from speaker to mic.

SPL is loudness, X is an unknown constant or variable, and D1 is the distance from speaker to mic.

Then you change another variable and see what happens. You move the mic closer to the sound source. The loudness of the sound system increases without causing feedback. So you make another equation:

L is loudness, X is an unknown constant or variable, and Ds is the distance from mic to source.

Combining those two equations, you get SPL ∝ D1*X/Ds. You are starting to make an equation that predicts gain-before-feedback.

Now you change another variable. You move the loudspeaker closer to the listener. The sound system gets louder at the listener without causing feedback. As a mathematical expression, you might say

where SPL is loudness, X is an unknown constant or variable, and D2 is the distance from loudspeaker to listener.

Combining those three equations, you get

SPL ∝ D1*X/(Ds*D2)

Our equation to predict gain-before-feedback is becoming more complete. It tells you this: if you want to increase loudness, then increase the distance from the speaker to the mic, decrease the mic-to-source distance, and decrease the speaker-to-listener distance. In other words, place the speaker far from the mic, place the mic close to the source, and place the speaker close to the audience.

Photo 2: Solving Engineering Problems – Using Math

X in that equation could be other variables such as as the frequency response and sensitivity of the mic in the direction of the speaker, the response and sensitivity of the speaker in the direction of the mic, the microphone polar pattern, the speaker polar pattern, the liveness of the room, the loudness of the sound source, etc.

X could also be an equation itself. We could start with the inverse square law relating SPL to distance, and derive our feedback equation from there.

Reality doesn’t follow equations. It just responds to circumstances in the only way it can. Humans write equations that describe how reality deals with circumstances, and we call those equations “laws of physics.” A law says, X always occurs when Y conditions exist.

A Direct Engineering Solution

Sometimes calculations are more efficient than trial-and-error. Suppose you want to send a rocket around the moon and back to earth. You could launch several rockets of various sizes and thrust, and pick one that did the job. But that’s very expensive and slow. Instead, you can work out the math first, design a rocket and set the thrust duration and vector to match that math, then launch the rocket and hope for the best. If your math modeled reality accurately, you can launch a rocket designed around that math and it will actually go around the moon and back.

In much of our engineering work, we combine the two methods to make educated guesses. Or we design a system using math, try it out in the real world, and adjust for the differences between theory and experience. Whatever works. :>) bb

Photo 3: Science doodles on paper with 3d fountain pen.

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Chapter 7: Thinking and Intelligence

Problem solving, learning objectives.

By the end of this section, you will be able to:

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving

People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

PROBLEM-SOLVING STRATEGIES

When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them ( [link] ). For example, a well-known strategy is trial and error . The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below ( [link] ) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

Here is another popular type of puzzle ( [link] ) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

Take a look at the “Puzzling Scales” logic puzzle below ( [link] ). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

PITFALLS TO PROBLEM SOLVING

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

Link to Learning

Check out this Apollo 13 scene where the group of NASA engineers are given the task of overcoming functional fixedness.

Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in [link] .

Please visit this site to see a clever music video that a high school teacher made to explain these and other cognitive biases to his AP psychology students.

Were you able to determine how many marbles are needed to balance the scales in [link] ? You need nine. Were you able to solve the problems in [link] and [link] ? Here are the answers ( [link] ).

Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

Self Check Questions

Critical thinking questions.

1. What is functional fixedness and how can overcoming it help you solve problems?

2. How does an algorithm save you time and energy when solving a problem?

Personal Application Question

3. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

1. Functional fixedness occurs when you cannot see a use for an object other than the use for which it was intended. For example, if you need something to hold up a tarp in the rain, but only have a pitchfork, you must overcome your expectation that a pitchfork can only be used for garden chores before you realize that you could stick it in the ground and drape the tarp on top of it to hold it up.

2. An algorithm is a proven formula for achieving a desired outcome. It saves time because if you follow it exactly, you will solve the problem without having to figure out how to solve the problem. It is a bit like not reinventing the wheel.

• Psychology. Authored by : OpenStax College. Located at : http://cnx.org/contents/[email protected]:1/Psychology . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/content/col11629/latest/.

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Trial and Error

Trial and error, or trial by error, is a general method of problem solving, fixing things, or for obtaining knowledge. “Learning doesn’t happen from failure itself but rather from analyzing the failure, making a change, and then trying again.” In the field of computer science, the method is called generate and test. In elementary algebra, when solving equations, it is “guess and check”.

This approach can be seen as one of the two basic approaches to problem solving and is contrasted with an approach using insight and theory. However, there are intermediate methods which for example, use theory to guide the method, an approach known as guided empiricism.

Methodology

This approach is more successful with simple problems and in games, and is often resorted to when no apparent rule applies. This does not mean that the approach need be careless, for an individual can be methodical in manipulating the variables in an attempt to sort through possibilities that may result in success. Nevertheless, this method is often used by people who have little knowledge in the problem area.

Simplest applications

Ashby (1960, section 11/5) offers three simple strategies for dealing with the same basic exercise-problem; and they have very different efficiencies: Suppose there are 1000 on/off switches which have to be set to a particular combination by random-based testing, each test to take one second. [This is also discussed in Traill (1978/2006, section C1.2]. The strategies are:

• the perfectionist all-or-nothing method, with no attempt at holding partial successes. This would be expected to take more than 10^301 seconds, [i.e. 2^1000 seconds, or 3·5×(10^291) centuries!];
• a serial-test of switches, holding on to the partial successes (assuming that these are manifest) would take 500 seconds; while
• a parallel-but-individual testing of all switches simultaneously would take only one second.

Note the tacit assumption here that no intelligence or insight is brought to bear on the problem. However, the existence of different available strategies allows us to consider a separate (“superior”) domain of processing — a “meta-level” above the mechanics of switch handling — where the various available strategies can be randomly chosen. Once again this is “trial and error”, but of a different type. This leads us to:

Trial-and-error Hierarchies

Ashby’s book develops this “meta-level” idea, and extends it into a whole recursive sequence of levels, successively above each other in a systematic hierarchy. On this basis he argues that human intelligence emerges from such organization: relying heavily on trial-and-error (at least initially at each new stage), but emerging with what we would call “intelligence” at the end of it all. Thus presumably the topmost level of the hierarchy (at any stage) will still depend on simple trial-and-error.

Traill (1978/2006) suggests that this Ashby-hierarchy probably coincides with Piaget’s well-known theory of developmental stages. [This work also discusses Ashby’s 1000-switch example; see §C1.2]. After all, it is part of Piagetian doctrine that children learn by first actively doing in a more-or-less random way, and then hopefully learn from the consequences — which all has a certain to Ashby’s random “trial-and-error”.

The basic strategy in many fields?

Traill (2008, espec. Table “S” on p.31) follows Jerne and Popper in seeing this strategy as probably underlying all knowledge-gathering systems — at least in their initial phase.

Four such systems are identified:

• Darwinian evolution which “educates” the DNA of the species,
• The brain of the individual (just discussed);
• The “brain” of society-as-such (including the publicly-held body of science); and
• The immune system.

An ambiguity: Can we have “intention” during a “trial”

In the Ashby-and-Cybernetics tradition, the word “trial” usually implies random-or-arbitrary, without any deliberate choice. However amongst non-cyberneticians, “trial” will often imply a deliberate subjective act by some adult human agent; (e.g. in a court-room, or laboratory). So that has sometimes led to confusion.

Of course the situation becomes even more confusing if one accepts Ashby’s hierarchical explanation of intelligence, and its implied ability to be deliberate and to creatively design — all based ultimately on non-deliberate actions. The lesson here seems to be that one must simply be careful to clarify the meaning of one’s own words, and indeed the words of others. [Incidentally it seems that consciousness is not an essential ingredient for intelligence as discussed above.

Trial and error has a number of features:

• solution-oriented: trial and error makes no attempt to discover why a solution works, merely that it is a solution.
• problem-specific: trial and error makes no attempt to generalise a solution to other problems.
• non-optimal: trial and error is generally an attempt to find a solution, not all solutions, and not the best solution.
• needs little knowledge: trials and error can proceed where there is little or no knowledge of the subject.

It is possible to use trial and error to find all solutions or the best solution, when a testably finite number of possible solutions exist. To find all solutions, one simply makes a note and continues, rather than ending the process, when a solution is found, until all solutions have been tried. To find the best solution, one finds all solutions by the method just described and then comparatively evaluates them based upon some predefined set of criteria, the existence of which is a condition for the possibility of finding a best solution. (Also, when only one solution can exist, as in assembling a jigsaw puzzle, then any solution found is the only solution and so is necessarily the best.)

Trial and error has traditionally been the main method of finding new drugs, such as antibiotics. Chemists simply try chemicals at random until they find one with the desired effect. In a more sophisticated version, chemists select a narrow range of chemicals it is thought may have some effect using a technique called structure-activity relationship. (The latter case can be alternatively considered as a changing of the problem rather than of the solution strategy: instead of “What chemical will work well as an antibiotic?” the problem in the sophisticated approach is “Which, if any, of the chemicals in this narrow range will work well as an antibiotic?”) The method is used widely in many disciplines, such as polymer technology to find new polymer types or families.

The scientific method can be regarded as containing an element of trial and error in its formulation and testing of hypotheses. Also compare genetic algorithms, simulated annealing and reinforcement learning – all varieties for search which apply the basic idea of trial and error.

Biological evolution is also a form of trial and error. Random mutations and sexual genetic variations can be viewed as trials and poor reproductive fitness, or lack of improved fitness, as the error. Thus after a long time ‘knowledge’ of well-adapted genomes accumulates simply by virtue of them being able to reproduce.

Bogosort, a conceptual sorting algorithm (that is extremely inefficient and impractical), can be viewed as a trial and error approach to sorting a list. However, typical simple examples of bogosort do not track which orders of the list have been tried and may try the same order any number of times, which violates one of the basic principles of trial and error. Trial and error is actually more efficient and practical than bogosort; unlike bogosort, it is guaranteed to halt in finite time on a finite list, and might even be a reasonable way to sort extremely short lists under some conditions.

Jumping spiders of the genus Portia use trial and error to find new tactics against unfamiliar prey or in unusual situations, and remember the new tactics. Tests show that Portia fimbriata and Portia labiata can use trial and error in an artificial environment, where the spider’s objective is to cross a miniature lagoon that is too wide for a simple jump, and must either jump then swim or only swim.

Issues with trial and error

Trial and error is usually a last resort for a particular problem, as there are a number of problems with it. For one, trial and error is tedious and monotonous. Also, it is very time-consuming; chemical engineers must sift through millions of various potential chemicals before they find one that works. There is also an element of risk, in that if a certain attempt at a solution is extremely erroneous, it can produce disastrous results that may or may not be repairable. Fortunately, computers are best suited for trial and error; they do not succumb to the boredom that humans do, can test physical challenges in a virtual environment where they will not do harm, and can potentially do thousands of trial-and-error segments in the blink of an eye.