trial and error problem solving in c

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.

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.


Method	Description	Example
Trial and error	Continue trying different solutions until problem is solved	Restarting phone, turning off WiFi, turning off bluetooth in order to determine why your phone is malfunctioning
Algorithm	Step-by-step problem-solving formula	Instruction manual for installing new software on your computer
Heuristic	General problem-solving framework	Working backwards; breaking a task into steps

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.).

A puzzle involving a scale is shown. At the top of the figure it reads: “Sam Loyds Puzzling Scales.” The first row of the puzzle shows a balanced scale with 3 blocks and a top on the left and 12 marbles on the right. Below this row it reads: “Since the scales now balance.” The next row of the puzzle shows a balanced scale with just the top on the left, and 1 block and 8 marbles on the right. Below this row it reads: “And balance when arranged this way.” The third row shows an unbalanced scale with the top on the left side, which is much lower than the right side. The right side is empty. Below this row it reads: “Then how many marbles will it require to balance with that top?”

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.


Bias	Description
Anchoring	Tendency to focus on one particular piece of information when making decisions or problem-solving
Confirmation	Focuses on information that confirms existing beliefs
Hindsight	Belief that the event just experienced was predictable
Representative	Unintentional stereotyping of someone or something
Availability	Decision is based upon either an available precedent or an example that may be faulty

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.

The first puzzle is a Sudoku grid of 16 squares (4 rows of 4 squares) is shown. Half of the numbers were supplied to start the puzzle and are colored blue, and half have been filled in as the puzzle’s solution and are colored red. The numbers in each row of the grid, left to right, are as follows. Row 1: blue 3, red 1, red 4, blue 2. Row 2: red 2, blue 4, blue 1, red 3. Row 3: red 1, blue 3, blue 2, red 4. Row 4: blue 4, red 2, red 3, blue 1.The second puzzle consists of 9 dots arranged in 3 rows of 3 inside of a square. The solution, four straight lines made without lifting the pencil, is shown in a red line with arrows indicating the direction of movement. In order to solve the puzzle, the lines must extend beyond the borders of the box. The four connecting lines are drawn as follows. Line 1 begins at the top left dot, proceeds through the middle and right dots of the top row, and extends to the right beyond the border of the square. Line 2 extends from the end of line 1, through the right dot of the horizontally centered row, through the middle dot of the bottom row, and beyond the square’s border ending in the space beneath the left dot of the bottom row. Line 3 extends from the end of line 2 upwards through the left dots of the bottom, middle, and top rows. Line 4 extends from the end of line 3 through the middle dot in the middle row and ends at the right dot of the bottom row.

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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Introduction

Characteristics and process

Applications.

When did science begin?
Where was science invented?

Blackboard inscribed with scientific formulas and calculations in physics and mathematics

means-ends analysis

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Table Of Contents

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.

Trial and Error Algorithms

Living reference work entry
First Online: 01 January 2015
Cite this living reference work entry

Xiaohui Bei 2 ,
Ning Chen 3 &
Shengyu Zhang 4

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Years and Authors of Summarized Original Work

2013(1); Bei, Chen, Zhang

2013(2); Bei, Chen, Zhang

Problem Definition

This problem investigates the effect of the lack of input information on computational hardness. The central question under investigation is the following:

How much extra difficulty is introduced due to the lack of input knowledge?

We explore this question by studying search problems. Suppose that on an input instance x , there is a set S ( x ) of solutions . A search problem is to find a solution s ∈ S ( x ) for the input x . More specifically, we consider the fairly broad class of Constraint Satisfaction Problems (CSPs): Suppose that there is an input space {0, 1} n and a space Ω = { 0, 1} m of candidate solutions. The problem is defined by a number of constraints C 1 , C 2 , … , C m (, … ), where each $C_{i} :\{ 0,1\}^{n+m} \rightarrow \{ 0,1\}$ is a 0-1 function on the input and solution variables. The valid solutions for input x are defined as those s that satisfy all...

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Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

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The Chinese University of Hong Kong, Hong Kong, China

Shengyu Zhang

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Dept. Electrical Engineering & Computer Science, Northwestern University, Evanston, Illinois, USA

Ming-Yang Kao

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Bei, X., Chen, N., Zhang, S. (2015). Trial and Error Algorithms. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27848-8_789-1

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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 and decision making

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 ( Table 7.2 ). 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.

Method	Description	Example
Trial and error	Continue trying different solutions until problem is solved	Restarting phone, turning off WiFi, turning off bluetooth in order to determine why your phone is malfunctioning
Algorithm	Step-by-step problem-solving formula	Instructional video for installing new software on your computer
Heuristic	General problem-solving framework	Working backwards; breaking a task into steps

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

Everyday Connection

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 ( Figure 7.7 ) 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 ( Figure 7.8 ) 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 ( Figure 7.9 ). 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? 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 they just need 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. Duncker (1945) conducted foundational research on functional fixedness. He created an experiment in which participants were given a candle, a book of matches, and a box of thumbtacks. They were instructed to use those items to attach the candle to the wall so that it did not drip wax onto the table below. Participants had to use functional fixedness to overcome the problem ( Figure 7.10 ). 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 about NASA engineers overcoming functional fixedness to learn more.

Bias	Description
Anchoring	Tendency to focus on one particular piece of information when making decisions or problem-solving
Confirmation	Focuses on information that confirms existing beliefs
Hindsight	Belief that the event just experienced was predictable
Representative	Unintentional stereotyping of someone or something
Availability	Decision is based upon either an available precedent or an example that may be faulty

Watch this teacher-made music video about cognitive biases to learn more.

Were you able to determine how many marbles are needed to balance the scales in Figure 7.9 ? You need nine. Were you able to solve the problems in Figure 7.7 and Figure 7.8 ? Here are the answers ( Figure 7.11 ).

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Is trial and error a bad problem solving method?

I have created a statement for Bee language that is a little bit unusual. It is called trial - error block. I will appreciate some thoughts about it. I think it is very powerful but I wander why most languages do not have it.

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.

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Everything Explained.Today
A-Z Contents
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.

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

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 ".

Trial and Error at a Glance

We already know how to factor quadratic polynomials that are the result of multiplying a sum and difference, or the result of squaring a binomial with degree 1. Once in a while, though, trinomials go through mood swings and stop cooperating, and then we have a bit more begging and pleading to do. What do we do in those instances? One method is to try trial and error.

Sounds like something your teacher would advise you not to do, but if you've got a talent for seeing patterns, you like guessing games, you’ve done all your homework and have a lot of time on your hands, or you’re just not a rule follower, this is the method for you. If none of this trial-and-erroring can get a quadratic polynomial out of its bad mood, about all there is left to do is take it for ice cream and then put it down for a nap. Hopefully it won't be quite so pouty when it wakes up.

Remember that a quadratic polynomial is a polynomial of degree 2 of the form ax 2 + bx + c .

These polynomials are easiest to factor when a = 1 (that is, the polynomial looks like x 2 + bx + c ), so we'll look at that case first. Those of you who like torturing yourselves can skip ahead to the harder stuff.

Before we start factoring, we'll revisit multiplication. Assume m and n are integers. You're not being presumptuous—they are integers, we swear. If we multiply:

( x + m )( x + n )

...then we find:

x 2 + mx + nx + mn

...which simplifies to:

x 2 + ( m + n ) x + mn

The numbers m and n multiply to give us the constant term in the final polynomial, and the sum of m and n is the coefficient of x in the final polynomial. Neither m nor n make an appearance alongside the first term in the final polynomial, which is probably just as well, since that x appears to be busy squaring itself.

Let's see how this can be used for factoring by looking at some examples.

Sample Problem

Factor the polynomial x 2 + 4 x + 3.

To get a trinomial with an x 2 term, we must have multiplied two binomials, each with an " x " term. Wow...it's like we're psychic. By the way, you shouldn't leave your house tomorrow. Don't ask questions.

The original binomials must have looked like this:

...where m and n are integers. We need to figure out the values of m and n . The constant term of the original polynomial is 3, so we need mn = 3.

What integers multiply together to give 3? The only choices are 1 and 3, or maybe -1 and -3.

If you can think of any others, congratulations! However, you're wrong. Gee, that victory was short-lived.

The coefficient of the x term in the original polynomial is 4, so we also need m + n = 4.

Since 1 and 3 multiply to give 3 and add together to give 4, we have m = 1 and n = 3. Therefore, we can factor our original polynomial like this:

x 2 + 4 x + 3 = ( x + 1)( x + 3)

If we let m = 3 and n = 1 we'll have the same factorization, except with the factors written in a different order. Either way is correct, so we won't fight about it. We can all take turns equaling 3.

Factor the polynomial x 2 + 4 x – 5.

We can factor this quadratic polynomial into two binomials of the form:

We need to have mn = -5. The integers that multiply to give -5 are -1 and 5, or 1 and -5.

We also need to have m + n = 4, which will limit our options. Not necessarily a bad thing when you're searching for the right answer. The correct choices for m and n are -1 and 5, and the polynomial factors are:

( x – 1)( x + 5)

Now that we've gotten some practice with the friendlier varieties of quadratic polynomials, we'll look at general polynomials of the form ax 2 + bx + c when a doesn't equal 1.

These guys are of the un friendly variety. Don't make them angry. You wouldn't like them when they're angry.

Here's another quick visit to multiplication before we start factoring. The binomials (2 x + 3) and ( x + 5) multiply to give us:

2 x 2 + 13 x + 15

The coefficient on the x 2 term is the product of 2 and 1, the coefficients of x in each of the binomials:

( 2 x + 3)( x + 5) = 2 x 2 + 13 x + 15

The constant term in the product is 3 × 5, the product of the constant terms in the binomials:

(2 x + 3 )( x + 5 ) = 2 x 2 + 13 x + 3 x + 15

The middle term, 13 x , is a bit of a mess, but we can make sense of it. Thinking of distribution, 13 x comes from multiplying the outer terms:

( 2 x + 3)( x + 5 ) = 2 x 2 + 10 x + 3 x + 15

...multiplying the inner terms:

(2 x + 3 )( x + 5) = 2 x 2 + 10 x + 3 x + 15

...and simplifying (adding the 10 x and 3 x together). If we're not greatly mistaken, 10 + 3 = 13. Voila.

Factoring quadratic polynomials involves a bit of trial and error. The more you practice factoring, the less error you'll run into, because you'll learn to see which trials will work without having to write down all the steps. It's like trying to teach yourself to play the piano. You can bang away randomly at the keys for a while, but eventually you'll develop a feel for what note each key is responsible for and your guesswork will become minimized. Hopefully the quadratic polynomials you'll be working on are more "Chopsticks" and less "Flight of the Bumblebee."

Factor the polynomial 3 x 2 – 2 x – 1.

If the polynomial factors into two binomials, they'll be of the form:

( ax + b )( cx + d )

We need the first numbers in each binomial to have a product of 3, so that means ac = 3. We also need the second numbers in each binomial to have a product of -1, so that means bd = -1. The only possibilities for a and c are 3 and 1, since 3 is prime. The last numbers b and d must be 1 and -1 in order for their product to be -1. With a problem like this, we don't even need to worry about using trial and error. It's more like trial and instant success.

The only question we have left is whether the answer is (3 x – 1)( x + 1) or (3 x + 1)( x – 1).

It's tempting to use "eenie-meenie-miney-mo," but resist the urge. To determine which binomials are the correct factors, we need to figure out which ones will produce the correct x coefficient of -2. When we multiply (3 x – 1)( x + 1), here's what we get:

(3 x – 1)( x + 1) = 3 x 2 + 2 x – 1

Well, poop. We want -2 x in the middle, not 2 x . Let's try our other option.

(3 x + 1)( x – 1) = 3 x 2 – 2 x – 1

Ah, that's more like it. Consider this puppy factored.

The more you practice factoring, the easier it'll become, and eventually you won't need to keep getting up to sharpen your pencil. In any given example, we can list every single possible factorization...or just the right one. Depends on how long it takes you to find what you're looking for. As long you have the right answer, no one will care if you checked all the possible factorizations. Unless the "All Possible Factorization Monster" truly does exist, but we doubt it. The evidence is shoddy at best.

Factor the polynomial -2 x 2 + 7 x – 3.

If this polynomial factors as ( ax + b )( cx + d ), the product of a and c must be -2, and the product of b and d must be -3.

So a and c could be -2 and 1, or 2 and -1.

And b and d could be -3 and 1, or 3 and -1.

We'll try all the possible factorizations and see which one works. In this case, there are a LOT of possibilities. In fact, it will benefit us to use some factorization organization.

(-2 – 3)( + 1) = -2 – 5 – 3

(-2 + 1)( – 3) = -2 + 7 – 3

(2 – 3)(- + 1) = -2 + 5 – 3

(2 + 1)(- – 3) = -2 – 7 – 3

(-2 + 3)( – 1) = -2 + 5 – 3

(-2 – 1)( + 3) = -2 – 7 – 3

(2 + 3)(- – 1) = -2 – 5 – 3

(2 – 1)(- + 3) = -2 + 7 – 3

From this table, we see that two different factorizations can give us a middle term of 7 x . What's going on here? What sorcery is this? Okay, let's not be overly dramatic. The fact is that either of these factorizations will work. Watch. We can rewrite (-2 x + 1)( x – 3) by factoring out -1 from the first factor to get:

(-1)(2 x – 1)( x – 3)

Then we can distribute that (-1) back into the second factor to find:

(2 x – 1)(- x + 3)

Either factorization is fine as a final answer. We didn't actually need to check all the possible factorizations, but it's easier to check them all than it is to figure out which ones we could safely ignore. Now we know exactly which ones to give the silent treatment to.

Don't worry if trial and error seems a little messy to you. If you like things a bit more clean and organized and all this guessing-and-checking drives you up the wall, we've got another method that works just as well. Read on.

We sort of gave away the answer with the wording of this problem. Oops. We have a problem with that. If you haven't seen , you should steer clear of us. We will blow the ending for you.

It isn't possible to factor this polynomial, but why not? If we could factor the polynomial as ( + )( + ), we would need = 9 and + = 8.

There aren't two integers that multiply together to give 9 and add together to give 8. We tried everything; we even took out an ad in the paper, but no luck: 1 and 9 don't work; 3 and 3 don't work; -1 and -9 don't work; -3 and -3 don't work. There aren't any pairs of numbers left to try that multiply to give 9, so we can't factor the polynomial. Now we're out $25 for that ad.

This polynomial isn't quadratic. However, all the terms have a common factor of 2 . Let's take that out and see what happens. First:

(2 )( – 4 + 3)

The second factor quadratic. Can we factor it further? We need two numbers whose product is 3 and whose sum is -4. Hey, we happen to know the two numbers that will fit the bill: -3 and -1 work, so we can factor the original polynomial like so:

(2 )( – 3)( – 1)

Remember, you can always check your answer to a factoring problem by multiplying out the factors. The product of the factors should be the original polynomial. If it isn't, you've gone wrong somewhere. Maybe you took a wrong turn at Algebraquerque.

Factor x 2 + 7 x – 8.

Find two numbers that multiply to -8 and add to 7.

( x – 1)( x + 8)

Factor x 2 + 9 x + 20.

The product of the numbers we factor with needs to be 20 and the sum needs to be 9.

( x + 5)( x + 4)

Factor x 2 – 5 x – 6.

The numbers need to multiply to -6 and add to -5. You could try to use 2 and 3, but we're telling you, it's not gonna work.

( x – 6)( x + 1)

Factor 3 x 2 – 3 x – 36.

Pull out a GCF first. Then factor what’s left. Just don’t forget about it at the end of the problem.

3( x + 3)( x – 4)

Factor 4 x 3 + 44 x 2 + 120 x .

Pull out a GCF first. Look for a number and variable combo that's common to all terms.

4 x ( x + 5)( x + 6)

Factor x 2 + 5 x + 4.

What numbers multiply to 4 and add to 5? They'll probably be important at some point here.

( x + 4)( x + 1)

Factor 2 x 2 + 13 x + 15.

The coefficients on the x terms have to multiply to 2 x 2 , while the constants have to multiply to 15.

( x + 5)(2 x + 3)

Factor 3 x 2 + 3 x – 18.

Pull out a GCF first. Just don’t lose it while you’re factoring the rest of the expression.

3( x – 2)( x + 3)

Factor -6 x 2 + 5 x – 1.

The coefficients on the x terms have to multiply to -6 x 2 and the constants have to multiply to -1.

(2 x – 1)(-3 x + 1)

Exercise 10

Factor 40 x 2 – 46 x + 12.

Pull out a GCF first. That would be a 2. Then factor what’s left. For the coefficients on the x terms, might we suggest a 4 and a 5?

2(4 x – 3)(5 x – 2)

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W hy's T his F unny?

Advantages and Disadvantages of Solving a Problem Through Trial and Error

Back to: Learning and Teaching – Unit 2

Introduction

E.L. Thorndike propounded the theory of trial and error. He believes that behavior is the result of a response to a stimulus. According to him, learning is associated with responses, impressions, and a sense of action. Thorndike’s views are often referred to as connectionism as it believes in the connection of stimulus and response. Thorndike referred to it as connecting and selecting or trial and error theory since learning results from repetition. Thorndike proposed three laws of learning namely, the law of readiness, the law of effect, and the law of exercise.

The disadvantages of solving a problem through the trial and error method are as follows:

Creative Approach

Trial and error is considered to be a creative approach for solving tasks because it makes individuals use both the right and left hemispheres of their brain.

Less Time Consuming

The trial and method consume less time to solve tasks that do not have a great depth of difficulty.

Division of Tasks

The trial and error method involves the division of tasks which makes it possible for individuals to search for a quick solution.

Allows one to Learn

It is not possible to get everything right on the first try due to trial and error is a good method to encourage learning.

Mistakes are Allowed

In the trial and error theory, mistakes are a part of learning. When people make errors, they can reflect on them and make changes to get better.

Disadvantages

Consumes a lot of energy.

The trial and error method can be a bit energy-consuming since it uses a lot of energy due to which it can limit the quantity of learning.

Emphasizes Rote Learning

The theory includes the use of repetition and therefore, encourages rote learning.

Ineffective for Bright Learners

Learners who do not focus on rote memorization and learn things quickly may find this method ineffective.

Ineffective for Higher Classes

The theory fails to provide adequate guidance for learners belonging to higher classes.

Losing Popularity

The trial and error method has been losing popularity in the modern age due to which its use might not be relevant in the future.

The trial and error method has various benefits for solving tasks but there are certain limitations that impact its prevalence.

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

PROBLEM-SOLVING STRATEGIES

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.

Problem-Solving Strategies
Method	Description	Example
Trial and error	Continue trying different solutions until problem is solved	Restarting phone, turning off WiFi, turning off bluetooth in order to determine why your phone is malfunctioning
Algorithm	Step-by-step problem-solving formula	Instruction manual for installing new software on your computer
Heuristic	General problem-solving framework	Working backwards; breaking a task into steps

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

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.

A four column by four row Sudoku puzzle is shown. The top left cell contains the number 3. The top right cell contains the number 2. The bottom right cell contains the number 1. The bottom left cell contains the number 4. The cell at the intersection of the second row and the second column contains the number 4. The cell to the right of that contains the number 1. The cell below the cell containing the number 1 contains the number 2. The cell to the left of the cell containing the number 2 contains the number 3.

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:

A square shaped outline contains three rows and three columns of dots with equal space between them.

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

Link to Learning

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

Summary of Decision Biases
Bias	Description
Anchoring	Tendency to focus on one particular piece of information when making decisions or problem-solving
Confirmation	Focuses on information that confirms existing beliefs
Hindsight	Belief that the event just experienced was predictable
Representative	Unintentional stereotyping of someone or something
Availability	Decision is based upon either an available precedent or an example that may be faulty

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] ).

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/.

A person using a laptop, presumably learning what C R M is

What is CRM?

Manage, track, and store information related to potential customers using a centralized, data-driven software solution.

Defining CRM

Customer relationship management (CRM) is a set of integrated, data-driven software solutions that help manage, track, and store information related to your company’s current and potential customers. By keeping this information in a centralized system, business teams have access to the insights they need, the moment they need them.

Without the support of an integrated CRM solution, your company may miss growth opportunities and lose potential revenue because it’s not optimizing operating processes or making the most of customer relationships and sales leads.

What does a CRM do?

Not too long ago, companies tracked customer-related data with spreadsheets, email, address books, and other siloed, often paper-based CRM solutions. A lack of integration and automation prevented people within and across teams from quickly finding and sharing up-to-date information, slowing their ability to create marketing campaigns, pursue new sales leads, and service customers.

Fast forward to today. CRM systems automatically collect a wealth of information about existing and prospective customers. This data includes email addresses, phone numbers, company websites, social media posts, purchase histories, and service and support tickets. The system next integrates the data and generates consolidated profiles to be shared with appropriate teams.

CRM systems also connect with other business tools, including online chat and document sharing apps. In addition, they have built-in business intelligence and artificial intelligence (AI) capabilities that accelerate administrative tasks and provide actionable insights.

In other words, modern CRM tools give sales, marketing, commerce, field service, and customer service teams immediate visibility into—and access to—everything crucial to developing, improving, and retaining customer relationships.

Some ways you can use CRM capabilities to benefit your company are to:

Monitor each opportunity through the sales funnel for better sales. CRM solutions help track lead-related data, accompanied with insights, so sales and marketing teams can stay organized, understand where each lead is in the sales process, and know who has worked on each opportunity.
Use sales monitoring to get real-time performance data. Link sales data into your CRM solution to provide an immediate, accurate picture of sales. With a real-time view of your pipeline, you’ll be aware of any slowdowns and bottlenecks—or if your team won a major deal.
Plan your next step with insight generation. Focus on what matters most using AI and built-in intelligence to identify the top priorities and how your team can make the most of their time and efforts. For example, sales teams can identify which leads are ready to hand off and which need follow-up.
Optimize workflows with automation. Build sales quotes, gather customer feedback, and send email campaigns with task automation, which helps streamline marketing, sales, and customer service. Thus, helping eliminate repetitive tasks so your team can focus on high-impact activities.
Track customer interactions for greater impact. CRM solutions include features that tap into customer behavior and surface opportunities for optimization to help you better understand engagement across various customer touchpoints.
Connect across multiple platforms for superior customer engagement. Whether through live chat, calls, email, or social interactions, CRM solutions help you connect with customers where they are, helping build the trust and loyalty that keeps your customers coming back.
Grow with agility and gain a competitive advantage. A scalable, integrated CRM solution built on a security-rich platform helps meet the ever-changing needs of your business and the marketplace. Quickly launch new marketing, e-commerce, and other initiatives and deliver rapid responses to consumer demands and marketplace conditions.

Why implement a CRM solution?

As you define your CRM strategy and evaluate customer relationship management solutions , look for one that provides a complete view of each customer relationship. You also need a solution that collects relevant data at every customer touchpoint, analyzes it, and surfaces the insights intelligently.

Learn how to choose the right CRM for your needs in The CRM Buyer’s Guide for Today’s Business . With the right CRM system, your company helps enhance communications and ensure excellent experiences at each stage of the customer journey, as outlined below:

Identify and engage the right customers. Predictive insight and data-driven buyer behavior helps you learn how to identify, target, and attract the right leads—and then turn them into customers.
Improve customer interaction. With a complete view of the customer, every member of the sales team will know a customer’s history, purchasing patterns, and any specific data that’ll help your team provide the most attentive service to each individual customer.
Track progress across the customer journey. Knowing where a customer is in your overall sales lifecycle helps you target campaigns and opportunities for the highest engagement.
Increase team productivity. Improved visibility and streamlined processes help increase productivity, helping your team focus on what matters most.

How can a CRM help your company?

Companies of all sizes benefit from CRM software. For small businesses seeking to grow, CRM helps automate business processes, freeing employees to focus on higher-value activities. For enterprises, CRM helps simplify and improve even the most complex customer engagements.

Take a closer look at how a CRM system helps benefit your individual business teams.

Marketing teams

Improve your customers’ journey. With the ability to generate multichannel marketing campaigns, nurture sales-ready leads with targeted buyer experiences, and align your teams with planning and real-time tracking tools, you’re able to present curated marketing strategies that’ll resonate with your customers.

As you gain insights into your brand reputation and market through customized dashboards of data analysis, you’re able to prioritize the leads that matter most to your business and adapt quickly with insights and business decisions fueled by the results of targeted, automated processes.

Sales teams

Empower sellers to engage with customers to truly understand their needs, and effectively win more deals. As the business grows, finding the right prospects and customers with targeted sales strategies becomes easier, resulting in a successful plan of action for the next step in your pipeline.

Building a smarter selling strategy with embedded insights helps foster relationships, boost productivity, accelerate sales performances, and innovate with a modern and adaptable platform. And by using AI capabilities that can measure past and present leading indicators, you can track customer relationships from start to finish and automate sales execution with contextual prompts that delivers a personalized experience and aligns with the buyer’s journey anytime, anywhere.

Customer service teams

Provide customers with an effortless omnichannel experience. With the use of service bots, your customer service teams will have the tools to be able to deliver value and improve engagement with every interaction. Offering personalized services, agents can upsell or cross-sell using relevant, contextual data, and based on feedback, surveys, and social listening, optimize their resources based on real-time service trends.

In delivering a guided, intelligent service supported on all channels, customers can connect with agents easily and quickly resolve their issues, resulting in a first-class customer experience.

Field service teams

Empower your agents to create a better in-person experience. By implementing the Internet of Things (IoT) into your operations, you’re able to detect problems faster—automate work orders, schedule, and dispatch technicians in just a few clicks. By streamlining scheduling and inventory management , you can boost onsite efficiency, deliver a more personalized service, and reduce costs.

By providing transparent communications with real-time technician location tracking, appointment reminders, quotes, contracts, and scheduling information, customers stay connected to your field agents and build trust with your business.

Project service automation teams

Improve your profitability with integrated planning tools and analytics that help build your customer-centric delivery model. By gaining transparency into costs and revenue using robust project planning capabilities and intuitive dashboards, you’re able to anticipate demands, determine resources capacity, and forecast project profitability.

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COMMENTS

What is Trial And Error?
Understanding the Concept of Trial and Error: An Accessible Guide in Everyday Language, Crafted by Expert Psychologists, Professors, and Advanced Students. ... provides valuable information. Reflecting on each attempt can improve future trials and hasten the problem-solving process. Embrace Failure. Viewing errors as learning opportunities ...
Trial and error
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Donate; Help; Learn to edit; Community portal; Recent changes; Upload file
Problem-Solving Strategies: Definition and 5 Techniques to Try
In general, effective problem-solving strategies include the following steps: Define the problem. Come up with alternative solutions. Decide on a solution. Implement the solution. Problem-solving ...
4 Main problem-solving strategies
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: Algorithms; Heuristics; Trial and error; Insight; 1. Algorithms. When you follow a step-by-step procedure to solve a problem or reach a goal, you're using an algorithm.
The Trial and Error Method: When to Use it and When to Avoid it
The trial and error method is a problem-solving technique that involves trying different approaches or solutions until you find the one that works best.
7.3 Problem-Solving
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 ...
Means-ends analysis
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
Problem solving (video)
Problem-solving skills are essential in our daily lives. The video explains different problem-solving methods, including trial and error, algorithm strategy, and heuristics. It also discusses concepts like means-end analysis, working backwards, fixation, and insight. These techniques help us tackle both well-defined and ill-defined problems ...
Trial and Error Algorithms
Given the verification oracle V, an algorithm is an interactive process with V. The algorithm chooses candidate solutions (i.e., trials), and the oracle returns violations (i.e., errors). The process is adaptive, i.e., a newly proposed solution can be based on the historical information returned by the oracle.
7.3 Problem Solving
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 ( Figure 7.7) is a 4×4 grid.
Is trial and error a bad problem solving method?
I would suggest implementing it in a language that makes it easy to implement and use custom control flow operators. {-# LANGUAGE LambdaCase #-} module Trial (TrialT, abort, retry, trial) where. import Control.Monad.Except (ExceptT, runExceptT, throwError) import Data.Bool (bool) type TrialT = ExceptT Bool.
Fail Your Way to Success: 8 Powers of Trial and Error
4. Adaptability: Dancing with Change. The essence of adaptability, particularly in the context of trial and error, is akin to a dance with ever-shifting rhythms and beats. This approach doesn't ...
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.
The Trial and Error Code: How to make the best decisions
Author: Lewis Harrison is a futurist, and professional forecaster.He is the Executive Director of the International Association of Healing Professionals, an educational organization that offers ...
Trial and error explained
What is Trial and error? Trial and error is a fundamental method of problem-solving characterized by repeated, varied attempts which are continued ...
Trial and Error at a Glance
Sample Problem. Factor the polynomial -2x 2 + 7x - 3. If this polynomial factors as (ax + b)(cx + d), the product of a and c must be -2, and the product of b and d must be -3. So a and c could be -2 and 1, or 2 and -1. And b and d could be -3 and 1, or 3 and -1. We'll try all the possible factorizations and see which one works.
Psychology--Ch. 7.3 Flashcards
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.
Problem Solving
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 ( [link]) is a 4×4 grid.
What is Trial and Error
In this video, we will explore What is Trial and ErrorTrial and Error is the process of experimenting with various methods of doing something until one finds...
psychology ch 7 Flashcards
psychology ch 7. list and describe the three problem solving strategies. Click the card to flip 👆. trial and error- continue trying different solutions until problem is solved. algorithm- step by step problem solving formula. heuristic- general problem solving framework. Click the card to flip 👆. 1 / 57.
Advantages and Disadvantages of Solving a Problem Through Trial and Error
Advantages and Disadvantages of Solving a Problem Through Trial and Error » E.L. Thorndike propounded the theory of trial and error. He believes that
Psychology-Chapter 7: Thinking, Language, and Intelligence
Ian must use the formula, a^2 + b^2 = c^2. Ian plugs in 3 into a and 4 into b, and after he solves the problem algebraically, Ian finds out that the hypotenuse is 5 inches. 3. Heuristics. A problem solving strategy that involves following a general rule-of-thumb to reduce the number of possible solutions.
Problem Solving
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.
What is CRM?
By implementing the Internet of Things (IoT) into your operations, you're able to detect problems faster—automate work orders, schedule, and dispatch technicians in just a few clicks. By streamlining scheduling and inventory management , you can boost onsite efficiency, deliver a more personalized service, and reduce costs.
How to fix a currency code error on my website?
Right now this resource is taking a very long time to respond, it seems to be getting a lot of requests. It looks like this script was added by the theme developers. I can help you remove this script from the site, but it would not be quite right. It is better to contact the theme developers with this problem.

Trial and Error

Understanding the term

Characteristics of the Trial and Error Method

The Trial and Error Process

Theoretical Background

Trial and Error in Everyday Life

Learning New Skills

Technological Advancements

Advantages and Disadvantages

H3: Advantages

H3: Disadvantages

Example 1: Learning to Code

Example 2: Medicinal Drug Discovery

Enhancing the Trial and Error Process

Learn from Each Attempt

Embrace Failure

4 Main problem-solving strategies

Problem-solving stages

Initial theory in problem-solving

Problem-solving strategies

1. Algorithms

2. Heuristics

3. Trial and error

Pilot problem-solving

Getting your causal thinking right

7.3 Problem-Solving

PROBLEM-SOLVING STRATEGIES

Additional Problem Solving Strategies :

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.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

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

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.

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

Answers to Exercises

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7.3 Problem Solving

Problem-Solving Strategies

Everyday Connection

Pitfalls to Problem Solving

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Is trial and error a bad problem solving method?

Trial and Error

Trial and error explained

Methodology

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Trial and Error at a Glance

Sample Problem

Exercise 10

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Advantages and Disadvantages of Solving a Problem Through Trial and Error

Introduction

Creative Approach

Less Time Consuming

Division of Tasks

Allows one to Learn

Mistakes are Allowed

Disadvantages

Emphasizes Rote Learning

Ineffective for Bright Learners