Problems involving transformation involve making a series of steps towards a certain goal. A good example of this kind of problem is a farmer who needs to bring his chicken, fox, and seeds to the other side of the river. He cannot leave the chicken and seeds or the fox and the chicken alone. In a series of steps, he manages to bring all of them across. In other words, he figured out the steps necessary to complete the goal and executed them.  

There are many resources at our disposal to solve problems. We can use trial and error, algorithms, deductive reasoning, inductive reasoning, dialectical reasoning, heuristics, forming sub-goals, and similar problems to help us approach the problem at hand. No single one method is measurably better than the other but some are more appropriate for particular problems.

Trial and error is an appropriate approach to a problem when the number of possible solutions is relatively small. If number of possible solutions were large, then using trial and error would potentially take too long and be ineffective. If someone is presented with five light switches, they might try each one until they find the correct one. If someone is presented with 300 light switches, then trial error might not be the best option.

All of these answers are examples of algorithms. Algorithms are problems involving a step-by-step procedure to get one goal. This is not restricted to just math as one might think. People use algorithms in day-to-day life whether baking cookies using a particular recipe or driving somewhere by using directions. 

Deductive and inductive reasoning differ in the path used to reach their respective conclusions. In deductive reasoning, the researcher starts with a general statement or hypothesis and examines possibilities in order to reach a specific conclusion. On the other hand, in inductive reasoning, the researcher attempts to make generalizations from specific occurrences. 

A heuristic is something commonly used in our reasoning as a general "rule of thumb". These are rules that hopefully guide use to the solution we need. For instance, a student taking a test wants to get a good grade. In order to reach that goal, they may follow the general "rule of thumb" (i.e. heuristic) of doing the easy questions first so they can use their focus for the more difficult problems.

Dialectical reasoning involves going back and forth between opposing points of view in order to come up with a satisfactory solution. This involves fully engaging in each side of the problem. This could be as simple as a person making a pros and cons list for what trip they want to take or as complex as a politician considering all positive and negative consequences of a bill being passed.

An efficient way of solving an analogy problem would be forming sub-goals. For instance take the analogy: "a school is to a student as a company is to a __________.” A sub-goal to reaching the end goal of actually solving the problem would be to figure out the relationship between a school and a student. After this sub-goal is reached, it would be easy to infer that the answer is "employee.”

The best definition of problem solving is making an active effort to achieve a goal that cannot be easily attained. At times, individuals view this unmet need as a problem and whatever means he or she comes up with to fulfill that need is the solution. The process of coming up with this solution is known as problem solving.

When a person is presented with a problem this problem may be presented with irrelevant information. That is, this information will not be useful when coming up with a solution. This is a common device used in riddles. Teasing out irrelevant information entails figuring out what precisely is being asked of you for the solution.