Making assumptions may make us skip over important information we may need to solve a problem. This can happen in a variety of problems, especially when they involve people. We carry around many preconceived notions about how people and our society work. If we have a problem understanding a certain phenomena in society, it may be due to these kinds of assumptions. For instance, patriarchal society once widely assumed that women were destined for housework and many people didn't understand why women were so happy. They attributed it to their "biology". Instead, it's better understood that women desire just as much as men to participate in and feel like they belong in their society.

Problems associated with arranging involve moving parts to fulfill a certain criterion. This manifests in many forms. Puzzles, anagrams, and block building are all forms of arrangement tasks. In the example provided in the answer, the letters are appropriately arranged to make the word “dancing.”

Divergent thinking is when one thinks of new solutions to problems. It's how people innovate and address recurring issues with new solutions that may actually fix the problem. It is not stereotypical, sadistic, or emotional, and rather engages the creative thinking processes. An example of divergent thinking would be the development of electric cars in response to the air pollution 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.

Researchers have identified several mental obstacles to our problem solving/reasoning processes. Functional fixedness, mental set, and making assumptions, and irrelevant information are just some of many. Although their precise definitions won't be defined here, the commonality they share is a misdirection in focus and to an extent being stuck on what has worked in the past.

Precognition is a term that depicts the correct prediction of future events. For example, if a child predicts that a certain team will win her soccer league and that prediction occurs, then the child has exhibited precognition of this event.

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.

The availability heuristic leads people to make decisions based on how available information is inside their brains. After recently watching shark-attack programs, this readily available information influenced John's judgments of the likelihood of shark attacks.

Belief perseverance is the distinct phenomenom in which we tend not to let go of our previous beliefs despite compelling or truthful evidence that contradicts them. For instance, we may believe that our spouse is faithful, but then find compelling evidence that contradict this. In spite of the evidence, we may continue to believe our spouse is faithful out of our inability to let go of our beliefs. Instead of confronting the problem, due to belief preserverance, we keep believing what makes us comfortable.

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.