Still more complex forms of realistic thinking seem to occur when tasks are presented in which the goal is impossible (or very difficult) to achieve directly. In such situations, people commonly appear to pass through intermediate stages of exploring and organizing their resources; indeed, one may first need to exert himself in understanding the problem itself before he can begin to seek possible directions toward a solution. Familiar examples of problem-solving tasks include anagrams (e.g., rearrange "lpepa" to spell "apple"); mathematical problems; mechanical puzzles; verbal "brain teasers" (e.g., Is it legal for a man to marry his widow's sister? answer below); and, in a more practical sense, design and construction problems. Also of interest are issues of human relations, games, and questions pertinent to economics and politics.

Trial and error.

Problem-solving activity falls broadly into two categories: one emphasizes simple trial and error; the other requires some degree of insight. In trial and error, the individual proceeds mainly by exploring and manipulating elements of the problem situation in an effort to sort out possibilities and to run across steps that might carry him closer to the goal. This behaviour is most likely to be observed when the problem solver lacks advance knowledge about the character of the solution, or when no single rule seems to underlie the solution. Trial-and-error activity is not necessarily overt (as in one's observable attempts to fit together the pieces of a mechanical puzzle); it may be implicit or vicarious as well, the individual reflecting on the task and symbolically testing possibilities by thinking about them.

Solutions through insight.

In striving toward insight, a person tends to exhibit a strong orientation toward understanding principles that might bear on the solution sought. The person actively considers what is required by the problem, noting how its elements seem to be interrelated, and seeks some rule that might lead directly to the goal. The insightful thinker is likely to centre on the problem to understand what is needed, to take the time to organize his resources, and to recentre on the problem (reinterpret the situation) in applying any principle that seems to hold promise.

Direction and flexibility characterize insightful problem solving. The thinker directs or guides his steps toward solution according to some plan; he exhibits flexibility in his ability to modify or to adapt procedures as required by his plan and in altering the plan itself. Both characteristics are influenced by the thinker's attitudes and by environmental conditions. If, for example, the task is to empty a length of glass tubing of water (without breaking it) by removing wax plugs about a half-inch up the tube from each end, and the only potential tools are a few objects ordinarily found on a desk top, the usual appearance and functions of such common objects may make it difficult for the problem solver to see how they can be adapted to fit task requirements. If a paper clip is perceived as holding a sheaf of papers in the usual way, such perception would tend to interfere with the individual's ability to employ the principle that the clip's shape could be changed: straightened out for use in poking a hole in the wax.

Formal, logical processes.

A special form of problem solving employs formal, systematic, logical thinking. The thinker develops a series of propositions, often as postulates; e.g., the shortest distance between two points is a straight line. He builds a structure of arguments in which statements are consistent with each other in reaching some goal, such as defining the area of a triangle. This kind of logical, mathematical reasoning applies formal rules in supporting the validity of successive propositions.

Both inductive and deductive processes may be used by a problem solver. In inductive thinking one considers a number of particular or specific items of information to develop more inclusive (or general) conceptions. After aspirin was synthesized, for example, some people who swallowed the substance reported that it relieved their particular headaches. Through induction, the reports of these specific individuals were the basis for developing a more inclusive notion: aspirin may be helpful in relieving headaches in general.

Deduction is reasoning from general propositions--or hypotheses--to more specific instances or statements. Thus, after the general hypothesis about the effectiveness of aspirin had been put forward, physicians began to apply it to specific, newly encountered headache cases. The deduction was that, if aspirin is generally useful in managing pains in the head, it might also be helpful in easing pains elsewhere in the body. Although a person may deliberately choose to use induction or deduction, people typically shift from one to the other, depending on the exigencies of the reasoning process.

Students of problem solving almost invariably have endorsed some variety of mediation theory in their efforts to understand realistic thinking. The assumptions in that kind of theory are that implicit (internal) representations of experience are stored in and elicited from memory and are linked together during the period between the presentation of a stimulus and the implementation of a response. Those theorists who prefer to avoid the use of unobservable "entities" (e.g., "mind") increasingly have been invoking the nervous system (particularly the brain) as the structure that mediates such functions.

Answer to brain teaser: dead men can't marry

Excerpt from the Encyclopedia Britannica without permission.