Problem solving

Problem solving gives lateral-thinking practice a concrete goal. Even when we have no particular incentive to generate new ideas, problems are thrust upon us. We have little choice but to try to solve them, and a problem need not be presented formally or worked out on paper. A problem is simply the difference between what one has and what one wants. It may involve resolving a difficulty, bringing about something new, getting rid of something unsatisfactory, or even discovering what one actually wants. Any question poses a problem. Generating and solving problems is the basis of forward thinking and progress. If description is a matter of looking back to see what one has, then problem solving is a matter of looking forward to see what one can get.

Problems can be categorized according to the kind of thinking they require:

1. The first type of problem calls for more information or better techniques for handling information. Such problems can be solved by vertical thinking.
2. The second type of problem requires no new information but a rearrangement of the information already available — an insight restructuring. Lateral thinking is needed here.
3. The third type is the problem of no problem. One is blocked by the adequacy of the present arrangement from moving to a much better one. There is no obvious point to focus on because one is not even aware that a better arrangement exists. The real task is to realize that there is a problem, to see that things can be improved, and to define that realization as a problem. This type also requires lateral thinking.

In any problem there is a desired end point — something one wants to bring about. What one wants to bring about may take a variety of forms: to resolve some difficulty, to bring about something new, or to do away with something unsatisfactory. All these are different aspects of the same process, which is to bring about a change in the state of affairs. For instance, the same traffic congestion problem can be phrased in three ways, each emphasizing a different aspect: resolving the difficulty of congestion, designing a road system for free traffic flow, or getting rid of the frustration and delay of congestion.

Problems may be open-ended or closed. Most of the problems used in this book are open-ended, because in a classroom setting we cannot try out solutions to a wide range of real-life problems. With open-ended problems we can only offer suggestions. Since these suggestions cannot be tested directly, they must be judged on the basis of what we think would happen if the solution were implemented. The emphasis is not on judging the suggestions but on generating different approaches. Where possible, a suggestion is acknowledged and even elaborated upon, rather than rejected. Judgment is only enforced when suggestions wander so far from the problem that one is no longer trying to solve it at all.

Closed problems have a definite answer. The solution either works or it does not. There may be only one solution, but more often there are several alternatives. Some solutions may be better than others, but for practice purposes it is enough that they work — and it is better to find a variety of solutions than to hunt only for the best one. Closed problems used in training must be relatively simple, because they must be solvable without elaborate equipment. One can create verbal problems that require only a shift in perception and perhaps the simplest of arithmetic. For example: “A line of ducks walking along had two ducks in front of a duck and two ducks behind a duck. How many ducks were there?” The answer is three. It is essential that these problems do not depend on verbal tricks or puns; students should never feel that the teacher is trying to trick them.

Another useful type is the artificial mechanical closed problem. These deal with physical objects, such as how to get a long ladder through a short room. Such problems can be created deliberately by taking a straightforward activity and restricting the starting position. For instance: “How would you empty a glass of water without lifting it off the table?” or “How could you carry three pints of water in a newspaper?” When using these problems, the starting position must be defined with extreme care. One cannot later add hidden assumptions. If you ask students to cut a postcard into a certain shape, you cannot then say, “But I didn’t say you could fold the card,” or “It was assumed you could not fold it, otherwise it would be too easy.” This point is crucial, because telling students to make assumptions and presume boundaries in their problem solving runs directly against the purpose of lateral thinking, which challenges the limiting effect of such assumptions.

There is a third format for classroom use that requires some preparation from the teacher. It involves presenting problems that have already been solved, but withholding the solution. The teacher must imagine how the problem might have been stated before the solution was found, using situations with which the students are not familiar. For example, students might be asked, “How would you make plastic buckets or plastic tubing?” The teacher, who knows about moulds, vacuum forming, extrusion, and other processes, would encourage suggestions and give the answer at the end. It is wise to check beforehand whether anyone already knows the answer; if so, that student can be asked to keep quiet or to explain the answer later. Having students write out their own suggestions also prevents the problem from being spoiled. This sort of problem can be generated by using one’s imagination, by reading science and technology magazines, or by wandering around exhibitions. There is no harm in reinventing things that have already been invented — it is excellent practice.

All these problem-solving formats, whether open-ended, closed, or historically solved, help develop a repertoire of thinking processes. The real aim is not merely to solve each puzzle but to internalize the mental moves that lateral thinking requires, so that they can be transferred to problems of every kind.