The Nine-Dot Problem
the problem correctly and generate appropriate alter- native solutions. The inability to separate the impor- tant from the unimportant, and to compress problems appropriately, serves as a conceptual block because it exaggerates the complexity of a problem and inhibits a simple definition.
How well do you filter out irrelevant information? Consider Figure 7. For each pair, find the pattern on the left that is embedded in the more complex pattern on the right. On the complex pattern, outline the embedded pattern. Now try to find at least two figures in each pattern. (See Appendix 1 for a solution.)
Try one more. What is the word written in Figure 8?
off limits, so they ignore them. For an illustration of this conceptual block, look at Figure 6. Without lifting your pencil from the paper, draw four straight lines that pass through all nine dots. Complete the task before reading further.
This compression block—separating figure from ground and artificially constraining problems—played an important role in the microwave oven and Post-It Note breakthroughs. George Foerstner’s contribution to the development and manufacture of the microwave oven was to compress the problem, that is, to separate out all the irrelevant complexity that constrained oth- ers. Whereas the magnetron was a device so compli-
By thinking of the figure as more constrained than it actually is, the problem becomes impossible to solve. Try to break out of your own limiting assumptions on the problem. (One four-line answer is presented in Appendix 1.) Now that you have been cued, can you do the same task with only three lines? Work on this problem for a minute.
If you are successful, now try to do the task with only one line. Can you determine how to put a single straight line through all nine dots without lifting your pencil from the paper? (No paintbrushes allowed!) Both the three-line solution and some one-line solu- tions are in Appendix 1.
Artificially constraining problems means that the problem definition and the possible alternatives are limited more than the problem necessitates. Creative problem solving requires that individuals become adept at recognizing their hidden assumptions and expanding the alternatives they consider.
Separating Figure from Ground
Another illustration of the compression block is the reverse of artificial constraints. It is the ability to con- strain problems sufficiently so that they can be solved. Problems almost never come clearly speci- fied, so problem solvers must determine what the real problem is. They must filter out inaccurate, mis- leading, or irrelevant information in order to define
SOLVING PROBLEMS ANALYTICALLY AND CREATIVELY