Every improvement or innovation is the result of solving some important problem. Simple problems lead to simple solutions, like using a net to catch a fish. More complex problems lead to more complex solutions, like developing a naval ship to get an army across an ocean, or building a rocket to reach outer space. Still other problems lead to solutions that save lives: vaccines, medicines, surgical procedures and the like.

In all of these diverse cases, the underlying problem-solving dynamics are the same: people either converge in their thinking to solve a problem or they diverge in their thinking to solve a problem—or they do both.

Another way to look at problem-solving styles is in terms of exploitation versus exploration. Guided by convergent thinking, exploitation is when you solve problems using what you readily understand inside a known paradigm. Guided by divergent thinking, exploration is when you move beyond known paradigms and existing knowledge to solve a problem. Some business problems require mostly exploitation, while others require mostly exploration, but all problems require some mixture of the two.

Thomas Edison is often called an inventor, but he mostly developed basic discoveries into better solutions for commercialization. Often credited with inventing the light bulb, Edison really conducted extensive experimentation and analysis to find the optimal conditions under which the tungsten wire in a bulb would glow continuously without interruption. While Edison did his own share of exploration, his basic strength and passion was in taking what was already known and refining it until it could solve some problem.

Alternatively, Einstein thought mostly outside the box of the prevailing wisdom of his day, or what was known at the time, and such exploration is the essence of solving problems in untried and untested ways. His theory of relativity questioned key assumptions of Newtonian physics. Einstein even characterized himself as a little strange—but strangeness is what it takes to solve ill-defined problems, or to solve fairly well-defined problems in new and unusual ways.

Thomas Edison borrowed new paradigms discovered by others and preferred to perfect them methodically, systematically and in a precise manner. Edison was more of an adaptor.	Albert Einstein questioned the existing Newtonian paradigm, which enabled him to discover the theory of relativity. Einstein was more of an innovator.

People in your organization, including you, are either more like Edison or more like Einstein. You might tend to solve problems through convergent thinking and such exploitation-oriented actions as study, analysis and working within known domains. Or you might tend to think divergently and explore new domains, question assumption, and generate many harebrained ideas until you solve your problem.

Different types of innovation problems require different degrees of exploitation and exploration to solve (See exhibit below).The solid boxes and lines represent the convergent exploitation of established paradigms and known knowledge, and the dotted boxes and lines represent the divergent exploration of new paradigms and fields.

Understanding each of these four problem-solving classes will enable you to characterize any problem in your organization. From there you can select the best and most appropriate techniques for solving your particular problem:

1. Class 1—The problem and the solution space are both well-defined. This dictates mostly exploitation and convergent activities within the current paradigm. Defects on a production line are a good example of Class 1 problems, which are usually solved with such process-improvement methods as Plan-Do-Check-Act (PDCA), Six Sigma, Lean and the like.

2. Class 2—The problem is well defined but the solution pathway is not so clear or directly discoverable. Therefore, the task is to explore new ideas and realms, searching for better solutions, while also exploiting known knowledge when necessary. For example, the job of illuminating a room in the dark was once accomplished with a candle, but candles have drawbacks, like dripping wax. Candles did not meet some important customer expectations very well, so this opened the door for better solutions.

   When your customers tell you they are largely satisfied with your product or service, you have a Class 1 problem: just optimize. However, if customers tell you they are unsatisfied with your product or service, you have a Class 2 problem and you need to discover or invent a better solution that closes the dissatisfaction gap. Stated differently, if customers are generally happy with candles, make better candles; if they are unhappy, discover a better way to illuminate the darkness.

3. Class 3—These problems are the reverse of Class 2 problems: the solution is clear but the problem is fuzzy. Class 3 problems are intriguing because they force you to consider new applications for existing technologies. For instance, engineer Richard James was working with tension springs in 1943 to develop a meter for monitoring horsepower on naval battleships. One of his springs fell to the ground and gave him a new idea about a different job to be done in a different market. Thus the Slinky was born.

   Sometimes, your existing solutions can be put to a different use, thereby solving a problem and opening a new market. In effect, Class 3 problems require you to turn your ideation efforts upward—beyond where your solutions reside into the realm of higher human needs—asking what jobs your solutions could do that they don’t do today.

4. Class 4—These problems are undefined, and their solutions are undefined as well. There is no particular mandate to solve any problem, and the objective is to simply explore because both the problem and the solution reside in unknown territory. Medical researchers, for instance, are always looking for new molecules—just for the sake of finding them. Once they’re found, they can always be studied, manipulated and exploited.

   Solving Class 4 problems is what you do when you don’t know what you’re doing—basic research, where discoveries are made but the path to commercialization is unclear.

The material on this webpage is excerpted from The Innovator's Toolkit: 50+ Techniques for Predictable and Sustainable Organic Growth(John Wiley & Sons, 2009)— authored by BMGI principals David Silversteinand Phil Samuel.