Principles of Problem Solving

There are no hard and fast rules that will ensure success in solving problems.
However, it is possible to outline some general steps in the problem-solving process and to give some principles that may be useful in the solution of certain problems. These steps and principles are just common sense made explicit. They have been adapted from George Polya’s book How To Solve It.

The first step is to read the problem and make sure that you understand it clearly. Ask yourself the following questions:

What is the unknown?
What are the given quantities?
What are the given conditions?

For many problems, it is useful to draw a diagram and identify the given and required quantities on the diagram.
Usually, it is necessary to introduce suitable notation
In choosing symbols for the unknown quantities we often use letters such as a, b, c, m, n, x, and y, but in some cases, it helps to use initials as suggestive symbols; for instance, for V volume or t for time.

Think of a Plan Find a connection between the given information and the unknown that will enable
you to calculate the unknown. It often helps to ask yourself explicitly: “How can I relate the given to the unknown?” If you don’t see a connection immediately, the following ideas may be helpful in devising a plan.

Try to Recognize Something Familiar Relate the given situation to previous knowledge.
Look at the unknown and try to recall a more familiar problem that has a similar unknown.
Try to Recognize Patterns Some problems are solved by recognizing that some kind of pattern is occurring. The pattern could be geometric, or numerical, or algebraic. If you can see regularity or repetition in a problem, you might be able to guess what the continuing pattern is and then prove it.