[G03] Solving problems

Polya's 1971 book How to solve it is a classic text on problem solving. According to Polya, most problem-solving strategies can be classified under four general principles:

• Understand the nature of the problem.
• Draw up a plan to solve the problem.
• Try out the plan.
• Monitor the outcome of the plan.

Let us highlight some important points to consider when we have to apply these four principles:

1. Understand the nature of the problem

• Is the problem well-defined? Can the problem be analysed into smaller sub-problems?
• What type of problem is it? (See the last tutorial on classifying problems.)
• What information can we gather about the problem?
• Have I / other people solve this problem before? What lessons might their experiences offer?
• What are the constraints (time, money, resources, etc) in solving the problem?

2. Draw up a plan

• Determine the time and resources needed.
• Carry out necessary preparations, e.g. research, coordination, etc.
• For solving problems that require a complex plan, write down the plan in a systematic manner.

3. Try out the plan

• Monitor progress to make sure that things go according to plan.
• Record errors or special considerations for future review.

4. Monitor the outcome of the plan

• This is the part of problem-solving that most people tend to ignore. One way for us to improve is to review past experiences and understand why we succeed or fail. So it is important to monitor our own performance review the whole exercise in order that we can do even better in the future.