This page is about a creative approach to problem solving rather than formal methods of mathematical deduction. I guess the most important thing is not to fear a problem because its difficult or to hurry it. Perhaps maths, physics and computer problems should be tackled with the same approach as crossword or sudoko problems, although not necessarily in a trial-and-error way.
- Find a similar problem. Can you apply to your own problem?
- Simplify the issue by removing some variables.
- When one approach fails, try the opposite.
- Dream: fantasies about a situation such as assuming that all restrictions have been removed.
- Establish sub-goals: break the problem into a number of smaller ones.
- List the assumptions you have made about solving the problem and challenge them.
- Try working through the situation from the way things are to the way you want them to be.
- Choose other words to describe the problem. An alternative definition can yield new possibilities.
- Looking at the bigger picture (an heuristic approach), instead of proceeding one step at a time (an algorithmic approach).
- Four phases: preparation, incubation, inspiration and evaluation.
- Ask what if? questions.
- What is the unknown? What are the data? What is the condition.
- Don't throw out any options at this stage or limit your thinking. Sometimes it helps to write things down but be careful that this does not constrain your thinking too early, its sometimes better to delay committing things to writing, diagrams can be good, or introduce some suitable notation, or mind maps. Different types of problem require different approaches.