How to Solve It
Heuristic Informal Description Formal analogue
Analogy Can you find a problem analogous to your problem and solve that ? Map
Generalization Can you find a problem more general than your problem ? Generalization
Induction Can you solve your problem by deriving a generalization from some examples ? Induction
Variation of the Problem Can you vary or change your problem to create a new problem ( or set of problems ) whose solution ( s ) will help you solve your original problem ? Search
Auxiliary Problem Can you find a subproblem or side problem whose solution will help you solve your problem ? Subgoal
Here is a problem related to yours and solved before Can you find a problem related to yours that has already been solved and use that to solve your problem ? Pattern recognition Pattern matching Reduction
Specialization Can you find a problem more specialized ? Specialization
Decomposing and Recombining Can you decompose the problem and recombine its elements in some new manner ? Divide and conquer
Working backward Can you start with the goal and work backwards to something you already know ? Backward chaining
Draw a Figure Can you draw a picture of the problem ? Diagrammatic Reasoning
Auxiliary Elements Can you add some new element to your problem to get closer to a solution ? Extension
Heuristics
The book contains a dictionary-style set of heuristics , many of which have to do with generating a more accessible problem . For example :
How to Solve It (1945) is a small volume by mathematician George Pólya describing methods of problem solving.