2.3 Specific heuristics
This list was written by A.H. Schoenfeld:

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draw a diagram (if at all possible)

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examine special cases

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choose special values to exemplify the problem and get a "feel" for it

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examine limiting cases to explore the range of possibilities

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set any integer parameters equal to $1,2,3,...$ in sequences and look for an inductive pattern.

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try to simplify the problem

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exploiting symmetry

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without loss of generality

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consider essentially equivalent problems

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replace the conditions with equivalent ones

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recombine the elements of the problem in different ways

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introduce auxiliary elements (e.g. substitutions)

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reformulate the problem

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change of perspective or notation

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considering argument by contradiction or contrapositive

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assuming you have a solution, and determining its properties (i.e. what would a valid answer look like)

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consider slightly modified problems

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choose subgoals (obtain partial fulfilment of the conditions)

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relax a condition and then try to reimpose it

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decompose the domain of the problem and work on it case by case

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consider broadly modified problems

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construct an analogous problem with fewer variables

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hold all but one variable fixed to determine that variable’s impact

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try to exploit any related problems which have similar

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form

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"givens"

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conclusions

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verifying solutions

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Does it pass these simple tests?

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Does it use all the pertinent data?

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Does it conform to reasonable estimates or predictions?

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Does it withstand tests of symmetry, dimension analysis, or scaling?

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Does it pass these general tests?

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Can it be obtained differently?

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Can it be substantiated by special cases?

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Can it be reduced to known results?

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Can it be used to generate something you know?

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