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I found a detailed classification in an article by Murray Klamkin, cited below.I added a few, and for some have not yet come across suitable examples. I would very much appreciate comments and additional examples. The most common way to approach a problem is by identifying a general class to which the problem belongs and using a method (if such exists) that is applicable to the problems of that class.
For a few more words and many additional examples see a separate file.
Very often, especially when a problem has been posed at an olympiad or in math circles, a solution that comes to mind first is not necessarily the best - the easiest to follows through.
Try one of the tactics, force yourself to speak aloud - something will come out.
Ray Bradbury, when short on ideas, taught himself to work with a dictionary picking random words and trying to put them together into something meaningful and relevant. Also, note that some of the tactics was previously mentioned - with additional advice - in a short assay of what constitutes a proof.
For the parallelipiped with sides $a,b,c$ and diagonal $d,$ we have $a^ b^ c^=d^.$ For a tetrahedron with three faces having right angles at the shared vertex and areas $A, B, C,$ $A^ B^ C^=D^,$ where $D$ is the area of the remaining face.
Being An argument by continuity assumes the presence of a continuous function whose properties could be used to solve a given problem.
Further reading I highly recommend the 1981 article The heuristic of George Polya and its relation to artificial intelligence by Alan Newell that offers penetrating analysis of Polya's problem solving heuristics prior to the discussion on its applicability to AI.
Specializaton, i.e., considering special cases, or introducing additional restrictions, while trying to solve a problem may highlight aspects of the original problem that have perhaps been missed at first glance.
It is incredibly powerful, although, at first sight, often appears innocuous.
The essence of WLOG is in making a random selection among a number of available ones for the reason of all possible variants being equipotent, i.e., leading to exactly same procedure and result.