Using the correct variables or using a symmetry of the structure underlying the problem to convert a problem to another: this is a principle that I try to use when I think about a question. What is the right representation for a given problem? What are the correct variables? I am curious if others think that this idea deserves a page of its own.
I tried to write an initial article on what I think to be a special case of this, namely use of bijections in counting. If a general article is written, a link to this special case could make both articles more useful.