What Polya suggests is, in essence, tinkering with attributes of a problem. Once understood, the problem is described in abstract terms - as a class. Assignment of specific values to the class attributes generates specific problems - objects of that class. Polya's thinking is very much object oriented. As a matter of fact, the same problem can be described in various ways.
Different descriptions correspond to different problem classes with different attributes.
Depending on what particular class is chosen for fiddling with its attributes makes the occupation more or less inspiring. This is still the same tinkering but with attributes of a different class. Being aware of a problem classification like the one above certainly helps in coming up with new problems. I think Polya, as a teacher , would have eventually regretted dubbing the student dull. Education is a process .