In any problem solving situation, if the solution doesn't come to mind, one wonders if it is even possible to use the methods in mind, and if it is something you haven't learned yet, or never have been invented yet.
So my question is: How can one systematically find out what kind of maths (elementary or advanced methods) can be used?
The famous example is the Collatz Conjecture. It has often been quoted as the easiest to state unsolved problem.
Which at first glance looks like an elementary problem.