I am sure that if we are trying to answer posts with title like "How do you approach a problem you are not sure has a solution?" then we have a big problem of run round in circles. The first step to solve a problem is to define well the problem, the title omitted the anxiety/paralysis bit, so I bited this. Anyway, to add something constructive, I recommend "How to Solve It" by Polya. From a reviewer: In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be “reasoned” out (don't know with or without anxiety).