With this I have two concerns :

1. If I was able to recollect the solution it would not really be beneficial as I am in effect memorising the solution and not really developing my capacity to solve problems. (Is this a fair assessment?)

2. If I try to break the problem down to the fundamental 'principles' applied or try to understand why that specific approach works over all others I feel overwhelmed by the 'data'. For every tricky problem involves a seemingly unique combination of fundamental principles or a unique perspective and thus keeping track of this for each and every tricky problem I encounter once again seems daunting and more of a memory challenge.

I believe that simply solving problems and struggling repeatedly over them will over time build a sort of intuition for the topic. To use an analogy, for a topic I have developed a feel/intuition for (say, Ratios and Proportions or Basic Arithmetic Operations), I somehow have the ability to navigate any problem with relative easy, simply because I spent a lot of time struggling with it in school (to the extent that I can apply these concepts almost unconsciously when they are required to used in some other topic entirely, for example the use of proportion in Stoichiometry). There could still be a whole collection of 'tricky' problems based on the simplest topics that I may still stumble over, but due to my existing 'intuition' for the topic I would be able to 'add' them to my 'inventory' much more easily.

But this leads to other questions :

3. When I learnt 'basic' topics I was too young to really question how it was that I developed this intuition, I never consciously attempted to inventory approaches I encountered or basic principles to go by. Yet, I somehow feel that this approach of coupling 'blind faith' with solving lots and lots of problems is inefficient (Is it?).

4. So are there some 'Principles of problem solving' that need to be kept in mind while going through a new and unfamiliar topic (say Integration or Fluid Mechanics)?