I find value in reading and doing exercises in books about areas of mathematics that I didn't get to explore while in school. I try to do each exercise in each chapter with only the material contained in each book, but I sometimes can't think of a solution in a reasonable amount of time without using outside resources. In short, here's my main question:
When is it appropriate to use outside resources to complete book exercises during self-study?
As background, I am a software developer with a bachelors degree in math.
In terms of technology, I consider using outside resources to solve technical problems as a short-cut. It is more efficient to use a proven statistical library to do computations on a data set, but that won't necessarily teach me what the results actually mean. When I decide to work through a book, I work under the assumption that the book is self-contained, except where it says otherwise in the book itself. I realize that outside resources can accelerate my understanding, but I fear that I may miss the subtle points the exercise intends to emphasize by doing so.
In other words, how can someone ensure that eir learning of a new subject isn't harmed by turning to Google for help?