In my experience, when solving difficult problems, the challenge can be to use theory to adequately cast/describe the problem in such a way that it becomes amenable to some standard solution approach, be that mathematical, algorithmic, or accepted design/heuristics/correlation.
(Sometimes just properly specifiying the problem is the most important element to arriving at a good solution; this consideration is trivialized in the classroom by purposefully overspecifying the problem or adding extraneous facts to the problem description).
