Sometimes you are confronted by problems with out any apparent solutions. [Well, one can argue, if there is no solution and nothing to solve then it is not a problem at all].
Sometimes you do know the solution but execution is not simpler [As one of my friend recently quoted, real life is not like solving cases in class or in paper]
Sometimes the problem is not worth solving at all!
Sometimes you have bigger problems to solve!
No matter, what state of above mentioned probem you are in, Logical approach in analyzing the hard empirical evidence and data will always tell you what needs to be done.
The difficult part is actually following the logic against your gut feeling!