[treya]

First and foremost - suspend any disbelief about whether you can solve it. This is hugely important. If it has a solution and you are going to be able to solve it, then it needs your full undivided attention and focus and motivation in order to make the best progress. The possibility that it doesn't have a solution and/or you aren't able to find one is the pathological case - you should only be concerned about the successful strategy and not be spending time on the pathological one. Secondly, be aware that difficult problems which haven't already been solved are unsolved for a reason. Be willing to be patient and dedicated to a long term investment of energy and time on your part to work on it