Types of problems

Trial points

Understand data: look how objects and requirements relate to each other, which units, theorems, notation, techniques might get useful.
Understand objective: use it to figure which techniques likely to be useful, and to create tactical goals which will bring us closer to solving the question.
Choose a notation: pick it to represent data in most terse way. It involves thinking of prev. two strategies.
Put the knowledge into the notation, perhaps draw something. Be careful to not overload with the data.
Modify the problem slightly (useful when can't even get started on it):

Consider extreme or degenerate cases
Try proving something that implies the problem, or some consequence of the problem.
Reformulate the problem (e.g. contrapositive)
Examine solutions to similar problems.
Generalize the problem (?)

Modifying the data significantly: removing data, swapping the data with objective, negating the objective.
Prove results about the question. Data is there to be used, so play with it. Can it produce more meaningful data?