A useful common problem-solving strategy is to divide a problem into cases. We can divide the problem into familiar and unfamiliar cases; easy and difficult cases; typical and extreme cases etc. The division is sometimes suggested by the problem, but oftentimes requires a bit of work first.
If you are stuck on a problem or you are not sure where to begin, gathering data by trying out easy or typical cases first might help you with the following (this list is not exhaustive):
Gaining intuition of the problem
Isolating the difficulties
Quantifying progress on the problem
Setting up or completing inductive arguments
Let us take a look at this strategy in action.