It is pretty often that I think of an interesting math problem, and similarly often that I get stuck. Historically I have found it difficult to locate solutions online, since I don't really know what to search. This, of couse, is why this site exists, but I feel like I would be well served by being able to locate solutions or even just papers on related subjects.
To give an example, I was recently looking at what distribution of circle sizes could completely fill the plane without gaps. Starting with a hexagonal packing of unit circles, it isn't very hard to identify that the next largest circle, the one that fits in the deltoid-shaped gap, has a radius of $\frac23\sqrt3-1$, but after that I couldn't come up with anything that wouldn't be really painful to implement. This seems like a problem that would have a known solution, and probably a satisfyingly clever one, but everything I Googled just pointed towards "normal" circle packing problems where the radii of the circles are already known.
What strategies can I use to improve my ability to find solutions?
