My 4 Steps to Solve Any Problem
(This is by no means advise, but it works surprisingly well for me)
Come up with the most ridiculous solution you can think of!
Pick out the parts that you know could work.
Figure out what gaps exist between these parts.
Repeat from step 1 for each gap.
Some Further Discussion and Clarification
When approaching step 1, the “most ridiculous idea” may be a bit too ridiculous. For me, this normally works but I also have practice with this and stay inside some constraints. A more accurate thing to say would be come up with a ridiculous idea instead of the most ridiculous idea.
For step 2, this involves breaking the idea into parts. Everything can be simplified down to smaller parts, so do that. Then take the things that you know could work (these can be things you’ve done before, or that aren’t a huge stretch for you), and do some initial figuring out. For me, this is typically an engineering or design problem, so I’ll do some theory and math here, but this can vary depending on the problem.
On to step 3. Identifying the gaps is kind of like figuring out your start point and end point on a map, where the parts from step 2 are roads. The roads aren’t connected though, so you need to figure out how to build new roads between them.
Step 4 is recursive. For each gap, go back to step 1 but dial back the ridiculousness for each recursive level that you’re at. You could also come up with a reasonable solution, so look around for a solution that may already exist or something that’s close but not quite there that could be adapted.