[Sir_Cmpwn]

From my experience, try having enough projects in your belt that at least one of them has something actionable to do, and work on that while you ruminate on the other problem for a few days/weeks/months. Don't worry about getting anything done soon, prefer getting them done correctly and pick something else up when you get stuck. Also, don't forget that "staring into space for an hour while you think about a problem" is also a valid form of working.

[ehead]

This is my solution, but it feels like there should be a better way.

I have replaced 'staring into space thinking' with taking a walk outside my office.

[zikzak]

Unless you are rich enough to have chosen it, or maybe a prisoner, you always have more than one thing to do. Laundry, groceries, complex engineering, it all needs to be done.

I think our minds evolved to track all these things and, probably in a time sensitive way more than projected future value, to prioritize them. For this reason, I think having multiple projects is the natural state as the mind is optimized for this. So maybe this is the "best way" and explains a lot of the strange ways in which putting a problem aside can help solve it.

[fwip]

It's hard to do laundry or grocery shopping while you're at work.

[collyw]

I like to work like this as well. Which is why a lot of technical tests seem quite nonsense. For complex problems I have stuff running in the background of my head for a day or two, weighing up the advantages and disadvantages of the various options. The best solution usually becomes apparent at some random time, like when I am cooking dinner, not concentrating on it for 5 minutes after first seeing the problem. And as you say there is usually plenty of other work that needs done in the meantime.