Ask HN: How do you unstuck yourself from a hard problem?

When stuck on a problem, I go for a walk, meditate, or just sleep over it. It's the concept of Hammock-driven development [1], using your subconscious, etc. I do this visibly to demonstrate to my team, that it's fine to do this on office time, because they're here to solve problems. My colleagues are unfortunately spell-bound by the prevalent mindset in the Philippines, where many companies value office time, screen time, typing time. That works for factories like call centers, data entry offices and ever-same small-project outsourcing. It does not work for us, because like with all interesting software development, we need to solve non-trivial problems. I'd love to point them to other examples of how people unstuck themselves. How do you do this?