One technique I have found to be helpful in solving a hard problem is to stuff my head full of as much information about the problem right before bed. Then I go to sleep. Many times, I wake up in the middle of the night, having figured out a solution.

John Cleese from Monty Python made many years ago a presentation about open and closed mode of thinking which is similar and how it related to their work. https://youtu.be/Pb5oIIPO62g

Being focused is often confused with being busy with random thoughts. Being focused on one thing feels like stretching out your brains - a very remarkable feeling. On the other hand, being busy with thoughts raises blood pressure and that makes head feel heavy. When we're working on something, we usually do the latter.

An interesting and tangentially-related concept is learning how to access "Right Brain Mode" for creative work, popularized in the book "Drawing on the Right Side of the Brain".

https://www.amazon.com/Drawing-Right-Side-Brain-Definitive/d...

Picked up the book this is based off at Half-Priced book. They give a really good example I’ll leave for the reader, but it’s a seemingly simple task but hard to solve. The book asks you to walk away and do something different for a while. When you return, you are able to finish. Demonstrates the idea very well and highly recommend the book.

I like to think of this as conscious thinking, and subconscious thinking.

By focusing your mind on a topic for a while and leaving it there to germinate ("sleep on it") for a while, you often come back to it with a clearer focus.

If your subsconscious didn't anchor on it, it's probably not worth pursuing (e.g. you don't care).

This is why I'm still on slack and HN... I need that step away from focussed thinking (let's pretend).