Evidence suggests that to grapple with a difficult problem, we must first put hard, focused-mode effort into it.
(We learned that in grade school!)
Here’s the interesting part:
The diffuse mode is also often an important part of problem solving, especially when the problem is difficult. But as long as we are consciously focusing on a problem, we are blocking the diffuse mode.
— A Mind For Numbers (Barbara Oakley), Loc. 415–7