"Banging your head" usually means lots of trial and error, that is all error. But beyond uploading information, every experiment creates new information. ("I haven't failed - I've discovered 1,000 ways that won't work!" https://quoteinvestigator.com/2012/07/31/edison-lot-results/)

When the search space is exponential, with too many combinations to try, pruning off a branch is enormously helpful (and perfectly harmless... provided the solution doesn't happen to lie on that branch - those are my most stuck times).

One signal is when I can't think of anything else to try - that means I've extracted all the information I can. The trouble is, I'm pretty good at thinking of things to try.