Thank you for this. We're only just now watching Brooklyn 99, and this episode just started and I realized I'd never be okay with not knowing the solution to the puzzle, or even if there WAS a solution to the puzzle, because I had a feeling they wouldn't actually tell us on the show.

I love solving puzzles, but I couldn't conceptualize it in my head. I'm not an engineer, but I was looking at it like what you described as binary-search and could see it was flawed.