[saagarjha]

It's actually not all that hard to stumble on the question at predictable spots. My process for solving a question I've seen before and one that is new to me actually doesn't differ all that much: as several clarifying questions at the start to confirm I understand the problem, then write a quick-n'-dirty solution as fast as possible. In this first pass I usually don't pay too much attention to things like bounds, which you wouldn't memorize anyways even if you knew the solution. Then I run a pass to polish the solution up, present it, then think of edge cases and how I'd test the solution. The only real difference is that I very rarely pretend not to have seen a question (I have done it twice, both in situations where it was clear the interviewer was out of questions and running down a list of things from memory, and I just wanted to humor them). You'd think that I'd be more sure of myself when I actually know the answer, but when I don't actually know what I'm doing I will usually come to the answer as I ask those clarifying questions and start stating the facts that usually score "this person at least has the gist of the problem" points, like "oh this is a graph and we're doing something with distance, let's see if Dijkstra is the right thing to apply".