The Hint System in Intandis

In intandis, after you play the puzzle for a while badly, then you get a hint. The hints are pretty early on in the process, right? Because, as ah zack pointed out nicely, it's a sequence of operations that you have to get from a to z. Um, and that seems not trivial to me, to find where you're going to put the hint. So i'm just curious, how did you figure out, for each individual puzzle, which was like the most important hint that you could give?