This may also be why students objected so vehemently when I would insist on doing "sideways" examples to the questions they had. For example, if they wanted to learn how to solve x/2 - 7 = 18, I'd present them with 3x + 5 = 10 (difficulty scaled depending on the particular student and my best judgement). They hated that, because I wasn't "answering the question." And no, I wasn't answering their specific "how do I solve this exact problem" question, but I was trying to get them to develop slightly more generalized tools. (By year's end I was able to get away with, "What would you try first?" and get responses most of the time. But early on, you have to guide them into a culture of problem-solving rather than a "received knowledge" model where the teacher is agent and problem-solver and the student is the passive receiver of tricks & tools.)
That's such a nice way of expressing the opposite of guessing the teacher's password.