In the case of "solve this puzzle" questions, upvote any answer that you think contains an insightful answer to the question. Even if it's wrong, there must be some value in it if you're even considering voting up. In the case of certain (kinds of) puzzles, a "wrong" answer may mean "not the canonical answer". In others, an answer that misses one "rule" might reach a very interesting alternate conclusion.
Of course, remember that this isn't a social site; an upvote doesn't mean "I like you and want you to get points" or "good job, you tried". Upvote answers based on the quality of the answer alone.
The bottom line, though, is that there is no proper way to vote. Upvote answers you think have value, downvote ones that don't. The community will vote their own opinion, and one or two weirdos will be drowned out if an answer is obviously one way or the other.