Turing tests and humans
The basic objective of a Turing test is to come up with such an intelligent machine, which actually mimics the human way of communicating.
For that purpose, we'll carefully need to think about what normal humans would like to talk about, in a casual manner. Starting the talks with a friendly, informal manner may be a good thing. After that, you might want to know about the interests of the person you're talking to; you might start with...say, football, or cricket, economical crisis, united nations; there are literally a lot of topics.
 Look up for the common trends in the humans...these can include some recent famous political scandals (I don't want to mention Panama Leaks here). Questions can be about the current good movies (hits and flops). You may even come up with a religious, or a philosophical discussion if that helps.
 Incomplete questions, and then stating "you know the rest" after a half phrase can also be a good practice, because of the common sense the humans have to infer the essence, and background meaning of the question.
 Last, but not the least, if you're going to ask the question from a chat-bot, then it is a real good thing that you place intentional grammatical mistakes, typos, and unclear phrases, that only a real human would be able to understand, because it's a natural thing for the humans to commit a mistake. Questions about past memories are also a good thing, especially when they are slightly offensive; discussing relationships, frustration, failures, fears etc. Emotion-based questions have more tendency to crack up the game.