Presumably the reason we created the AI in the first place is so it could solve problems for us, so someone needs to ask it questions. It might be safe-ish to restrict it to answering yes or no to purely mathematical questions.
I think yes/no to mathematical questions wouldn't be safer than yes/no to other questions: you still have a real-world reason for asking them, and the AI can lie about as well as it can on any yes/no question.
Asking for formalized proofs might be more promising, if you are able to produce a proof-checker that you have high confidence can't be hacked (this seems difficult but possible; proof checkers can be very simple programs but you need to guard both against ordinary attacks against the entire stack you're running on and against creative attacks like wa...
Eliezer proposed in a comment:
>More difficult version of AI-Box Experiment: Instead of having up to 2 hours, you can lose at any time if the other player types AI DESTROYED. The Gatekeeper player has told their friends that they will type this as soon as the Experiment starts. You can type up to one sentence in your IRC queue and hit return immediately, the other player cannot type anything before the game starts (so you can show at least one sentence up to IRC character limits before they can type AI DESTROYED). Do you think you can win?
This spawned a flurry of ideas on what the AI might say. I think there's a lot more ideas to be mined in that line of thought, and the discussion merits its own thread.
So, give your suggestion - what might an AI might say to save or free itself?
(The AI-box experiment is explained here)
EDIT: one caveat to the discussion: it should go without saying, but you probably shouldn't come out of this thinking, "Well, if we can just avoid X, Y, and Z, we're golden!" This should hopefully be a fun way to get us thinking about the broader issue of superinteligent AI in general. (Credit goes to Elizer, RichardKennaway, and others for the caveat)