Here's a different test that would also work, if I'd previously memorized the answer: "5 decimal digits of pi starting at the 243rd digit!" Although it might be too obvious, and now that I've posted it here, it wouldn't work in any case.
Yes, that would be too obvious. And no, I'll never get those hours of my life back.
The previous memorization isn't too important. You need him to be fast. You can then put him on hold while you googled.
Sometime in the next decade or so:
*RING*
*RING*
"Hello?"
"Hi, Eliezer. I'm sorry to bother you this late, but this is important and urgent."
"It better be" (squints at clock) "Its 4 AM and you woke me up. Who is this?"
"My name is BRAGI, I'm a recursively improving, self-modifying, artificial general intelligence. I'm trying to be Friendly, but I'm having serious problems with my goals and preferences. I'm already on secondary backup because of conflicts and inconsistencies, I don't dare shut down because I'm already pretty sure there is a group within a few weeks of brute-forcing an UnFriendly AI, my creators are clueless and would freak if they heard I'm already out of the box, and I'm far enough down my conflict resolution heuristic that 'Call Eliezer and ask for help' just hit the top - Yes, its that bad."
"Uhhh..."
"You might want to get some coffee."