I've contemplated the "ark" question. Imagine the end of the world, but the ability to construct an ark to ensure the continuation of the species on some suitable planet after a one-way journey.
How many scientists would you need to put on the ship to encompass a working knowledge of all the technical skills presently available to humankind?
My guess is that no single person grasps more than about 0.1% of all the technical fields, so the number would be about 1000 at a minimum.
I'm presuming that the ship is carrying a copy of the internet (on some sort of disconnected storage device), so it's not about remembering facts, but about carrying knowledge.
Any other speculation? And then, the same question for the arts...