Looking for a question which has a definate, immediately recognizable answer, that we just do not know yet.
Not looking for metaphysical, probably not logic questions either.
My best, and another answer, follow below.
The question was posed to me over coffee this morning, with one question; give proof of fermat's last theorum. We don't have one, but if one was given it could be 'proven' correct. So, it would be advanced knowledge, thus the 'alien' part of the game.
I first suggested a unified theory of relativity, but hey, maybe that was asking too much.
My best question is an improved construction method. Truss, girder, rebar... I answered that perhaps 'they' could produce plans for a 'weave' that could be used to for a building. Perhaps the whole structure sharing the load, and made safe b/c it is so over powered that one section will not fail, so no cascade failures. I figured this 'weave' could be tested out on a design program easily enough to show if it worked.
My friend then told me that after 4 years of eng, one thing he learned was, " you can't push a rope."