For Shiggily and math lovers, Prob1: Beam them up , scotty!

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Aha, I finally get it now. Pretty clever. I'll remember that to challenge some of my classmates.

Actually I do have a niggling issue with this answer. To lead us to the issue, I'll rephrase it.

Given one settler with blue eyes in a group, the settler would leave within the first day.
Given two settlers with blue eyes in a group, each would reckon that if they do not have blue eyes, the other would leave within the first day. Or if the other does not leave within the first day, they themselves would have blue eyes. So the two settlers would leave within the first two days.
And so on.

Given one hundred settlers with blue eyes in a group, the one hundred settlers would leave within the first one hundred days.

What I have done which is different is that I have set an upper bound on the time for the blue-eyed settlers to leave (by "within") as opposed to just flat-out saying what it is, because I'm not entirely convinced that there is a rigorous proof as to their definitely leaving at the 100 day mark and not before. For that, I might need an argument that it is absurd that the blue-eyed settlers would come up with some other line of reasoning that would enable them to leave in less than 100 days.

So nobody wants to have a go at my riddle?

Um... you need to ask the same question to the three guardians, one you know the answer to. Two answer one way, one answers differently. Then you ask the different guardian, "is this the door to wealth beyond measure?" about two doors.

And if the question you asked had a true answer and the Guardian answers the same to one door, go through that one. And if the guardian answers negatively to both doors, go through the last one.