Puzzle thread? Puzzle thread.

[Arra]

I got this one really quickly and I have no idea how. Can you remember anything about your thought processes prior to the insight, Di? Interesting that you went for a smoke. The guy told me the puzzle at the pub and I think I went to pee. I recall realising how to do the prisoner one in the same circumstance. That is odd. :/ Spoiler for mundane thought process: It was nothing special, just chance. I randomly thought about the fact that there are an even number of prisoners (if it wasn't random I don't remember what led to this thought), then thought about all the possible combinations of whether the white/black hats are even or odd. Either there are odd numbers of both, or even numbers of both, but they can't be different. Then I considered that maybe that knowledge might be used to solve it somehow (not really believing it would). The back person knows the colors of those in front of him... but that knowledge is of 59 prisoners, an odd number, so one color must be even and the other odd. What if the back person just shouted black if black was odd and white if white was odd? Would the second person know his color? *epiphany moment* yes he would, and after he said his color the next one would know too. EDIT: The island one sounds interesting. It doesn't seem anyone can leave... The guru saying anything before anyone has left will do nothing, since everyone will see multiple blue-eyed and brown-eyed people so it's not like one could realize "everyone else has brown eyes so I must have blue eyes." But before she says anything no one can know either. They have absolutely no information about their own eye color. I'm assuming they can't communicate beforehand to plan out that the guru will speak on the nth day where n is the number of blue-eyed people, or something like that. Unless they're all supposed to figure out that that will give them all the best chances. But I doubt that's the answer, and it's hard to believe there is an answer.