Toadfish wrote:
Whatever floats your boat! But I mean, the Guru is one of the residents, so if she had blue eyes she'd have left too. At least that's how I interpreted the riddle. And in fact, the riddle could still be solved had she begun with 'I have blue eyes.'

The original question specifically said the Guru's eye color does not matter, and they are not attempting to get off the island. I used that to solve the answer, but I suppose you found a way to solve it another way.

I think the single most useful hint to really understanding the solution is thinking of the riddle in terms of a chain of hypotheticals: 'let's say I have brown eyes, what would the person next to me do on the Nth day?'

Essentially this becomes the correct way to look at it. My hint was more of an approach to start the puzzle - never to fully solve it.
CauTi0N: That's (the guru not playing) a very trivial detail related to this specific wording of the riddle. The Guru might as well be a player and the solution works just the same.
Hm. Well, if the Guru was one of the islanders, than there is no reason for a guru, right?

I solved it due to the Guru being not a part of the islanders. Think of the case where it's 1 blue eyed, 1 brown eyed. If the Guru says I see someone with blue eyes and are external, then the answer is obvious, and both will leave the first day.

However, say the Guru is an islander. The guru can't say anything now, because the islanders cannot communicate, and therefore neither islander can leave because they have no way of knowing what they are.

The same works for 2 blue and 2 brown. Without the words being said aloud, if the Guru were a blue eyed person, we have no idea that the other blue eyed person knows there is another blue eyed person or not. Therefore, you can't assume that the logic would work like in the original puzzle.

The Guru must not be an islander because of the specific wording which is found here:

"Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate."

However, my interpretation was that the Guru does not play due to their change in eye color. If the Guru were an islander but was still allowed to speak, then you and I are both correct. I just assume the Guru doesn't play because she's allowed to speak. Follow?
You mistake the forest for the trees. The information that "the Guru's eye color does not matter, and they are not attempting to get off the island" is not necessary for the solution and the riddle is solved either way; we may as well see the Guru as an "islander who can speak once".
"You mistake the forest for the trees." I like that. I think I'll use that some day.
It's actually a pretty well-known proverb where I live.
If the guru was an islander (with the ability to communicate once), the answer would not be the same.

Consider a group of 4 people, 2 blue and 2 brown. If the Guru is blue-eyed, then the other blue-eyed person would leave the first day. The Guru, however, does not know their own eye color, and then has to wait for the brown-eyed people to leave in order for themselves to leave.

However, say the guru is brown-eyed. Now, the two blue-eyed people would perform the normal logic and leave on day 2, which is not the same situation as the first scenario. The guru's eye color is important, and only when the guru is external can the answer always remain true.

I'm not saying it's not solve-able either way (or if I was, then I retract that statement), I'm saying that the clarity that the Guru is detached from the islanders allows for one, solid answer for any scenario. Also, when the Guru is an islander, the answer becomes dependent on the Guru's eye color, which I showed above.
I hand over that one to you, but it seems like a very minor detail related to this specific phrasing of the riddle. Taking more liberty, the Guru, being a perfect logician herself, would say "there is someone with blue eyes" rather than "I see someone with blue eyes"; as that's what she needs to say in order to find out her own eye color. Only place that bugs up is when there's nobody but the Guru that has blue eyes (in which case admittedly, there's a need for an outsider) (are those kind of cases automatically excluded by the assumption the Guru is truthful?).
That rephrasing would indeed cause it to work out exactly the same :)
What if the Guru lied, and no one had blue eyes? Everyone there would assume they were the one, but they'd be wrong.
Yeah, if the Guru lied you're screwed. P=
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