I no longer believe this either.

ah I see, I guess I didn't notice when you switched...

↪Philosophim I'm asking you to imagine something. That's it. Either you can, or you can't. If you cannot imagine any different scenario than the one presented, then you will be incapable of understanding the logic of the solution. — flannel jesus

Ok, so I'm going to assume that YES, its always 201 people, but that the eye color can vary at any one time. In that case, the solution is trivial. Obviously if the eye color can vary, then in the case where one person could see everyone else did not have blue eyes, they would know they have blue eyes. Flannel, your logic puzzle needs another pass on clarity. People not understanding the rules of your puzzle isn't a puzzle, that's just confusing.

My disagreement is that you need the guru to say something just to make the counterfactual work.

"people" aren't misundedrstanding anything. Only you. Person, singular. You're getting tripped up on literally nothing. You're inventing stuff to be confused about.

I didn't invent this logic puzzle. This isn't mine. This was invented by a smart guy, and many smart people did the puzzle and liked it. People aren't confused, you're confused.

Obviously if the eye color can vary, then in the case where one person could see everyone else did not have blue eyes, they would know they have blue eyes. — Philosophim

So, now imagine this:

2 blue eyed people, 198 brown eyes. Guru says "I see someone with blue eyes". What do you think happens then?

My disagreement is that you need the guru to say something just to make the counterfactual work. — hypericin

Here's my best attempt to prove this:

1. As of right now, everyone has come to know that everyone knows that green sees blue through some means or another
2. If (1) is true and if I do not see blue then I am blue and will leave this evening
3. If (1) is true and if I see 1 blue then if he does not leave this evening then I am blue and will leave tomorrow evening
4. If (1) is true and if I see 2 blue then ...
...

[repeat for brown]

That as a practical matter (1) is true in counterfactual scenarios (2) and (3) only if someone says "I see blue" isn't that someone must say "I see blue" in every counterfactual and actual scenario for (1) to be true and for this reasoning to be usable.

The only requirement is that (1) be true, and in the actual scenario in which there are 100 brown, 100 blue, and 1 green, (1) is true even if nobody says anything. Our perfect logicians know (1) from the moment they lock eyes, and so immediately apply the above reasoning and start their daily counting, allowing the blues and browns to leave on the 100th day knowing their eye colour without anyone having to say anything.

2 blue eyed people, 198 brown eyes. Guru says "I see someone with blue eyes". What do you think happens then? — flannel jesus

If this answer is something like, "Everyone will turn and stare at the two blue eyed people, I'm going to be angry. That's not a logic puzzle, that's a riddle. Logically it is not definite that people will turn around and all stare at the blue-eyed people at the same time, as the blue eyed people would need to be looking at both blue eyed and green eyed people to see who's staring at who.

Logic puzzles leave no room for human error or uncertainty.

If this answer is something like, "Everyone will turn and stare at the two blue eyed people, I'm going to be angry. That's not a logic puzzle, that's a riddle — Philosophim

so you're inventing nonsense to be confused about, and now you're inventing stuff to be angry at.

Try to use logic and think about it. Let me know if you want the answer to this scenario with 2 blue eyed people.

so you're inventing nonsense to be confused about, and now you're inventing stuff to be angry at.

Try to use logic and think about it. — flannel jesus

No, I'm done if you won't confirm that I had the rules right at this point. I just feel like you're trolling. If you want me to keep playing, please confirm my understanding that there are at the time the elder is speaking, 100 blue eyes, 100 brown eyes, and 1 green eyed elder.

you won't confirm that I had the rules right at this point. — Philosophim

There were no "rules" about how many people can be on the island. It's an island. However many people you want are on the island. I laid out the scenario and told you how many people of each eye color ARE on the island. That's not a rule, that's just a fact. I don't know why you want it to be a "rule" - seems like something you're just actively confusing yourself about.

There are 100 blue eyed, 100 brown eyed, 1 green eyed. That's not a "rule", that's just the scenario.

Those people can't see their own eye color, so they don't know that's the scenario. A blue eyed person thinks it could be the case that there are 99 blue eyed, 101 brown eyed, 1 green eyed, or maybe his eyes are green instead of brown, or maybe his eyes are amber.

There are 100 blue eyed, 100 brown eyed, 1 green eyed. That's not a "rule", that's just the scenario. — flannel jesus

This is a logic puzzle, every detail is an important rule. If you misunderstand or don't think critically about everything, you're going to miss out. Thank you, I'll think about your scenario again. I find it odd that you mention the day they would leave.

You won't find it odd if you allow me to show you the rest of the logic. Shall I lay out what happens with 2 blue eyed people?

Sure I'm game. I'm not seeing how either could know.

So, we've established that IF there were only 1 blue eyed person, he'd leave on the first night, right?

"They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island"

So, in the case of 2 blue eyed people, let's get into one of their heads. I'm going to be thinking as the blue-eyed person right now:

I see 1 blue eyed person and 198 brown eyed people and 1 green eyed guru. The guru just said she sees someone with blue eyes.

either (a) the blue eyed person I see is the ONLY blue eyed person,
or (b) my eyes are blue as well, and we both have blue eyes..

If (a) is true, the blue eyed guy I see will leave the first night.

<So I wait the first night, wake up second morning, and look around, and I see that the blue eyed guy is still on the island>

So that means (a) isn't true, and (b) must be true, so I can catch the ferry on the second night.

You might think that they shouldn't reason this way, but nonetheless if they do reason this way then they know that either 199 or 200 of them will leave knowing their eye colour. — Michael

Ok, I concede. You are unteachable.

I see, the detail I was missing was not thinking in terms of days later. It just takes glossing over one detail to throw you off. I can see that working for two. If you looked around and saw only one, and they didn't leave, then yes, that would mean one other person had to have blue eyes, and logically that would be you.

Alright, let me tackle 3 now as I think I see what you're getting at. From my perspective, I would see 2 blue eyed people. I don't know if I have blue or green eyes. But if I had green eyes, I would see one more blue-eyed person than someone with blue eyes. So after the second day, if no one left, from the blue eyes perspective people, they would know that the other two blue eyes see one more blue eyed person. So by day 3, all blue eyed people will leave.

I'm assuming this pattern continues up to day 100. The reason why blue can do this is because green eyed people will be doing the same calculus, but one day behind blue. Ok, that's pretty cool!

So by day 3, all blue eyed people will leave.

I'm assuming this pattern continues up to day 100 — Philosophim

Yes!

green eyed people will be doing the same calculus, but one day behind blue. — Philosophim

Will they?

in his defense, he did learn that the logic he laid out doesn't work for 2 blue eyed people, nor 3. I think he's teachable but just impatient. He keeps trying to skip right to the final conclusion without taking his time building up solid premises

Yeah, I follow, there is definitely a case to be made. This puzzle has been confusing the fuck out of me. The core problem is, I think you understand, at what point is (1)?

n=3: no, every blue thinks it could be 2
n=4: no, every blue thinks it could be 3
n=5: no, every blue thinks it could be 4
...

that's my take, for the "guru says nothing" scenario. I have no reason to think that logic doesn't hold all the way to to 100, or any other number

And yet, it is wildly unintuitive that (1) is false when n=100, or 1000, or 10000, or...

Hey no editing.

For (1) to be false, blue A must see blue B , and know that B sees blue C, but not know that B knows that C sees a blue.

This doesn't seem possible when n=100.

Actually Michael still keeps green:

1. As of right now, everyone has come to know that everyone knows that green sees blue through some means or another — Michael

So for this to be false, we must find some blue that can find some blue that they aren't sure knows green sees a blue.

How will you do this when n=100?

don't start at 100. Start at the minimum possible number of blue eyes.

It's gotta be something like 3 or 4 right?

To clarify, this calculus is to see if they have blue eyes. And I mixed up colors, I meant brown eyed people, not the elder. Once all the brown eyed people leave, then at that point the same thing would happen with the brown eyes people. On day 101 the game would begin again for the brown eyes, and at day 200 they would all leave as well. Finally the elder would leave at day 201. Do I have it right?

I don't think so. I only think blue eyed people can leave. Anybody else can have any possible eye colour, they have no way of knowing

↪Philosophim I don't think so. I only think blue eyed people can leave. — flannel jesus

Ok, and I might be wrong on this, but I'll put my logic out.

Once all the blue eyed people leave, then everyone else sees just brown eyed people and the elder. Meaning that essentially the elder just said, "I see someone with brown eyes". And at this point, I think I was wrong on it taking another 100 days. If you see 99 people with the same eye color and they don't leave, they all are uncertain of their own eye color. But, since all 99 don't leave the next day after blue eyes leave, that's because they each brown eyed person realizes 'I must have brown eyes, otherwise they all would have left'. So its day 101, that none of the brown eyes people leave, then they leave on day 102. Finally day 103 the elder would leave as no one is left on the island.

But, since all 99 don't leave the next day after blue eyes leave, that's because they each brown eyed person realizes 'I must have brown eyes, otherwise they all would have left'. — Philosophim

Why would they have?

Why would they have? — flannel jesus

Let me think through it again. The elder has green, first person view doesn't know if they have green, brown, or some other color eyes.

After all the blue eyes leave, everyone sees that there are only brown and one green eyed person. No one would leave the first day. But what do we learn from that? The elder learns they do not have brown eyes, nor blue eyes, but, something I missed, they'll never know they have green eyes so can't ever leave the island.

Since the elder doesn't leave, the brown eyes who don't know their own color know they don't have blue or green eyes. So I guess this leaves the idea that they could have some unknown color like red. At this point it means there is only one eye color that is uncertain, each brown eyed person doesn't know if they have brown eyes. So perhaps I was right the first time and they would simply follow the logic that the blue eyes people did. I would think further, but I have to go to work. Again, fun puzzle. :)