Problem in logic

[boobatuba]

Exactly. That's what the guru is doing - telling them to solve for blue. That's the only "new information" I see.

Here's another thought to ponder.

If you consider the probability trees that everyone on the island would have designed before the guru spoke, no one could know for sure whether there were fewer people with blue eyes or brown eyes. They can't "solve" for either because they don't know which color to choose.

Almost everyone knows that there are either one or two people with green eyes...except for the guru! Since she doesn't know this, she can't leave on the first night. Everyone else also knows that the guru can't possibly know this. "Solving for green" is out before and after the guru speaks (nothing changes for the guru, after all).

They obviously can't "solve" for any other color that each of them might have themselves for the same reason they can't "solve for green."

After the guru speaks, everyone on the island knows for a fact that there are either less blue-eyed people than non-blue-eyed people or the same amount of each. They literally can't "solve for brown" anymore.

The only logical choice after the guru speaks is to "solve for blue."

 

[Ha'kiv]

After the guru speaks, everyone on the island knows for a fact that there are either less blue-eyed people than non-blue-eyed people or the same amount of each. They literally can't "solve for brown" anymore.

Wha.. Why? A brown-eyed person can, before and after the guru speaks, think there could be 100 blue-eyed people or 101 blue-eyed people (= more than brown-eyed people). Why would this change after the guru speaks? They can still think their eyes are blue or brown or any other color.

 

[Yoda]

The new information is that someone specific the guru was looking at has blue eyes.

That is not new information for the 'perfect logician.' Sure, for the case where there is 1 blue eyed person, it would inform them that they have blue eyes. In every other case everyone would see at least one blue eyed person, and therefore could generate the statement that the Guru sees someone with blue eyes. Since we have 100 people with blue eyes in the actual situation the Guru adds nothing.

 

[Ha'kiv]

I can't help but agree.

 

[boobatuba]

After the guru speaks, everyone on the island knows for a fact that there are either less blue-eyed people than non-blue-eyed people or the same amount of each. They literally can't "solve for brown" anymore.

Wha.. Why? A brown-eyed person can, before and after the guru speaks, think there could be 100 blue-eyed people or 101 blue-eyed people (= more than brown-eyed people). Why would this change after the guru speaks? They can still think their eyes are blue or brown or any other color.

Yeah, I missed that one scenario on the left hand side of the chart. Sorry.

I suppose, then, that only the people with blue eyes will be "solving for blue." But, since it will only take them 100 days to exhaust all possibilities and it would take the brown-eyes 101, it still works out that the blue-eyes will leave on the 100th day. They'll all have the chart on the right and not know any different.

Remember, after the guru speaks everyone is asking themselves the same question..."Am I the one she saw that has blue eyes?"

ETA: And that question everyone is asking themselves is important. It's why they can know what eye color they have when 99 blue-eyed people don't leave on the 99th day. And it's why, logically, everyone would be "solving for blue."

 

[Ha'kiv]

Well, I agree with all of that. The issue is what sort of new information is the Guru providing?

 

[boobatuba]

Well, I agree with all of that. The issue is what sort of new information is the Guru providing?

Again, she's providing information that one specific person she's looking at has blue eyes. That puts a binary condition into the equation...namely, she's looking at me or she's not. That binary condition is what allows the probability trees to shrink dramatically and allows the problem to be solved.

Maybe tomorrow I'll try and do a chart of the probability trees before the guru speaks that will more adequately illustrate the problem of solving the riddle without the guru's statement.

 

[Ha'kiv]

Still everyone is already aware of this so there is no new information. To me it only seems like.. an initiative.

 

[Yoda]

Again, she's providing information that one specific person she's looking at has blue eyes. That puts a binary condition into the equation...namely, she's looking at me or she's not. That binary condition is what allows the probability trees to shrink dramatically and allows the problem to be solved.

Maybe tomorrow I'll try and do a chart of the probability trees before the guru speaks that will more adequately illustrate the problem of solving the riddle without the guru's statement.

Nonsense.

I have no idea what color my eyes are, therefore I may have blue eyes or some other eye color.

Only blue matters because those are the only people who get to take the ferry.

I see one green eyed person, the poor bastard (I hope I don't have green eyes.)

I am a blue/other eyed person (I do not know this), I see 99 or 100 blue eyed people. I see 100 or 99 brown eyed people, the poor fucks (I hope I'm not one of them) and of course the one green eyed person in both cases.

In the case that I see 99 blue eyed people:
The green eyed person sees the same 99 I see, and then possibly me, so 99 or 100.

In the case that I see 100 blue eyed people:
The green eyed person sees the same 100 I see, and then possibly me, so 100 or 101.

Therefore the statement "The green eyed person sees a blue eyed person" is true.

If the green eyed person comes out and says "I see a blue eyed person" then they are not saying anything that isn't already known by a perfect logician, since the perfect logician has already come to that conclusion.

The solution in its simplest and easiest to comprehend form basically boils down to using the number of ferry trips as a counter. You leave on the trip iteration that corresponds to number of blues you see plus one, knowing that if everyone follows that rule the others would be a day behind and let out a big "FUCK!" on ferry ride #100 when all the blues they saw boarded.

The Guru's statement is pretty much something thrown into the riddle by whoever wrote it because they were thinking in terms of mathematical induction, not because it's necessary to solving the problem. If anything, it leads you to an incorrect conclusion in the case that the Guru doesn't speak before the first ferry trip.

 

[Ha'kiv]

The Guru's statement is pretty much something thrown into the riddle by whoever wrote it because they were thinking in terms of mathematical induction, not because it's necessary to solving the problem. If anything, it leads you to an incorrect conclusion in the case that the Guru doesn't speak before the first ferry trip.

Implying it's possible to figure out the color of your own eyes without the Guru's statement?

 

[boobatuba]

The Guru's statement is pretty much something thrown into the riddle by whoever wrote it because they were thinking in terms of mathematical induction, not because it's necessary to solving the problem. If anything, it leads you to an incorrect conclusion in the case that the Guru doesn't speak before the first ferry trip.

Implying it's possible to figure out the color of your own eyes without the Guru's statement?

No. By Yoda's method, everyone except the guru would board the ferry on the 100th day. Half would think they are part of the lucky blue-eyed people, and the other half would think they are part of the lucky brown-eyed people.

It's the restraints of the riddle that show this to be wrong. They can't "guess" their own eye color. Seeing 99 other people with a particular eye color tells you nothing about your own. The guru's statement sets the stage for the solution. The only reason the brown-eyed people and the guru can't leave is because they see 100 blue-eyed people instead of 99. They're all waiting to see if the 100 blue-eyed people they see leave on the 100th day. Then they say "fuck."

 

[Ha'kiv]

*sigh* I still see no new information. I give up. I'm just going to become a cleaning lady.

 

[Yoda]

No... my rule is leave on iteration number of blues I see plus one (me).

All browns (and the Guru for that matter) will see 100 blues. They will be scheduled to leave on day 101. All blues will see 99 blues, and be scheduled to leave on day 100.

Of course the 100 leaving on day 100 would interrupt the browns + Guru, they're not going to get on day 101, I thought I covered that by them saying FUCK!

The inductive loop of doom serves as a proof of why that works.

You're not even trying to address the main point. The point that the green eyed Guru can see blues, and everyone can deduce that the Guru can see blues because they're all looking at the same fucking people.

 

[Ha'kiv]

Why can't the browns leave, later?

 

[Yoda]

The act of leaving is based on the assumption of being blue. The actual blues will leave one turn earlier than the others, so the others will never leave because they will see the blues have already left, and thus they aren't blues.

 

[boobatuba]

No... my rule is leave on iteration number of blues I see plus one (me).

All browns (and the Guru for that matter) will see 100 blues. They will be scheduled to leave on day 101. All blues will see 99 blues, and be scheduled to leave on day 100.

Of course the 100 leaving on day 100 would interrupt the browns + Guru, they're not going to get on day 101, I thought I covered that by them saying FUCK!

The inductive loop of doom serves as a proof of why that works.

You're not even trying to address the main point. The point that the green eyed Guru can see blues, and everyone can deduce that the Guru can see blues because they're all looking at the same fucking people.

You're missing the point. How do they know that the blue-eyed people are the "chosen ones" before the guru speaks? How does everyone know the blue-eyed people are the ones destined to leave before the guru speaks?

You said the guru's statement was not necessary for them to solve the problem. How can you logically explain how it is that everyone knows the "chosen" people?

You can't. And that's why the guru's statement is necessary.

 

[Yoda]

You're right. I got the initial conditions wrong. I thought blue were the chosen people, not anyone who could figure out their eye color.

Now I'm leaning towards the "nobody not ever" is getting off the island answer that is explicitly stated as not being the solution.

Because the Guru's statement still isn't necessary. Everyone can still deduce that the Guru sees at least one blue eyed person. They can also deduce that the Guru sees at least one brown eyed person. That is all still in the initial conditions. So by being perfect logicians I'm not sure they can go any further.

 

[boobatuba]

Let's try looking at this another way.

Before the guru speaks, I can either see 99 blue-eyed people and 100 brown-eyed people OR 100 blue-eyed people and 99 brown-eyed people. I know nothing about my own eye color. I can't rely on a certain group leaving because I know that among that group all of them are in the same situation I am. No solution.

The guru speaks. I know from her statement that she is either talking about me or someone else.

If she is talking about me, then I know that there must be one more blue-eyed person than I can see (either 100 or 101 total). If she's not talking about me, then I know there's either 99 or 100 blue-eyed people (depending on how many I can see) and she's talking about one of them. Everyone else has the same realization.

No one can make any further deductions about the number of brown-eyed people. Everyone still thinks there's either 99, 100, or 101 of them.

Here's the tricky part. If you have brown eyes (unknown to yourself), you see 99 people with brown eyes and 100 people with blue eyes. On the 99th day after the guru's statement, the fact that the brown-eyed people you see don't leave still tells you nothing about your own eye color. Yours could be purple for all you know. You are still waiting on the blues to do something, as well, because you still don't know if there's 100 or 101 of them. You're going to be screwed, but you don't know it yet.

If you have blue eyes (unknown to yourself), you see 99 people with blue eyes and 100 people with brown eyes. You know for a fact there's either 99 blue-eyed people or 100 blue-eyed people (including yourself). You know that all the blue-eyed people see 98 others with blue eyes, 100 with brown eyes, and you. You know that those blue-eyed people you can see have come to the conclusion that either only 98 people have blue eyes (if you don't and they don't), 99 people have blue eyes (if you do and they don't OR you don't and they do), or 100 people have blue eyes (if both of you do). They don't leave on the 98th day. They don't leave on the 99th day. The only conclusion left is that you have blue eyes and you leave with them on the 100th day.

So, you see, the guru's statement makes all the difference in the world (or, on the island). It allows each person with blue eyes to possibly include themselves in the "blue group" and leave when they realize they must be in that group.

Whew.

 

[Yoda]

The guru speaks. I know from her statement that she is either talking about me or someone else.

If she is talking about me, then I know that there must be one more blue-eyed person than I can see (either 100 or 101 total). If she's not talking about me, then I know there's either 99 or 100 blue-eyed people (depending on how many I can see) and she's talking about one of them. Everyone else has the same realization.

Hmm, I think we're going in circles here. Do you disagree that from the initial conditions that all 200 non-Gurus know that the Guru sees at least one brown and one blue? If you can deduce that, the statement the Guru makes is redundant. It's only useful if the Guru would say something like "And the blue eyed should leave" putting them into that frame of mind.

It's not logical to "assume blue" based on the "I see at least one blue" statement, at best that's reading between the lines.

 

[boobatuba]

Hmm, I think we're going in circles here. Do you disagree that from the initial conditions that all 200 non-Gurus know that the Guru sees at least one brown and one blue? If you can deduce that, the statement the Guru makes is redundant. It's only useful if the Guru would say something like "And the blue eyed should leave" putting them into that frame of mind.

It's not logical to "assume blue" based on the "I see at least one blue" statement, at best that's reading between the lines.

Not really. She says "I see someone with blue eyes." Everyone then knows that she either sees them or someone else. This introduces a new set of probability trees.

You'd be correct if she said "I see at least one blue."

And, yeah. Everyone knows that the guru sees either 99 browns, 100 blues, and them OR 100 blues, 99 browns, and them. It just doesn't give them a solution to the problem.