Interesting Logic Problem

[BeanDip4All]

nobody leaves for the first 99 midnights, then all the blue eyed people leave at once.

once the phrase is uttered a blue eyed person needs to wait 99 midnights before they can make the decision (because each of the other 99 people who have blue eyes can leave any midnight). after 99 days a blue-eyed person knows that every other blue-eyed person sees at least 99 other blue-eyed people, so s/he leaves. a brown-eyed person has to wait a day more, because they have 100 blue-eyed observations, but at that time all 100 blue-eyed people are left.

f2f is on the right track.

My answer was, on the 100th day, all 100 blue eyed people will leave the island.

Think about if there was just one person with blue eyes on the island- he would know that they would leave the first night, becuase he knows he is the only person the Dr. was talking about. He would look around, see no one else, and know he should leave. So (THEOREM 1) if there is one blue eyed person, they would leave the first night.

Now consider there are two blue eyed people. On day 1, X thinks to himself, "Suppose that I don't have blue eyes. Since I can see one person (Y) with blue eyes, this must be the one-person case. Thus, Y, seeing nobody else with blue eyes, will leave tonight." (THEOREM 1) But Y doesn't leave that night, so on day 2, X thinks to himself, "Well, Y didn't leave, so Y must seen somebody else with blue eyes. That is, because they are all perfect logicians, Y must not have gone through the reasoning I went through. Thus, I must also have blue eyes." X does the same thing with Y, and they both leave the second night.

Thus, (THEOREM 2): If there are two blue-eyed people on the island, they will each leave the 2nd night.

This continues with the group leaving en mass on the corresponding night of the # of people in their group. When you reach the 99th night and no one has left, all 100 blue eyed people will leave together on the 100th night. Think of it as all the blue eyed people on the island playing a big game of chicken with each other, right up until the 100th night. Good thing they are all "perfect logicians!"

The fact that the time of day the Doctor speaks, as well as the fact that the ferry comes once a day, is included in the question implies that the daily cycle has some significance. If the Doctor only spoke once, the daily cycle would be meaningless. So....

If he speaks only one time, then I'm with AbsolutStoli, ferry pilot. But if the Doctor speaks once a day every day, then there is another answer...but that's not how the question was worded.

Yes, but the critical point is that he only speaks once. He doesn't reveal anything the people on the island don't already know, they can all look at each other and see someone with blue eyes. The Doctor speaking merely starts the cycle of blue eyed people leaving.

When I was talking it over last night, I was having fun asking, "What if there's a blind person on the island?" Also, when do they make a Wilson volleyball for company?

[Viva]

And its flat wrong b/c the doc only speaks once... ever... proving that this is a fucking retarded island to live on and they should all die.

Maybe a Japanese whaling ship will stop and rescue all of them.

[Boomer28]

100th day, all blue eyed people leave

[summit]

This is starting to make some sense... but the lifts open in 5 minutes and I still think ya oughta kick the prof in the nuts for creating such a miserable life for these people.

[berko]

My woman left the island with a brown eyed man, well I still dont seem to care.

[Tippster]

They should all leave the island on the first night because it is retarded, like Summit said.

Or have an orgy.

[Steven S. Dallas]

Or have an orgy.

They're a bunch of logicians. To them, this is an orgy.

[Tippster]

That's sad. Let's dose them all with Acid.

[Woodsy]

bad idea
logicians/mathies on acid will melt your fucking mind
trust me.

[MeatPuppet]

f2f is on the right track.

My answer was, on the 100th day, all 100 blue eyed people will leave the island.

That seems to work...assuming that everyone on the island had their synapse replaced with transistors

Do you think your Prof will be buying dinner for many people?

[MeatPuppet]

They should all leave the island on the first night because it is retarded,

The first group who tried that died under the treadmill.

[TeleMang]

How about another one just to keep things rolling.

There is a hallway that is 'x' yards long. Every yard there is a lamp with a string attached (for switching the lamp on/off). The first person walks down the hallway pulling every string (thus turning every light on). The second person sees this (and for some unknown reason is really pissed) and decides to go through pulling every second string. The third person, not be left out, goes through pulling every third string. This continues for a total of 'n' people. How many lights are left on after every person has walked through?

[pechelman]

question here
why is it important that the doctor had to speak?

everyone on the island also "saw someone with blue eyes"

why is this supposedly the catalyst for the logic?
i guess we dont know how many days the people have been there.
would be worth mentioning

[Tippster]

Are there any Polar Bears on this island?

[Steven S. Dallas]

The doctor is a polar bear, but he's wearing dark glasses.

[edg]

How about another one just to keep things rolling.

There is a hallway that is 'x' yards long. Every yard there is a lamp with a string attached (for switching the lamp on/off). The first person walks down the hallway pulling every string (thus turning every light on). The second person sees this (and for some unknown reason is really pissed) and decides to go through pulling every second string. The third person, not be left out, goes through pulling every third string. This continues for a total of 'n' people. How many lights are left on after every person has walked through?

1, the first one?

edg

[Long Duck Dong]

My woman left the island with a brown eyed man, well I still dont seem to care.

Hey, good times, bad times, I know I've had my share.

[BeanDip4All]

1, the first one?

edg

Correct. The logic of the problem dictates that each additional person skips X + 1

X equals 2 for the first person, 3 for the second, 4 for the third, etc.
so eventually every light will be turned out except for the first one b/c X will never equal zero

[TeleMang]

1, the first one?

edg

Nope,

To make it easier... lets say x=100=n

[Viva]

The doctor is a polar bear, but he's wearing dark glasses.

He came to the island because he wanted to fuck a zebra.

[Steven S. Dallas]

He came to the island because he wanted to fuck a zebra.

Correct. This is all taking place at Hedonism II.

[TeleMang]

Correct. The logic of the problem dictates that each additional person skips X + 1

X equals 2 for the first person, 3 for the second, 4 for the third, etc.
so eventually every light will be turned out except for the first one b/c X will never equal zero

Not quite,
Person 1 goes through pulling the string on every light (on, on, on, on, on, on)
Person 2 goes through pulling the string on every other light (on, off, on, off, on, off)
Person 3 goes through pulling the string on every other on every third light (on, off, off, off, on, on)

Note person 3 turns back on one of the light that person 2 turned off.

Perhaps the initial question was worded poorly.

[pechelman]

^^^ nah i understood it'
pretty complex

looking at the light pattern right now
craziness

is the answer is a mathematical formula?
seems like it would have to be

[BeanDip4All]

question here
why is it important that the doctor had to speak?

everyone on the island also "saw someone with blue eyes"

why is this supposedly the catalyst for the logic?
i guess we dont know how many days the people have been there.
would be worth mentioning

Because while everyone is capable of the inductive modeling described with or without the Dr's information, the Dr. is still necessary to start the countdown for when they leave the island. He provides nothing quantitative.

Why the dr. is needed is that he provides a definitive starting point. We know everyone is present for his statement and it creates a logical timeframe for a new set of logical modelling, because it is the first time everyone knows that everyone knows, etc...;

Pechelman, I agree with you that the information he provides isn't needed for the modeling, provided they had a logical starting point already.

[Woodsy]

ya know,
pictures of you & girlski togeter in the shower in the Cliff lodge make the whole thing moot.