A logic puzzle

e36Adz · 18 Oct 2006 at 12:28

Arcade Fire said:
The hint I gave before is quite good, I think.

What would happen if there was only one person with green eyes?
What if there were two people with green eyes?

If there was only one person with green eyes, he would see 49 people with blue eyes and leave after the first day since he KNOWS that he must be the one with green eyes, if 'at least one person has green eyes'.

If there were two people with green eyes, they would erm see 48 blue and 1 green eyed person, therefore assume that the 1 green eye person may have been the one the visitor was talking about? But wait a minute, if that guy doesnt leave he must assume that he is also viewing a green eyes person, which would be HIM therefore the next day he would leave, im onto it

edit: the above might not make much sense and I might not really be onto anything

sarutobi · 18 Oct 2006 at 12:31

all of whom have either blue eyes or green eyes.

we could read that as the islanders know that either everyone has blue eyes or everyone has greeneyes and not a mix

There's an odd tradition on this island, whereby anyone who finds out that they have green eyes must leave the island at sunrise the next day.

we could read that as the islanders know that either everyone has blue eyes or everyone has green eyes and not a mix.

so when the stranger tells them that at least one person has green eyes then they deduct that everyone must have green eyes, and then they all leave one day after the other?

rangor gubbins · 18 Oct 2006 at 12:31

ok. I think i have it (from your clue).
If there is only one person on the island he/she must leave straight away.
If there is two people (A and B) on the island and at least one has green eyes, then first they will wait one sunrise to see if the other leaves. If one (person A) leaves straight away it must be because he/she sees person B has blue eyes, and that only leaves person A to have green eyes. If neither A nor B leaves on the first night, then they must both leave on the following sunrise, as they realise both of them have green eyes.

therefore
After 50 days all the islanders leave at once

Snow-Munki · 18 Oct 2006 at 12:31

they all start mating and then from their kids deduce if they have green or blue eyes ?? :confused:

sarutobi · 18 Oct 2006 at 12:36

rangor gubbins said:
ok. I think i have it (from your clue).
If there is only one person on the island he/she must leave straight away.
If there is two people (A and B) on the island and at least one has green eyes, then first they will wait one sunrise to see if the other leaves. If one (person A) leaves straight away it must be because he/she sees person B has blue eyes, and that only leaves person A to have green eyes. If neither A nor B leaves on the first night, then they must both leave on the following sunrise, as they realise both of them have green eyes.

therefore
After 50 days all the islanders leave at once

yeh, i change my answer to this too

Arcade Fire · 18 Oct 2006 at 12:38

Aye, you guys have it. Good skills.

Now, the more interesting question is this. Given that the stranger only tells everyone something that they already know, why is the stranger necessary at all?

Amp34 · 18 Oct 2006 at 12:41

rangor gubbins said:
ok. I think i have it (from your clue).
If there is only one person on the island he/she must leave straight away.
If there is two people (A and B) on the island and at least one has green eyes, then first they will wait one sunrise to see if the other leaves. If one (person A) leaves straight away it must be because he/she sees person B has blue eyes, and that only leaves person A to have green eyes. If neither A nor B leaves on the first night, then they must both leave on the following sunrise, as they realise both of them have green eyes.

therefore
After 50 days all the islanders leave at once

Why wait 50 days?

And as there is 50 people, all of who have to leave you cant really compaire it to just two. If there were 3 people it wouldnt work either as the third would assume both A and B think it is each other. :confused:

rangor gubbins · 18 Oct 2006 at 12:42

because he did something the islanders could never do which was state that at least one person must leave. Without the stranger the islanders all know that the other 49 of them must leave, but can't mention it.

rangor gubbins · 18 Oct 2006 at 12:46

if there is 3 people (A, B, and C) and C has blue eyes. A and B will wait to see if either A or B leaves. If neither of them do, then they must assume they both have green eyes.

Amp34 · 18 Oct 2006 at 12:57

rangor gubbins said:
if there is 3 people (A, B, and C) and C has blue eyes. A and B will wait to see if either A or B leaves. If neither of them do, then they must assume they both have green eyes.

But all of them have green eyes so that analogy doesn't work. C will assume both A + B can't work out who has the green eyes and assume that he has blue. A will assume the same about B + C and B will assume the same about A + C. When you multiply that to 50 people it gets even worse.

Arcade Fire · 18 Oct 2006 at 12:57

Amp34 said:
Why wait 50 days?

And as there is 50 people, all of who have to leave you cant really compaire it to just two. If there were 3 people it wouldnt work either as the third would assume both A and B think it is each other.

Let's say there are three people, and they all have green eyes.

A knows that B and C can see at least one person with green eyes, because they can see each other. Therefore neither of them will leave on the first day.

If A doesn't have green eyes, then B and C will both have to leave on the second day - since they both see that the other hasn't left.

However, B and C are both applying the same logic, so they don't leave on the second day - B is waiting for A and C to leave, and C is waiting for A and B to leave.

Since none of them have left on the second day, there is only one possibility - they all know that each of the others can see two people with green eyes, and so each of them works out that they must have green eyes too. Hence everyone leaves on the third day.

Exactly the same process applies to an island of fifty people, it just takes longer and is more complicated.

Amp34 · 18 Oct 2006 at 13:00

Ah ok I see now. That makes sense.

Helium_Junkie · 18 Oct 2006 at 14:26

You killed my brain.

unwashed potato! · 18 Oct 2006 at 22:36

i just got it i think,

this thing everyone saying about how they watch and see if anyone leaves, well as there is 50 people they all watch to see if one goes on day one, but then no one leaves, and as there is 50 peopel it will take 50 days for them to reailse then that it must be them, and they all leave on day 50?

must be right? maybe my explanatnion doesn't make most sense but im sure its right

[EDIT]
actually reading above i tinhk the guy beat me to it

[EDIT 2]
ok they guy is the OP anyways, well after reading most of this thread i worked it out though no one will ever know or care

Pudney · 18 Oct 2006 at 23:00

Arcade Fire said:
Aye, you guys have it. Good skills.

Now, the more interesting question is this. Given that the stranger only tells everyone something that they already know, why is the stranger necessary at all?

Because you're ignorant of your current state.