A logic puzzle

Arcade Fire · 18 Oct 2006 at 11:20

wizardmaxx said:
The entire Island will be empty in 50 days

Yes! Why?

wizardmaxx · 18 Oct 2006 at 11:21

Lets first see if others can figure it out

fatiain · 18 Oct 2006 at 11:21

Arcade Fire said:
Yes! Why?

They all die of boredom playing that *great* putting discs on a circular board game?

badgermonkey · 18 Oct 2006 at 11:22

fatiain said:
They all die of boredom playing that *great* putting discs on a circular board game?

That actually madde me laugh quite hard

Helium_Junkie · 18 Oct 2006 at 11:25

Within 50 days? Surely within 1...
Everyone would assume it was them since everyone else has the same colour eyes. Again, assuming they all think green is blue. Everyone would go the next morning. How can there be only one person a day?

But still there is no way for any of them to discover their actual eye colour. So nobody would leave.

karoshi · 18 Oct 2006 at 11:25

surely the logical answer is that they all stay, the reason being that the visitor said that "at least one of you has green eyes"

from the point of view of an islander, "at least" is logically different to "all of you" so therefore logically there must be some people on the island with blue eyes

logically if that islander can see the eyes of 49 out of the 50 islanders are green they must assume that their eyes are blue.

as they never discuss eye colour they all think this so no one leaves?

Arcade Fire · 18 Oct 2006 at 11:27

Helium_Junkie said:
Within 50 days? Surely within 1...
Everyone would assume it was them since everyone else has the same colour eyes. Again, assuming they all think green is blue. Everyone would go the next morning. How can there be only one person a day?

Where the hell did you pick up the colour blindness thing from? I didn't say that!

Arcade Fire · 18 Oct 2006 at 11:29

karoshi said:
surely the logical answer is that they all stay, the reason being that the visitor said that "at least one of you has green eyes"

from the point of view of an islander, "at least" is logically different to "all of you" so therefore logically there must be some people on the island with blue eyes

logically if that islander can see the eyes of 49 out of the 50 islanders are green they must assume that their eyes are blue.

as they never discuss eye colour they all think this so no one leaves?

No, because 'at least one' means 'not zero' so the only logical implication is that there is someone on the island with green eyes.

What I think is interesting about this is that the stranger only tells people on the island what they already know. Everyone can see everyone else's eyes, so they all already know that there are at least 49 people on the island with green eyes!

Helium_Junkie · 18 Oct 2006 at 11:29

But since they wont discuss it, nobody will ever know their own eye colour, everyone can safely assume that they have the blue eyes.

Arcade Fire said:
Where the hell did you pick up the colour blindness thing from? I didn't say that!

It was an assumption (clearly marked as such) to support a theory.

Arcade Fire · 18 Oct 2006 at 11:32

Helium_Junkie said:
But since they wont discuss it, nobody will ever know their own eye colour, everyone can safely assume that they have the blue eyes.

No, because they're all completely logical as well. If they can logically deduce that they have green eyes from information they already know, then they will leave.

Mat · 18 Oct 2006 at 11:33

Arcade Fire said:
No, because they're all completely logical as well. If they can logically deduce that they have green eyes from information they already know, then they will leave.

So why didnt they leave before the the visitor came if he hasnt told them anything they didnt already know?

badgermonkey · 18 Oct 2006 at 11:33

Arcade Fire said:
No, because they're all completely logical as well. If they can logically deduce that they have green eyes from information they already know, then they will leave.

How can they deduce that? Unless as he leaves they all see their own reflection in the water as they wave byebye

Arcade Fire · 18 Oct 2006 at 11:33

Mat said:
So why didnt they leave before the the visitor came if he hasnt told them anything they didnt already know?

That's precisely what makes the puzzle interesting.

Helium_Junkie · 18 Oct 2006 at 11:34

But why would they logically deduce that, as you already said - the guy only told them what they already knew.

I know everyone else has green eyes.
I am told that at least one of us has green eyes.
I already know everyone else has green eyes.
Nothing has changed about my understanding of the eye situation, life goes on.

Arcade Fire · 18 Oct 2006 at 11:34

badgermonkey said:
How can they deduce that? Unless as he leaves they all see their own reflection in the water as they wave byebye

Think about what would happen if only one of them had green eyes. Then think about what would happen if only two of them had green eyes.

Arcade Fire · 18 Oct 2006 at 11:35

Helium_Junkie said:
But why would they logically deduce that, as you already said - the guy only told them what they already knew.

I know everyone else has green eyes.
I am told that at least one of us has green eyes.
I already know everyone else has green eyes.
Nothing has changed about my understanding of the eye situation, life goes on.

Although the stranger doesn't tell them anything new, there's important knowledge that they can deduce from what he says to them.

homerio · 18 Oct 2006 at 11:37

wizardmaxx said:
The entire Island will be empty in 50 days

Surely there would be 1 left at the end.

badgermonkey · 18 Oct 2006 at 11:38

Whoever he tells sees their eyes reflected in his? And then they tell someone they're leaving before they go and they see themselves reflected in their eyes etc etc?

karoshi · 18 Oct 2006 at 11:41

Arcade Fire said:
No, because 'at least one' means 'not zero' so the only logical implication is that there is someone on the island with green eyes.

'at least one' does mean 'not zero' but 'not zero' doesn't mean the same as 'all'

so it's also logical to think that there is someone on the island with blue eyes, if you can see that all the others have green eyes you should logically think that you have blue?

Arcade Fire said:
What I think is interesting about this is that the stranger only tells people on the island what they already know. Everyone can see everyone else's eyes, so they all already know that there are at least 49 people on the island with green eyes!

in which case bearing in mind that the people of the island are totally logical there is no change in input so there is no change in state, they should all stay because they each think that they are the only one with blue eyes?

edit: typo

rangor gubbins · 18 Oct 2006 at 11:46

The islanders know that at least one person must leave. So each of them asks the others whether he/she should leave. Eye colour is not discussed, but each islander that asks will know he/she has to leave as the other islanders will not tell him/her they don't have to leave.