A logic puzzle

Mat · 18 Oct 2006 at 11:48

rangor gubbins said:
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.

Thats very astute of you considering whats in your sig

SpeedFreak · 18 Oct 2006 at 11:51

They are all colour blind.

Helium_Junkie · 18 Oct 2006 at 11:52

Then surely they would have told others they had to leave long before this tourist came...

SpeedFreak said:
They are all colour blind.

Tried that, was told off

SpeedFreak · 18 Oct 2006 at 11:53

lol, I should read the posts and the questions properly next time

Arcade Fire · 18 Oct 2006 at 11:54

karoshi said:
'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?

Just because there's at least one person with green eyes, that doesn't mean that there has to be at least one with blue eyes.

'At least one' includes 'all' within it - it doesn't mean the same thing as 'all' but equally 'at least one' doesn't imply 'not all'.

Arcade Fire · 18 Oct 2006 at 11:55

rangor gubbins said:
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.

Nah, that would amount to talking about their taboo, which they don't do. In any case, just because someone doesn't answer a question you ask them, you can't infer that the answer must have been something you don't want to hear. It's equally possible that the person you ask just doesn't want to talk to you.

rangor gubbins · 18 Oct 2006 at 11:57

Before the tourist came along they could live in ignorant bliss as eye colour is a taboo. Before the tourist left the island the fact that at least someone had to leave was never brought up. After the tourist leaves they know someone must leave, but each one doesn't know if he/she should leave. Hence each asks if he/she should leave.

edit: bu**er. Thought i was onto something there

karoshi · 18 Oct 2006 at 11:58

Arcade Fire said:
Just because there's at least one person with green eyes, that doesn't mean that there has to be at least one with blue eyes.

true, but with the information they have, and not being able to discuss eye colour, they cannot logically prove that there are no people on the island with blue eyes..

they cannot see their own eyes and cannot be told that their eyes aren't blue?

Arcade Fire · 18 Oct 2006 at 11:59

karoshi said:
true, but with the information they have, and not being able to discuss eye colour, they cannot logically prove that there are no people on the island with blue eyes..

Yes they can. Although it might take a while...

Hugogo · 18 Oct 2006 at 11:59

Theres now one person there that will talk about eye colour and tell people if they have green or blue eyes?

rangor gubbins · 18 Oct 2006 at 12:00

they all leave the island to some place sensible where they can look in mirrors and talk about eyes. They all realise they can't go back to the island as they all have green eyes.

I know, i know. i'm getting stupid now.

rangor gubbins · 18 Oct 2006 at 12:02

it doesn't have anything to do with genetics does it?

Belly · 18 Oct 2006 at 12:08

They were all born that day and intended to leave at sunrise?

karoshi · 18 Oct 2006 at 12:15

Arcade Fire said:
Yes they can. Although it might take a while...

ok so am i right in thinking that on the first sunrise after the visitor no-one leaves?

rangor gubbins · 18 Oct 2006 at 12:16

They all already know that they all have green eyes, but because it was never mentioned nobody had to leave.
After the stranger leaves one person must leave. One of them leaves, but as he/she leaves the island he/she also turns round and says "at least one you has green eyes". The next sunrise one more has to leave. and so on, until all of the islanders have left.

manoz · 18 Oct 2006 at 12:18

Battle Royale?

Arcade Fire · 18 Oct 2006 at 12:18

karoshi said:
ok so am i right in thinking that on the first sunrise after the visitor no-one leaves?

Yes.

Arcade Fire · 18 Oct 2006 at 12:19

rangor gubbins said:
They all already know that they all have green eyes, but because it was never mentioned nobody had to leave.
After the stranger leaves one person must leave. One of them leaves, but as he/she leaves the island he/she also turns round and says "at least one you has green eyes". The next sunrise one more has to leave. and so on, until all of the islanders have left.

No. You don't need to make any extra assumptions - everything you need is in the first post.

e36Adz · 18 Oct 2006 at 12:20

rangor gubbins said:
They all already know that they all have green eyes, but because it was never mentioned nobody had to leave.
After the stranger leaves one person must leave. One of them leaves, but as he/she leaves the island he/she also turns round and says "at least one you has green eyes". The next sunrise one more has to leave. and so on, until all of the islanders have left.

but if you were on the island and had blue eyes, and saw 49 people around you with green eyes, why would you ever leave and how would you ever know your own eye colour?

the stranger only said 'at least one of you has green eyes' in which case you can quite happily see everyone else with green eyes around you so assume he may have been talking about them.

I can't see how anyone would know their OWN eye colour from the info given, but i'l keep thinking.

Arcade Fire · 18 Oct 2006 at 12:22

e36Adz said:
but if you were on the island and had blue eyes, and saw 49 people around you with green eyes, why would you ever leave and how would you ever know your own eye colour?

the stranger only said 'at least one of you has green eyes' in which case you can quite happily see everyone else with green eyes around you so assume he may have been talking about them.

I can't see how anyone would know their OWN eye colour from the info given, but i'l keep thinking.

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?