Village of the Damned

[Paul Howe]

As promised, my villager eye colour puzzle. Its a long description but a good puzzle:

An archaeologist is exploring deep in the heart of the Indonesian rainforest, looking for signs that humans once lived here. Amazingly, he stumbles across a tribe of humans living in a village almost perfectly concealed by thick vegetation, and after observing them for a while realizes that he's the first person in the wider world ever to set eyes on these people.

Eventually, his intellectualy curiosity overcomes his fear of being slaughtered, and he makes himself known to the tribe. They are warm and hospitable, providing the archaeologist with food, drink and shelter. Over the next few months, the archaeologist turns anthropologist and stays with the tribe, observing their customs and slowly learning their language. During this time, he comes to realise two remarkable facts

1) The tribe is perfectly logical: given some piece of information, any member of the tribe is able to work out all the cosequences of that information in short time
2) The tribe has a bizarre taboo. Should any member come to know their own eye colour, they must make their way to the edge of a nearby cliff and commit ritual suicide by throwing themselves to their doom at the next sunset.

Making note of this taboo, the archaelogist compiles a census of the villagers and finds 100 with brown eyes and 100 with blue eyes. The villagers, being keen observers, also know the eye colour of all their fellows, except of course their own.

Finally, it's time for the archaelogist to leave. At midday the villagers gather to bid him farewell and the archaelogist makes a closing speech, during which he makes the following seemingly harmless comment: "Its so unusual to see people with blue eyes in this part of the world"

What are the consequences of the archaeologist's comment?

If seen this puzzle in a couple of different places on the internet so if you've seen it too and still post the answer here, needless to say you're a massive cock

[Charlie Reams]

An excellently told rendition, but I have seen it before so I'll zip it.

[Jon Corby]

I think this is the same as the "unfaithful husbands" one, although I'm not certain. I'll have a proper look later.

[Paul Howe]

I think this is the same as the "unfaithful husbands" one, although I'm not certain. I'll have a proper look later.

I've just looked this up and it is indeed the same puzzle. Buggery

[Gavin Chipper]

They all work out from that what colour their eyes are??? That's clearly what you're driving at, so that is my answer. What do I win?

[Jon Corby]

I think this is the same as the "unfaithful husbands" one, although I'm not certain. I'll have a proper look later.

I've just looked this up and it is indeed the same puzzle. Buggery

Are you sure, because that all stems from some people thinking that there are some people who think that there are some people that think there are some people .... [snip] ....who think that nobody is unfaithful [has blue eyes]. Which can't be the case here. Oh I don't fucking know, I argue with myself for several weeks about whether the "unfaithful" version worked, I'm not sure whether I should even begin to think about this one

[Paul Howe]

I think this is the same as the "unfaithful husbands" one, although I'm not certain. I'll have a proper look later.

I've just looked this up and it is indeed the same puzzle. Buggery

Are you sure, because that all stems from some people thinking that there are some people who think that there are some people that think there are some people .... [snip] ....who think that nobody is unfaithful [has blue eyes]. Which can't be the case here. Oh I don't fucking know, I argue with myself for several weeks about whether the "unfaithful" version worked, I'm not sure whether I should even begin to think about this one

Yes, it's the same prinicple in a different setting.

[Paul Howe]

They all work out from that what colour their eyes are??? That's clearly what you're driving at, so that is my answer. What do I win?

You have to be correct to win things, matey.

[JimBentley]

I must be missing something, but I don't get this one at all. If the blue-eyed members of the tribe already know that there are 99 other blue-eyes and 100 brown-eyes, and the brown-eyed members already know that there are 99 other brown-eyes and 100 blue-eyes, then what difference would the archaeologist's vague statement make? Or when he says "So many", does he mean that the blue-eyes are not a minority?

Also, I never thought I'd type "brown-eye" so many times in a post.

[Paul Howe]

I must be missing something, but I don't get this one at all. If the blue-eyed members of the tribe already know that there are 99 other blue-eyes and 100 brown-eyes, and the brown-eyed members already know that there are 99 other brown-eyes and 100 blue-eyes, then what difference would the archaeologist's vague statement make? Or when he says "So many", does he mean that the blue-eyes are not a minority?

Also, I never thought I'd type "brown-eye" so many times in a post.

The wording "so many" isn't really significant, the point is the archaeologist conveys to the tribe that he's observed at least one of them has blue eyes. As Gevin says, it's obvious that some people kill themselves or it wouldn't be a very interesting puzzle, you should try thinking about who kills themselves and when they do it.

Noone seems to have got anywhere so I'll drop a hint: suppose there are only 2 blue eyed and 2 brown eyed tribesmen and the archaelogist says something like "I see someone with blue eyes" What happens then? What if there are 3 blue and brown eyed tribesmen? Start by figuring those out and extend the solution upward.

[Gavin Chipper]

Noone seems to have got anywhere so I'll drop a hint: suppose there are only 2 blue eyed and 2 brown eyed tribesmen and the archaelogist says something like "I see someone with blue eyes" What happens then? What if there are 3 blue and brown eyed tribesmen? Start by figuring those out and extend the solution upward.

I've thought about reducing the numbers and working up, but can't get anywhere. So he says "I see someone with blue eyes" (presumably at least one because he actually sees two), and all four of them say "Yes, so do we." Then they politely suggest to him that, since he has joined their tribe, albeit temporarily, and he knows his own eye colour, he should kill himself.

[Gavin Chipper]

Also, I never thought I'd type "brown-eye" so many times in a post.

When this forum first opened, I had in my mind that at some point in the first year you probably would manage about six in one post. I'm less sure now though.

[Gavin Chipper]

OK, so with the 2 and 2, both the blue-eyeds think that the other blue-eyed might only see brown-eyeds. When the revalation is made, they each see that the other does not immediately commit suicide (or at the next sunset), so this means that they now know they have blue eyes and must kill themselves. The browns presumably then work out their eye-colour from that as well and kill themselves the next day. Or something.

So 3 and 3 - the blues can each see two other blues and know that everyone must see at least one blue. But from the viewpoint of a particular blue, he thinks he could have brown eyes so the other blues might only see one other and therefore might not know that everyone sees at least one blue. I'm too tired to think about this now though.

[Paul Howe]

You're on the right track there. Although it's not true the brown eyes would kill themselves beause for all they know their eyes could be a different colour altogether.

[Mikey Lear]

I reckon all the blues kill themselves a hundred days later. Also I reckon that if the archaeologist wanted to save them all rather than just study buildings like he learnt at school, he could tell them that the whole tribe only has only two types of eye colour. So that's another puzzle, if you like - why would that save them? Or if it wouldn't, why did I think it would?

[Paul Howe]

I reckon all the blues kill themselves a hundred days later.

This is indeed the correct answer. Having realised I'm too tired to do a proper explanation right now, I've decided to borrow someone else's

Also I reckon that if the archaeologist wanted to save them all rather than just study buildings like he learnt at school, he could tell them that the whole tribe only has only two types of eye colour. So that's another puzzle, if you like - why would that save them? Or if it wouldn't, why did I think it would?

Or he could just keep his mouth shut. I can't see how any tribesman could infer their eye colour from the revised statement: even if there were say 1 blue and 1 brown eyed tribesman, the best knowledge they could have of their eye colour is "not brown" and "not blue" respectively. Meaning there doesn't seem to be a basis from which the larger solution can be built.

[Mikey Lear]

I don't think you totally understood what I was saying then, but it's ok because I have since discovered that I was talking rubbish. I think I just about understand the puzzle now though. It's a good one.

[Gavin Chipper]

I think our effort on the forum was a bit shit with this one (sorry Paul). I was going to pursue the line of thought I had the other day when I was too tired but never got round to it.

[JimBentley]

I think our effort on the forum was a bit shit with this one (sorry Paul).

Seconded, especially mine (I think the sort of logical reasoning necessary for something like this is a bit beyond me). It's clever, now I understand how it works, but I'd never have got to the right conclusion in a million years. Cheers, Paul, it's a good one. Got any more?

[Paul Howe]

I don't think you totally understood what I was saying then, but it's ok because I have since discovered that I was talking rubbish. I think I just about understand the puzzle now though. It's a good one.

Cheers. Not really related to the topic, but I very much enjoyed your asymmetrical beard as I have a small patch of skin in what should be prime beard real estate on my left jaw that just refuses to grow any hair, so I can only hope this style catches on.

I think our effort on the forum was a bit shit with this one (sorry Paul). I was going to pursue the line of thought I had the other day when I was too tired but never got round to it.

Yep, it wasn't the greatest You were on the right track with what you said before though, and the answer is in the link I posted earlier should you wish to check it.

Cheers, Paul, it's a good one. Got any more?

A couple, although I might leave off posting them for a bit as I haven't got time atm to check the forum regularly and answer people's questions. Most of my favourites are probably a touch too mathematical for c4c though.

[Charlie Reams]

A couple, although I might leave off posting them for a bit as I haven't got time atm to check the forum regularly and answer people's questions. Most of my favourites are probably a touch too mathematical for c4c though.

Generally I think you are way too helpful with question answering. Your patience with that "guess higher or lower" puzzle was unbelievable, I would've just told everyone to STFU and take a course in probability. In fact I think I did do that. Humm.

Anyway, please do post maths one, there are plenty of mathematical types around here (including some who I know read but don't post, and might be drawn out by the bait of a good puzzle.)

[Michael Simmonds]

I must be missing something, but I don't get this one at all. If the blue-eyed members of the tribe already know that there are 99 other blue-eyes and 100 brown-eyes, and the brown-eyed members already know that there are 99 other brown-eyes and 100 blue-eyes, then what difference would the archaeologist's vague statement make? Or when he says "So many", does he mean that the blue-eyes are not a minority?

Also, I never thought I'd type "brown-eye" so many times in a post.

The wording "so many" isn't really significant, the point is the archaeologist conveys to the tribe that he's observed at least one of them has blue eyes. As Gevin says, it's obvious that some people kill themselves or it wouldn't be a very interesting puzzle, you should try thinking about who kills themselves and when they do it.

Noone seems to have got anywhere so I'll drop a hint: suppose there are only 2 blue eyed and 2 brown eyed tribesmen and the archaelogist says something like "I see someone with blue eyes" What happens then? What if there are 3 blue and brown eyed tribesmen? Start by figuring those out and extend the solution upward.

Sorry, I know this isn't really the point of the puzzle, but i'm with Jim on this one.

The tribe members would always have observed that their fellow members had different eye colourings, but had never had reason to question their own. Why should they now, just because the archaeologist tells them something that they already know?

[Gavin Chipper]

The tribe members would always have observed that their fellow members had different eye colourings, but had never had reason to question their own. Why should they now, just because the archaeologist tells them something that they already know?

It's not very intuitive but if you follow the reasoning, the conclusion is inevitable.

It reminds me a bit of the thing where some prisoner is told he will be executed during the next week but know which day until the day itself. Completely different probably, but it still reminds me of it.

[Paul Howe]

The tribe members would always have observed that their fellow members had different eye colourings, but had never had reason to question their own. Why should they now, just because the archaeologist tells them something that they already know?

The link I posted earlier explains things pretty well. It's a cool puzzle because it illustrates a gap between what seems intuitively and powerfully true, and the conclusions that can be reached by logical reasoning, a gap that exists in many other situations but goes unnoticed thanks to our intuitive surety.