Here's a surprisingly subtle and rich logic puzzle, based on one that you can find in various places:
Imagine a tribe of people who are legendary logicians, but who have a curious religious commitment that if they are ever able to determine the color of their own eyes, they must commit ritual suicide in front of the whole tribe at the tribe's daily meeting. The tribe lives on an island with virtually no contact with the outside world, they have no mirrors or reflecting surfaces (for obvious reasons), and they never discuss eye color in any way because they all know what great logical brains they have and so are very hesitant to give away any clues about eye color.

One day, a well-meaning anthropologist visits the tribe, and at their morning meeting, gets up and makes an effort at good relations by saying "Your people and mine are not so different. For example, I see that you have both brown-eyed and blue-eyed people in your tribe, just like I do in my own family". A gasp goes out in the crowd, and the expressions of these logical thinkers rapidly becomes as dark as a grave. The curse of the tribe's commitment is explained to the observer, and he says, "sorry, I didn't realize, but you can all see that what I said is true. So why is everyone acting so crestfallen?"

Let's say the tribe has 20 members, and 5 have blue eyes. The puzzle has two parts:
1) what is going to happen to this tribe that is so awful?
2) what information did the visitor give that the tribe did not already know?

Pretty nice puzzle. I won't spoil it with the answer, but it was a toughie. There is a real answer, although I doubted it on first reading the puzzle.

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The ether of general relativity therefore differs from that of classical mechanics or the special theory of relativity respectively, in so far as it is not 'absolute', but is determined in its locally variable properties by ponderable matter.

Albert Einstein, "On the Ether", 1924

And even if you know the answer to part (1), I wager you may not know the answer to part (2)! Return when we get to that point.

So, you weren't satisfied with the outcome of the "Make a buck" thread, you had to start this one also

Clarification needed:

The visitor says, "you have both". He doesn't say, "you have only". Would that be correct?

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Each tribe member has instanteously realized that (s)he is colour-blind, since (s)he had never noticed the blue and brown eyes the visitor mentions. The entire tribe is therefore about to undergo a crisis of religious faith, having lost a central tenet of their religion.

Grant Hutchison

Oh yes, I do! I stumbled onto part 2 first which led me to the proof for part 1.

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The ether of general relativity therefore differs from that of classical mechanics or the special theory of relativity respectively, in so far as it is not 'absolute', but is determined in its locally variable properties by ponderable matter.

Albert Einstein, "On the Ether", 1924

Let's see...
If there was only one with blue eyes, he/she would see only brown eyes, and immediately know that he was the odd one out. After he committed suicide, all the others would know the reason, and do the same. Now, if there were only two with blue eyes, those two would notice that only one other person had blue eyes, and as that person did not commit suicide, he must be able to see someone with blue eyes, which could only be you, so both would commit suicide, and afterwards the other 18.
Fine so far? But it goes on. If there were only three people with blue eyes, one of those three would see only two people with blue eyes, wonder why they didn't commit suicide (like above), decide that he had blue eyes as well, and kill himself. Etcetera.

So Question 1: they are all going to kill themselves, and question 2: they didn't know that there were only two different colours (everyone before could have guessed that he had a third colour).
This does only count though if there are indeed only two colours in the tribe, which the puzzle doesn't make clear. If that is not the intention, I don't think anything bad will happen to the clan, and I don't think any new info is given.
It would be different if there were only two people with brown (or blue) eyes, as the info "you can all see that what I said is true" means that there have to be at least two of each colour. If there were only two, anyone with that colour would see the problem, knwo his own colour, and kill himself, so even if there were more than two colours (or if the info of the anthropoligist left open that possibility), in this case, two people (or four people in the worst case) would kill himself (four if you had two blue- and two brown-eyed people, and 16 other coloured).
But I guess I have made a logical error again somewhere

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Knowledge is a curse, but ignorance is worse

If there were three people with blue eyes, then any of the three with blue eyes who saw the other two with blue eyes could logically assume they, themselves, could have had either blue or brown eyes.

The only new info given to the tribe is that there are only two colors of eyes. Provided there are three or more people with each color, the solution is indeterminant, same as the socks in the drawer puzzle (drawer full of socks, two colors - how many socks must one pull out in the dark before they have a matching pair? Answer - three).

Wait. The man said "people" referencing the number who had each color. Thus, implying two or more. That's the info.

Thus, if there were two people who had blue eyes, then one or the other, looking around, realizing that there was only one other person with blue eyes, would kill himself. The other, looking around, seeing no more blue eyeed people would kill himself, too. The rest of the tribe, looking around, would see nothing but brown eyes, but would know because of the logical conclusion of the first two that they all had brown eyes and would kill themselves.

But with three people or more with blue eyes, this logic falls.

Thus, the tribe wouldn't do anything, as each of the blue eyed people would see four others with blue eyes and rightly conclude the requirements of the person's statement were met, regardless of their eyes, and do nothing.

But they would now know that there were only two colors of eyes among themselves.

That's the new pice of information.

[/QUOTE]

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If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

Your neat ratio of 5 blue-eyed to 15 brown-eyed (if indeed only two colours are implied) makes me think of the Mendelian inheritance of eye-colour: but a logical and observant tribe should already have deduced that fact for themselves, without having to hear of the visitor's family and see the visitor's eye-colour.
Thus, a mother who bore a brown-eyed child to a blue-eyed father would realize she must have brown eyes, and kill herself. The father would realize from his partner's suicide that he must have blue eyes, and kill himself. And the child, grown to adulthood, would realize from tales of her parents' suicides that she must have brown eyes, and so kill herself.
Tut. Tragic. But presumably not the answer.

Grant Hutchison

True, but you have to think further.
Case one: you have brown eyes. Then the two people with blue eyes would each only see one person with brown eyes (and as you agreed, would kill themselves).
So because these people have not yet killed themselves, you must have blue eyes as well. Aaaargh (sorry, Monthy Python popped in).

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Knowledge is a curse, but ignorance is worse

I think we need to assume that, if one of the tribe members learns his/her eye color during the daily meeting, s/he acts on this knowledge the next day, neither sooner nor later. Otherwise, we have a little problem if they think at different speeds. Also, they can't disclose what they have learned, but it seems this one is already covered in the problem statement.

Yes, 7 pages wasn't good enough, I'm shooting for 8 here! (Actually, this one might prove less paradoxical, but no less subtle.)

For simplicity, let's just say that brown and blue are the only possibilities. So he could have said "you have only".

Correct! We can introduce a timing to it, and say that the next day there would be nobody who had figured out their eye color by the morning meeting of the tribe. But the day after, etc., your answer comes into play. Given that view, how long will the tribe survive?

No, we can assert that they all know brown and blue are the only possibilities. The bad stuff still occurs even if this is assumed by the tribe.

Your answer is clever, but not what I had in mind. This tribe is great at logic, lousy at biology.

So non-suicides contain information.
If I see only one blue-eyed person, and on the first day that person has not committed suicide, it implies they can see a blue-eyed person to account for the visitor's remark: so I must have blue eyes. I'll kill myself on the second day, as will the other blue-eyed person, who has used the same logic.
But if I see two blue-eyed people, and by the second day they haven't committed suicide, then I must have blue eyes.
And so on: so on the fifth day, all five blue-eyed people commit suicide. This informs the brown-eyes of their brown-eyed status, and they all commit suicide on the sixth day. (Assuming the tribe is aware that only two eye-colours are possible.)

Grant Hutchison

Correct! This completes Fram's solution of part (1). But the fun is only beginning. What is the answer to part (2)?

It seems to me, before the anthropologist arrived, everyone knew that there were at least four blue-eyed people. Furthermore, everyone knew that everyone knew there were at least three blue-eyed people. And everyone knew that everyone knew that everyone knew that there were at least two blue-eyed people. And everyone knew that everyone knew that everyone knew that everyone knew that there was at least one blue-eyed people. But not everyone knew that everyone knew this last statement. When the anthropologist spoke up, they did.

From the anthropologist's remark that some villagers had blue eyes and all the rest had brown eyes, the villagers learned that if there had been only one blue-eyed person he would now be able to realize on the first day that he had blue eyes. This knowledge would allow them to begin a series of deductions that would eventually result in their committing suicide. It is interesting to note that the new knowledge is only about what would have happened in a situatuion that is patently contrary to fact, yet it enables valid deductions about the actual state of affairs in the real world.

If the anthropolgist had subsequently kept his mouth shut, the five blue-eyed people would have committed suicide on the fifth day. When the anthropologist then remarked that everyone had already been able to see that the tribe contained both blue-eyed and brown-eyed members anyway, he expedited the process because now if there had been exactly two blue-eyed people they would have realized their eye color on the first day (since the remark insures that there are at least two blue-eyed people, it would allow a person seeing only one blue-eyed person to conclude that he, himself, had blue eyes). Hence, the five blue-eyed people would now commit suicide on the fourth day.

You're no fun montebianco-- Right! That was quick work, we're not going to make 7 pages. But to amuse yourself further, I'll add part (3): what can the tribe do to save itself from annihilation?

There is more specific information than that conveyed, involving what people know about what other people know. See montebianco's resolution.

Excellent! I had not even intended this subtle alteration to the solution to (1), but you are right. The full solution to (1), counting the second remark by the anthropologist, dooms the tribe a day earlier. Once again you have found an unintended subtlety in my logic problems, cut it out! For the purposes of continued analysis of what the tribe can do to save itself, let's pretend the second statement never occured, or occured in confidence, since this day-faster clock is a complication we don't want. Very clever indeed, Fortunate.

I was not counting what they could then deduce from this seed; I only mentioned the seed itself, but, of course, this seed allowed them to deduce more.

No, the information about what other people know is delivered instantly when the visitor speaks. There's no deduction involved.

They can structure the meeting so the whole tribe is never in the same room at the same time. That would render it impossible to commit suicide "in front of the whole tribe." How can one be compelled to perform an impossible act.

Perhaps we need to introduce some uncertainty, maybe about whether others are acting or have acted rationally. What kinds of mushrooms grow on this island?

What about some quantum weirdness? I don't care how smart they are.

As for 3, they can just renounce religion...

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The tribe can save themselves by sacrificing one blue eyed man.

Before the next day, each member submits the name of a blue eyed person to the leader. The leader randomly selects a name and kills that person at midnight.

In the case of two blue eyed people, the absense of a suicide on the first day communicates to each blue eyed person that the other blue eyed person didn't think he was the odd one out.

But, if this person is killed, the absense of a suicide no longer means anything. He might have known, and he might not have known.

The logic continues for three, four, and five blue eyed persons.

Yes, that would work. Anything less fatal? They may find murder distasteful. Also, they can't denounce their religion or their daily meeting, without those they may as well just return to mainland society and become mathematicians or something...

Well, and this is a bit extreme, they could all put out their eyes.

Edit: Oh. They could all immediately cover their eyes as well.

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