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Originally Posted by Ken G
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?
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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
