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# blue Eyes

## Question

Perhaps you've heard this one before, it's the best example i've heard of an inductive reasoning puzzle.

There are 200 hundred inhabits on an island. 100 of them have blue eyes, the other 100 do not (their eye color is irrelevant). These numbers are not known to the inhabitants, and for the moment they do no know their own eye color. On this island there are 3 rules that all the inhabits must follow.

1. No one may know his/her’s own eye color

2. If some one figures out their own eye color they must leave the island

3. When they leave it must be at midnight of the day they discovered it

Now a strangers comes to the island and the 200 gather before him. He calls out “I see someone with blue eyes” Then he leaves.

The puzzle is: How many people leave the island and on what day?

(And all the inhabitants are completely logical, there are no mirrors and the answer is also completely logical i.e. nothing cheep and it's not a lateral thinking puzzle)

The answer: 100 people and on the 100th day.

The logic is thus: Lets say that their was only one person with blue eyes and 199 without. That one could look around and see (asumming that this is a perfuctly logical world they can see all of eachother) that no one else had blue eyes and thus conclude the stranger must be addressing him. He would then leave at midnight of that day.

Now let us say that there are 2 people with blue eyes and 198 without. Let us label those two people A and B. Person A looks and see person B and thus concludes that the strangers could not be referring to him. But on the second day when A again sees B, A realizes that B must see someone with blue eyes. Because A can not find anyone else with blue eyes and because B is thinking likewise at midnight on the second day they leave.

Now lets take 3 people with blue eyes A, B, C and 197 without. They each go though a process similar to the one above. A realizes that he, himself, may have blue eyes so he waits 2 nights and when the third day has come and no one has left then he knows he must have blue eyes. If he didn’t have blue eyes then the other two guys would have gone though the above process and left on day two. So all three leave on day 3 at midnight.

This process is expanded until on the 100 day all the people with blue eyes, realizing they have blue eyes, would leave that night at midnight. Hope you followed all that!

- He's not dead... he's electroencephalographically challenged

## Recommended Posts

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nice one ... I have published a variation on that a while ago - check puzzle called Josephine

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