The Green-Eyed Logic Puzzle

In the green-eyed logic puzzle, there is an island of 100 perfectly logical prisoners who have green eyes—but they don't know that. They have been trapped on the island since birth, have never seen a mirror, and have never discussed their eye color.

On the island, green-eyed people are allowed to leave, but only if they go alone, at night, to a guard booth, where the guard will examine eye color and either let the person go (green eyes) or throw them in the volcano (non-green eyes). The people don't know their own eye color; they can never discuss or learn their own eye color; they can only leave at night; and they are given only a single hint when someone from the outside visits the island. That's a tough life!

One day, a visitor comes to the island. The visitor tells the prisoners: "At least one of you has green eyes." 

On the 100th morning after, all the prisoners are gone, all having asked to leave on the night before. 

How did they figure it out?


Here is the solution! 

The Green-Eyed Puzzle Solution

Here is that Puzzle! 

Nobody is going to dare to go the guard unless he is absolutely sure that he is green eyed; otherwise it would be suicidal move.

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For a moment, let's assume there are only 2 prisoners named A & B trapped on island.

On first day, A is watching green eyed B & B can see green-eyed A. But both are not sure what is color of their own eyes. Instead, A(or B) waited B(or A) to escape from island since he is green-eyed. Rather both are sure that other too doesn't know anything about color of own eyes.

On next morning both see each other still on island. Here is what A thinks.

If I was non green-eyed then B would have realized that the person pointed by visitor in his statement ('at least one of you have green eyes') is himself. Hence, B would have realized that he is green-eyed & could have escaped easily. Since B didn't try to escape that means I too must have green eyes.

So A can conclude that he too have green eyes. Exactly same way, B concludes that he too has green eyes. Hence, on next day both can escape from the island.
 
Note that, if the night of the day on which visitor made statement is counted then next day would have 1st morning & 2nd night since visitor's visit. Now since A & B left on 2nd night, we can't see anybody on 2nd morning next day.

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Now let's assume there are 3 prisoners named A,B and C trapped on island.

Let's think from A's point of view as an example.What he thinks.

Let me assume I don't have green eyes.Now each B and C could see 1 green-eyed & other non green-eyed person. But still they don't know color of own eyes.So on that night nobody tries to escape.

On first morning I see both B and C still present there.

Now B can think that if he has no green eyes then C could have concluded that the person pointed by visitor's statement ('at least one of you have green eyes') is C himself (as both A & B are non green-eyed. This way, C would have realized that he is green-eyed.

In a very similar way, B would have realized that he too is green-eyed.

Now both of them could have escaped on that night as they are sure that they are green-eyed.

But on the second morning, I see again both of them are still there. So now I can conclude that I too have green eyes.

If A can conclude then why can't B and C?  So after seeing each other on 3rd day, each of 3 can conclude color of eyes is green. Now on 3rd night they all can escape safely.

This is called as inductive logic.

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If observed carefully, 2 prisoners need 2 nights and 3 prisoners need 3 nights to logically deduce that the each of them is green-eyed.

Hence, 100 prisoners would require 100 nights to absolutely make sure that each of them is green eyed.

That's why on the 100th morning day, there is no prisoner present on island. 

The Bus Driver

You are the bus driver. At your first stop, you pick up 29 people. On your second stop, 18 of those 29 people get off, and at the same time 10 new passengers arrive. At your next stop, 3 of those 10 passengers get off, and 13 new passengers come on. On your fourth stop 4 of the remaining 10 passengers get off, 6 of those new 13 passengers get off as well, then 17 new passengers get on. What is the color of the bus driver’s eyes?

 Find answer here! 

Source 

Color of Bus Driver's Eyes

What's the question? 

Answer is hidden in very first statement! What's color of your eyes then?