An island, 100 prisoners, a dictator… No one on the island is allowed to talk to each other. Everyone can see each other during the day only during the morning roll call.
There is no possibility of escaping the island, but anyone who wishes can ask the guards to let him go.
The guards can only be allowed to leave the island at night. There is only one factor that determines whether it is allowed, green eyes.
If the person who wants to leave the island has green eyes, his request is granted. But if his eyes are not green, he will be thrown into a volcano.
In fact, the eye color of all 100 captives on the island is green; but none of them are aware of what their eye color is. Because the dictator has taken every precaution to prevent them from learning the color of their eyes.
After pressure from human rights groups against this attitude on the island, one person is allowed to come to the island and talk to the prisoners, and it’s you! Of course, in exchange for two things:
You can only make a statement, and in that statement you can’t tell the prisoners something they don’t know. You think about how you will wake up these people by making a statement without getting angry and breaking the rules, and you say:
“At least one of you has green eyes.”
This interesting statement makes the dictator suspicious; however, he is convinced of the situation as he realizes that he does not give them any new information. You leave the island, life continues normally on the island for 99 days. But on the 100th night, all the prisoners on the island leave the island after taking the permission of the guard.
The question is: How could you defeat the dictator in a single sentence? If you’ve thoroughly thought through the answer, we can move on to the explanation.
For the first time, let’s assume that there are only two people on the island. After hearing the explanation, they both see that the other person has green eyes and thinks that that person will leave at night.
But the next morning, they both see that the other has not left the island. So he says in his mind, “So I’m the one with the green eyes, so he didn’t leave and thought I was going to leave.”
Let’s consider the three person situation and call it X, Y, Z. X will see that the other two people have green eyes and therefore will not be able to clearly understand that he has green eyes.
So he waits the first night and the next morning finds that the other two people are waiting just like him. He says, “If I am not green-eyed, these two people have observed each other. Therefore, they will go tonight” and waits for the second night.
In the morning, he sees that no one went last night and realizes that they were watching him too. This means that he also has green eyes. As all three people reach the same conclusion, they all leave the island on the third night.
As you can see, the number of people doesn’t really matter. If there are n people, everyone leaves the island n. takes place at night. Therefore, all 100 people wait until the 100th night, and when they see that no one has left the island, they realize that everyone, including themselves, has green eyes, and they leave the island the same night.
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