Your idea matters-7
In a magical island,there lived mathematicians.All of there eyes were green but they knew that there were at least one person whose eyes were green.There was a cruel king who was torturing the mathematicians.He(K) said that if anybody tells the colour of his(M) eye and the answer is true,then he will be free.And if the answer is wrong,then they will be killed.The mathematicians doesn't want to take any risk.They cannot talk with others.Then in which night(1st night-1,2nd night-2 etc) all of the mathematicians will surely free from the island?
The answer is 100.
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1 solution
Assume there is only one green-eyed mathematician. He knows that there is at least one person whose eyes were green. Of course, he knows it is himself, and leaves the first night.
Now assume there are two green-eyed mathematicians. Each one looks at the other and sees a green eyed mathematician. This does not show anything about the color of their own eyes, and so no one leaves the first night. However, the next morning, the two wake up and see that neither of them left. That means that both mathematicians saw a person with green eyes. In other words, if one of the mathematicians had, say, blue eyes, the other mathematician would have left the first night. However, no one left. This means that both mathematicians had green eyes. They both leave the second night.
The same logic applies to three green-eyed mathematicians. No one leaves after the first or the second night. But the third morning, because all three are still there, they can all figure out logically that all three of them had green eyes (otherwise the green eyed ones would have left a previous night). The three green-eyed mathematicians leave the third night.
Likewise, if there are one hundred green-eyed mathematicians, they will leave the one hundredth night.