On a certain island, people are gifted with assorted eye colors. There are a hundred green colored and a hundred grey colored pair of eyes. On that island, there is no mirror available. Thus no one knows the eye color of their own. They could have asked each other but that is prohibited. They are not allowed to converse with each other. However, they can study and analyze other's eyes. They don't even know the statistics and so it is believable to them that their eyes can be blue as well. There is a chance of freedom from the island. If anyone is able to guess the color of his own eyes correctly, he will be set free and can leave the island.
On one particular day, an outsider comes to the island and makes an announcement that he has seen someone with grey color eyes. What will happen now?
If there is only one person with grey colored eyes, he will see all other people and find out that no one has grey eyes. Thus he will come to know that he himself has grey eyes. Thus, he will leave the island that very day.
If there are two people with grey eyes, they will find only one pair of grey eyes and will think that that is the person with grey eyes. So they both won't leave the island. On the next day however, they will see that no one left the island and they will understand that both of them has the same eye color that is grey color.
Now through induction, since there are 100 people with grey eyes, all of them will leave the island on the 100th day after the announcement was made by the outsider.