There is an island where people are not allowed to communicate with each other. There are total 200 people out of which, 100 have green eyes while 100 have black eyes. But no one knows their own eyes color as there is no mirror available on the island. Also, they are not aware of how many people with n colored eyes are there. They don't even know that there are only two color set of eyes. But they can observe and analyze other people's eyes.
There is a catch to the things. It is a rule that if anybody is able to deduce the color of his own eyes and he is right, he will be free and can leave the island.
On a certain day, an outsider visits the island and tells the people that he has seen someone with green eyes. What will happen now?
Solution:
This puzzle is quite similar to the cheating husbands puzzle. The same logic applies here.
After the announcement, if there is only one person with green eyes, he will observe everyone and will come to the conclusion that he himself has green eyes.
If two persons have green eyes, they will see everyone and find out that there is one person with green eyes. So they will expect him to leave. But if no one leaves on that day, on the next day both of them will understand that they both have green eyes and will leave the island.
Thus if you keep going like this or apply the rules of induction, you will find that since there are 100 green eyed people on that island, all of them will leave the island on the 100th day after the announcement.