On a certain island there are people with assorted eye colors. There are 100 people with blue eyes and 100 people with brown eyes. Since there are no mirrors on this island, no person knows the color of their own eyes. The people on the island are not allowed to talk or communicate with each other in any way. They are also NOT aware of the number of blue or brown eyed people on the island. For all they know, they could have red eyes too. But they are allowed to observe other people and keep count of the number of people with a certain eye color. There is a rule that the people on the island have to follow – any person who is sure of their eye color has to leave the island immediately.
One day, an outsider comes to the island and announces to the people that he sees someone with blue eyes. What do you think happens?
Thursday, April 15, 2010
Subscribe to:
Post Comments (Atom)
Consider there is only 1 blue eyed and 1 brown eyed person on the island. After the announcement, the blue eyed person will know he is the one, since he sees the only other person on the island has brown eyes, so he will leave the same night. The next morning, the brown eyed person will see that the blue eyed person has left. He cannot leave since though he knows his color is not blue, he does not know what it is.
ReplyDeleteConsider 2 blue eyed and 2 brown eyed people.
Both blue eyed people will think that the other blue eyed person will leave at night. On the second day, since they see that the other has not left, they deduce that there is one other person with blue eyes, whom they cannot see, i.e. themselves. So on second night, both blue eyed people leave.
The brown eyed people stay behind, since they do not know their own eye color.
Consider 3 blue and 3 brown eyed people.
Each blue eyed person knows there is at least one blue eyed person, and sees two blue eyed people. If they are the only 2 blue eyed people, they will both leave on second night. Since no one leaves on second night, all blue eyed people understand that they are blue eyed, and leave on the third night. Brown eyed people do not leave since they do not know the color of their eyes.
In this way, for 100 blue and 100 brown eyed people, all 100 blue eyed people will leave the island on the 100th night and all brown eyed people will stay behind on the island.