25th March 2007, 4:34 PM
Allow me to explain.
You need to think of it from the perspective of one of the blue eyed people. Now, let's assume that there is only one blue eyed person. That blue eyed person already knows the color of every single other islander. If the guru says she sees someone with blue eyes, that person knows they have blue eyes and will leave that night.
That much is obvious. Now let's assume there are TWO people. Well, you have to realize that the person not only knows the colors of everyone else's eyes, but also they know that everyone ELSE knows that person's eye color. So, if after a night has passed, the other person with blue eyes hasn't left, that can only mean it's because the other person is unsure what his or her own eye color is. The only way that could be the case is if that person sees someone else with blue eyes. Since the first person only knows of one other person with blue eyes and knows exactly the eye color of everyone else, that MUST mean that that person has blue eyes, and the other person is realizing the exact same thing because both are perfect logicians. It takes one night to pass before they figure it out because they have to see the other person has not left, but there ya go.
Once you accept that with two people, you just increase the days for each subsequent person.
The answer is correct.
You need to think of it from the perspective of one of the blue eyed people. Now, let's assume that there is only one blue eyed person. That blue eyed person already knows the color of every single other islander. If the guru says she sees someone with blue eyes, that person knows they have blue eyes and will leave that night.
That much is obvious. Now let's assume there are TWO people. Well, you have to realize that the person not only knows the colors of everyone else's eyes, but also they know that everyone ELSE knows that person's eye color. So, if after a night has passed, the other person with blue eyes hasn't left, that can only mean it's because the other person is unsure what his or her own eye color is. The only way that could be the case is if that person sees someone else with blue eyes. Since the first person only knows of one other person with blue eyes and knows exactly the eye color of everyone else, that MUST mean that that person has blue eyes, and the other person is realizing the exact same thing because both are perfect logicians. It takes one night to pass before they figure it out because they have to see the other person has not left, but there ya go.
Once you accept that with two people, you just increase the days for each subsequent person.
The answer is correct.
"On two occasions, I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able to rightly apprehend the kind of confusion of ideas that could provoke such a question." ~ Charles Babbage (1791-1871)