A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate. Everyone on the island knows all the rules in this paragraph.
On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.
The Guru is allowed to speak once (let's say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:
"I can see someone who has blue eyes."
Who leaves the island, and on what night?
Only the BLUES leave, and on night 100. We can simplify this problem to this equation:
There's 2 blues, 2 browns, and 1 green (The Guru), and they follow the aforementioned rules.
[Day 1]
I see a blue, two browns, and a green. Since I myself am unsure of my eye color, I cannot leave. I must wait to see if the other of the blues leave.I see two blues, a brown, and a green. Since I myself am unsure of my eye color, I cannot leave. I must wait to see if the other of the blues leave.I see two blues, and two browns.[Day 2]
I see a blue, two browns, and a green. Since he is probably unsure of his eye color (as he sees another blue), then I must be the other blue eyed since I cannot see anyone else with blue eyes. Therefore, I leave tonight (as does he!)I see two blues, a brown, and a green. Since there are two blues left, they must still be unsure of their eye color, as if they were the only two blue eyes on the island, they will leave tonight or tomorrow.I see two blues, and two browns. Since there are two blues left, they must still be unsure of their eye color, as if they were the only two blue eyes on the island, they will leave tonight or tomorrow.[Day 3]
I see a brown and a green. If I were with blue eyes, then the blue eyes would have left tonight instead of last night. This means that I have an eye color different from blue, but because of this, I cannot tell what my eye color is, since I do not know if there is at least one brown eye, one green eye, or at least one of my own eye color. I will never leave this island!I see two browns. If I were with blue eyes, then the blue eyes would have left tonight instead of last night. This means that I have an eye color different from blue, but because of this, I cannot tell what my eye color is, since I do not know if there is at least one brown eye, one green eye, or at least one of my own eye color. I will never leave this island!We can simplify this down further:
There's at least X blues. Therefore, I will know by day X+1 whether I myself am blue or not. If they all leave on day X, I am not blue. However, if they do not leave on night X, I am blue.
What do the poor have and the rich want?
What is bigger than god and more evil than the devil?
And if you eat it you will die
The poor have nothing, the rich want nothing (as they already have everything)
Nothing is greater than god or more evil than the devil.
If you eat nothing, you will die from starvation.
And now, here's my riddle:
There's four lightbulbs in a row inside of a closed room, corresponding to a row of 4 switches outside of the room labeled A, B, C, and D respectively. The catch is that you may only enter the room once, afterwards you may not enter again. You may not see into the room unless you are in it. How can you tell which lightbulb corresponds to which switch?
Post has been edited 1 time(s), last time on Nov 19 2008, 2:52 am by Greo.
None.