Jerious1154 said:
This the hardest riddle I've ever heard that doesn't require guesswork or random wordplay:
100 logicians are abandoned on a desert island by pirates. 50 have blue eyes and 50 have brown eyes. None of them knows their own eye color, but they can see the eyes of everyone else. The pirates leave them a note that says the following: "Every night at 8:00 sharp we will come by in our boat. At that time, if anyone correctly guesses their own eye color they will be allowed off the island. If anyone guesses their eye color incorrectly, we kill everyone. We will stop coming to the island after the first person, or group of people, gets off. Everyone else will be left there. By the way, at least one of you has blue eyes".
Since these people are logicians, you can assume that they will figure out their own eye color as soon as it is logically possible to do so. How many people guess their eye color and get away, and on what night do they do so?
Hypothetically, say there was only one person with blue eyes. She can look around and see that everyone else has brown eyes, yet the pirates said that at least one person has blue eyes, and so she knows it must be her. So the first night she says she has blue eyes and leaves.
When this doesn't happen, all the logicians know that there are at least two people with blue eyes, because they all trust each other's logic. The next night, anyone that only saw one other person with blue eyes would know that she had to be the other, so they'd both be able to leave. When this doesn't happen the second night, everyone knows there must be at least three people with blue eyes.
This continues until night 50. Now on this night, all of the logicians know that there are at least 50 people with blue eyes. Yet half of them can only see 49 blue eyed people, and so each one knows they must be the 50th, and will happily announce to the pirates their eye colour. Of course, as soon an people started to correctly guess their colour on day 50, all the logicians knew that there are exactly 50 pairs of blue eyes on the island. Assuming that brown is the only possible other colour, all the brown eyed people also now know their own colour (because they already see 50 people with blue eyes). So everyone guesses correctly and leaves on night 50.
Unless they think there might be eyes other then blue or brown.
Or unless the pirates are jerks.