nuthut Posted June 5, 2012 Share Posted June 5, 2012 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? There are no mirrors or reflecting surfaces, nothing dumb. It is not a trick question, and the answer is logical. It doesn't depend on tricky wording or anyone lying or guessing, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me." And lastly, the answer is not "no one leaves." A word of warning: The answer is not simple. This is an exercise in serious logic, not a lateral thinking riddle. There is not a quick-and-easy answer, and really understanding it takes some effort. Link to comment Share on other sites More sharing options...
shought Posted June 5, 2012 Share Posted June 5, 2012 It's unsolvable like this. 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: Should be: The Guru is allowed to speak once (let's say at noon) every day. Standing before the islanders, she says the following: Edit: wait, no, it makes no difference, lol. Link to comment Share on other sites More sharing options...
Avitar Posted June 5, 2012 Share Posted June 5, 2012 100 blue eyed people leave on the 99th day. 100 brown eyed people leave the next day. The guru leaves the island last ( i think... either last or before the brown eyed people ) WOW! that was some serious logic~! 100 if... then... statements with new conditions each iteration! WTF??? You owe me a pizza my friend ;) They are all perfect logicians... Link to comment Share on other sites More sharing options...
shought Posted June 6, 2012 Share Posted June 6, 2012 100 blue eyed people leave on the 99th day. 100 brown eyed people leave the next day. The guru leaves the island last ( i think... either last or before the brown eyed people ) WOW! that was some serious logic~! 100 if... then... statements with new conditions each iteration! WTF??? You owe me a pizza my friend ;) They are all perfect logicians...The brown eyed people and the guru never leave the island though... When all the blue-eyed people leave none of the others can logically deduce that they all have the same color. (For all the guru and the brown eyed people know is that they do not have blue eyes). Link to comment Share on other sites More sharing options...
Avitar Posted June 6, 2012 Share Posted June 6, 2012 The brown eyed people and the guru never leave the island though... When all the blue-eyed people leave none of the others can logically deduce that they all have the same color. (For all the guru and the brown eyed people know is that they do not have blue eyes). Yes they do. The blue eyed people leave, then the guru leaves... so they conclude that everyone who is left who didn't leave after the guru "MUST HAVE THE SAME COLOUR EYES AS ME!!" Link to comment Share on other sites More sharing options...
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