Originally posted by ubannoying
Here's a more advanced one (although I may have simplified it a little too much and made it easier):
There is a remote island populated by monks. Some monks have green eyes and some have brown eyes. Since none of the monks speak, and there are no mirrors on the island, each monk does not know the color of their own eyes. It is a tradition, among this order, that monks with green eyes commit suicide at dawn as soon as they find this out. A visitor comes to the island one day and says "Hey, some of you have green eyes and some of you have brown eyes!" The monks were obviously disturbed by this fact, and the visitor left right away. Three days later, some number of monks committed suicide at dawn. The question is how many, and why did they wait three days to do so.
That day (day zero), the monks all look at one another.
(1) If there is only one monk with green eyes, he will see only brown eyes, and therefore knows his eyes are green. So, any monk who sees only brown eyes will kill himself next morning. However, nobody does kill himself next morning, so there must be at least two green-eyed monks.
Day one dawns, and no-one is dead. The monks look at one another again.
(2) If there are only two monks with green eyes, each one of them will see only one pair of green eyes among the other monks. Since he knows (by the absence of dead monks) that at least two monks must be green-eyed, he now realises that
he has green eyes. So, at the second dawn, any monk who only sees one pair of green eyes will kill himself.
Day two dawns, and again nobody is dead. The monks now know that
at least 3 monks have green eyes.
(3) Any monk now who sees three or more sets of green eyes is still none the wiser about his own eye colour. However, any monk who sees only two sets of green eyes has the sickening realisation that
he is the third pair (he knows, after all, that there must be at least 3, and can account for only two...). Any monk seeing two sets of green eyes must kill himself on the morning of day three.
So, day three dawns and
three monks lie dead. The reason it took so long was that the full information required was not available to them until after the dawn of day 2.
EDIT: The number of monks in general terms is the same as the number of days it takes them to kill themselves.....