Blue-eyed islanders puzzle. I first heard it more than ten years ago, and it's still one of my favourites. This one doesn't involve any arithmetic or calculations, but there's also no "trick" to it: it's purely a logic problem.
- 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?
By the way, I prefer to think of them as performing seppuku at midnight rather than leaving the island. :)
Not particularly hard if you think recursively. In case of a single blue eyed person, he would see 199 people with other eye colours, telling him the colour of this own eye, causing him to leave on the first night. This is the base case. If he doesn't leave, there is at least one more person with blue eyes, causing the second blue eyed person to realize that he is the other blue eyed person on the second noon, as he sees that there are 198 people with other eye colours, letting them leave on the second night. Repeat until all blue eyed people realize their eye colour
Does the Guru sees only one person with blue eyes or at least one? If the Guru sees only one person with blue eyes, each goes one by one to look from the perspective of the Guru. If they don't see anyone with blue eyes, it means it's them. If they see the blue-eyes person, they know they have green eyes. Everyone in the room at that moment leaves the island. If more than one person has blue eyes, it does not work tho. Also, I know you said there is not trick but if there were, you could assume that by saying "I can see someone who has blue eyes" the Guru means that green eyes people are invisible to her. If the guru can see you, you thus have blue eyes :P (Bullshit answer, I know it's not this)