On an otherwise deserted and isolated island, 200 perfect logicians are stranded. The islanders are perfectly logical in every decision they make, and they will not do anything unless they are absolutely certain of the outcome. However, they cannot communicate with each other. They are forbidden from speaking with one another, or signing, or writing messages in the sand, else they be shot dead by the captain of a mysterious ship that visits the island each night. Of the 200 islanders, 100 have blue eyes, and 100 have brown eyes. However, no individual knows what color their own eyes are. There are no reflective surfaces on the island for the inhabitants to see a reflection of their own eyes. They can each see the 199 other islanders and their eye colors, but any given individual does not know if his or her own eyes are brown, blue, or perhaps another color entirely. And remember, they cannot communicate with each other in any way under penalty of death. Each night, when the captain of the ship comes, the islanders have a chance to leave the barren and desolate spit of land they have been marooned on. If an islander tells the captain the color of his or her own eyes, they may board the ship and leave. If they get it wrong, they will be shot dead. Now, there is one more person on the island: the guru, who the islanders know to always tell the truth. The guru has green eyes. One day, she stands up before all 200 islanders and says: I see a person with blue eyes. Who leaves the island? And when do they leave?