201 residents

Question:

There is an island with exactly 201 residents, 100 with blue eyes, 100 with brown eyes, and the island leader (who has green eyes). To leave the island, one must know their own eye color. There are no reflective surfaces on the island and no on can communicate with each other other than the leader to the residents. No one on the island knows how many of each eye color there is. Everyone on the island is a perfect logician, meaning that if there us a solution they’ll find it. Every morning the leader gives anyone a chance to leave the island by guessing their eye color. One morning, the leader gathers all 200 residents to make an announcement, he says “at least 1 person on this island has blue eyes” How many people leave the island and in how many days after the announcement?

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Solution: All 100 blue-eyed people in 100 days.

EXPLANATION: imagine there is only 1 person on the island, he will look around and see that there are no blue eyed people, he will then know his eye color in 1 day, if there are two, each will see that there is 1 blue eyed person, of this person, doesn’t leave on the 1st day, that means that he must also have blue eyes so that the same rules apply to the other man’s perspective, following this logic, n= blue eyed people and d= days so d=n because, for each person added, one more day is needed to know their own eye color. if you would like more info, search “100 blue eyes riddle”

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