100 blue eyes island

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? Notes: this is known as one of the hardest riddles ever

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