A remote island contains a tribe whose members have either blue or brown eyes. Tribe members do not know the color of their eyes and if they learn it, they must kill themselves the same night. Every member of the tribe always behaves logically. So one day, a sailor visits the island and makes an observation that at least one of the members of the tribe has blue eyes. On the 10th night after that, all people with blue eyes kill themselves. How many blue-eyed people were there in the tribe?
Ten. The logic goes as follows. If there were only one person with blue eyes on the island, then he would see that no one else has blue eyes and will kill himself on the first night. If there were two people with blue eyes, then one of the people with blue eyes would see that the second blue-eyed person did not kill himself on the first night, leading him to conclude that since he sees no one else with blue eyes, he must be one of them and will kill himself on the second night. The other blue-eyed person will follow the same logic and also kill himself on the second night. The same idea applies to the rest of the problem.
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