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There are 101 normal people on an island. 2 have blue eyes and the rest have red eyes. The people with red eyes can leave the island. But the people with red eyes always tell the truth and the people with blue eyes always lie. But the red eyes don't know that the blue eyes always lie, and the blue eyes don't know that the red eyes always tell the truth. The people can only ask yes or no questions. Also, red eyes can only speak with blue eyes and blue eyes can only speak with red eyes. Only after all the red eyes leave the island the blue ones can also leave.

There is a king with brown eyes who can lie or tell the truth. He chooses what to say. The king can leave after everyone leaves. The king only answers one question per year but the thing is there is a tsunami in one year so you only have one year to solve everything.

How will everyone leave the island? Please include the question each person will ask and the answer.

Note: The red eyes don't know how many blue eyes there are and the blue eyes don't know how many red eyes there are.

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    $\begingroup$ Relating to noedne's answer below: What happens if someone with red/blue eyes tries to speak to someone with the other color of eyes? Will they know of the rule that they cannot do so and then be able to deduce their own eye color, or is there just some mysterious force on the island that prevents islanders from connecting the dots to why their attempt failed? $\endgroup$
    – Synchronous
    Commented Apr 2, 2022 at 18:50
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    $\begingroup$ Yes since this is an imaginary land people just cant talk with anyone. $\endgroup$
    – Varun W.
    Commented Apr 2, 2022 at 19:41

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Here's how everyone can leave the island.

Because 2 people have blue eyes, each person can find someone else with blue eyes and try to speak with them. If successful, they know they have red eyes and can leave the island. If unsuccessful, they know they have blue eyes and can leave after everyone with red eyes has left. Finally, the king can leave after everyone with blue eyes has left.

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  • $\begingroup$ This is not the answer in mind but this is a wonderful answer. Very efficient. $\endgroup$
    – Varun W.
    Commented Apr 2, 2022 at 19:42

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