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3 hours ago, Nameless said:

Because then everyone would have seen that person's eye color, and, knowing there was only one person with that eye color, left that night. Then the remaining person would know that their eye color.

How are the people on the island supposed to logically infer anything about what he would have said?

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Oh oops I just saw that in the original post. I was editing mine as you posted that :P

I think I finally got it. They all leave on the 100th night. This took me forever, but here's my logic: 

If there was one blue eyed person, they would obviously leave the first night, since they could see that there were no other blue eyes people and know the activist was talking about them.

If there were two blue eyed people, both would see one other blue eyed person. They would know that if that other person saw no one else with blue eyes, they would have left on the first night for the reason above. Because the other person did not leave, both people would realize that they must also have blue eyes. Then both would leave on the second night.

This is the part that took me a while to figure out: if there were three blue eyed people, they would each wait three nights. They would each know that if the two blue eyed people that they saw were the only two, they would have left on the second night. They didn't, so each person realizes that they have blue eyes and leaves on the third night.

This process repeats for each prisoner with blue eyes, so that with 100 prisoners, they all leave on the 100th night.

Edited by HeyLookItz
I inserted the entire answer to not double post
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21 hours ago, HeyLookItz said:

Oh oops I just saw that in the original post. I was editing mine as you posted that :P

I think I finally got it. They all leave on the 100th night. This took me forever, but here's my logic: 

If there was one blue eyed person, they would obviously leave the first night, since they could see that there were no other blue eyes people and know the activist was talking about them.

If there were two blue eyed people, both would see one other blue eyed person. They would know that if that other person saw no one else with blue eyes, they would have left on the first night for the reason above. Because the other person did not leave, both people would realize that they must also have blue eyes. Then both would leave on the second night.

This is the part that took me a while to figure out: if there were three blue eyed people, they would each wait three nights. They would each know that if the two blue eyed people that they saw were the only two, they would have left on the second night. They didn't, so each person realizes that they have blue eyes and leaves on the third night.

This process repeats for each prisoner with blue eyes, so that with 100 prisoners, they all leave on the 100th night.

You got it! Good job. Couple clarifications: there are no reflective surfaces and they can't communicate. I didn't include this, but the standard riddle says that the activist was only allowed to say something that everyone on the island already knew.

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