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But on the hundredth morning after your visit, all the prisoners are gone, each having asked to leave the previous night.
但是在你拜訪之后的第一百個早上，所有的居民都離開了，每一位居民，都在前一天晚上要求離開。
So how did you outsmart the dictator?
你是用什么方法智取獨裁者的？
It might help to realize that the amount of prisoners is arbitrary.
把居民的數目任意化也許可以有所幫助。
Let's simplify things by imagining just two, Adria and Bill.
讓我們先把情況簡化，想像只有兩個居民 Adria 和 Bill。
Each sees one person with green eyes, and for all they know, that could be the only one.
他們各自看到對方擁有綠色眼睛。所以他們都知道：對方是可以離開島上的那一位。
For the first night, each stays put.
第一天晚上，兩個居民都留下來了。
But when they see each other still there in the morning, they gain new information.
但是到了隔天早上，當他們看到彼此都還在，他們得到了新的訊息。
Adria realizes that if Bill had seen a non-green-eyed person next to him,
Adria的想法是：如果Bill看到的人沒有綠色眼睛，
he would have left the first night after concluding the statement could only refer to himself.
那Bill在第一天晚上就會要求離開。當他得到這個結論的時候，就會推論出：自己有綠色眼睛。
Bill simultaneously realizes the same thing about Adria.
而Bill也會得到相同的結論。
The fact that the other person waited tells each prisoner his or her own eyes must be green.
由于另一個人還在等待，沒有離開島嶼，這個事實告訴每位居民：他們自己的眼睛一定是綠色的。
And on the second morning, they're both gone.
根據第二天早上的結果，他們兩個都會要求離開。
Now imagine a third prisoner.
現在，假設島上有三個居民。
Adria, Bill and Carl each see two green-eyed people,
Adria，Bill和Carl都看到其他兩位擁有綠色眼睛，
but aren't sure if each of the others is also seeing two green-eyed people, or just one.
但無法確定其他兩位，也同樣看到兩個綠眼的人，或是只看到一個(綠眼的人)。
They wait out the first night as before, but the next morning, they still can't be sure.
他們像之前一樣度過第一個晚上，到了隔天早上，他們還是不能確定。
