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But she only sees one, so she deduces that her hat is also black.
但是她只看到了一個，所以她推測出自己的也是黑帽子。
Prisoners five through nine are each looking for an odd number of black hats,
第五個人至第九個人每個都尋找奇數個黑帽子，
which they see, so they figure out that their hats are white.
他們找到了，所以他們推測自己的帽子都是白色的。
Now it all comes down to you at the front of the line.
現在到了站在最前面的你了。
If the ninth prisoner saw an odd number of black hats, that can only mean one thing.
假如第九個人看到的是奇數個黑帽子的話，那就只有一種可能（最后一個人是黑帽子）。
You'll find that this strategy works for any possible arrangement of the hats.
你會發現這個策略對所有的排列組合都是適用的。
The first prisoner has a 50% chance of giving a wrong answer about his own hat,
最開始的那個人有50%的幾率出錯，
but the parity information he conveys allows everyone else to guess theirs with absolute certainty.
但是他傳達的奇偶性的信息讓其他所有人都可以猜對自己帽子的顏色。
Each begins by expecting to see an odd or even number of hats of the specified color.
每個人在開始時都假定自己應當在身前看到奇數或偶數個特定顏色的帽子。
If what they count doesn't match, that means their own hat is that color.
如果他們的數字不對的話，意味著他們自己的帽子就是那種特定的顏色。
And everytime this happens, the next person in line will switch the parity they expect to see.
每次這樣的情況發生后，下個人就知道他們需要看到奇數還是偶數個特定顏色的帽子。
So that's it, you're free to go.
好了成功了，你們可以走了。
It looks like these aliens will have to go hungry, or find some less logical organisms to abduct.
看起來這些外星人只好餓肚子了，或者去找些其他邏輯差的生物來綁架。
