by super intelligent alien overlords.

被非常聰明的外星人首領抓走了

The aliens think humans look quite tasty,

這些外星人們覺得人類看起來很好吃

but their civilization forbids eating highly logical and cooperative beings.

但是他們的文化是禁止食用具有高度邏輯和合作能力的生物的

Unfortunately, they're not sure whether you qualify,

不幸的是，他們不確定你們是否符合這樣的條件

so they decide to give you all a test.

所以他們決定測試一下你們

Through its universal translator,

根據宇宙翻譯機

the alien guarding you tells you the following:

守衛外星人告訴你們以下的測試內容：

You will be placed in a single-file line facing forward in size order

你們會依據身高大小被排列成一直線，所有人向前看

so that each of you can see everyone lined up ahead of you.

所以你們每個人都會看到排在你們前面的人

You will not be able to look behind you or step out of line.

你不能往後看或是離開這條隊伍

Each of you will have either a black or a white hat on your head

你們每一個人頭上都會戴著黑色或白色的帽子

assigned randomly,

誰戴什麼顏色是隨機的

and I won't tell you how many of each color there are.

我不會告訴你們每個顏色的帽子各有多少頂

When I say to begin, each of you must guess the color of your hat

當我說開始的時候，你們每個人就要猜出自己戴了什麼顏色的帽子

starting with the person in the back and moving up the line.

從隊伍最後面的人開始依序猜

And don't even try saying words other than black or white

不能說出除了「黑色」或「白色」之外的詞

or signaling some other way, like intonation or volume;

也不能用改變音調或音量的方式提示其他人

you'll all be eaten immediately.

不然你們會立刻被吃掉

If at least nine of you guess correctly, you'll all be spared.

如果你們至少有9個人猜對，你們就會被赦免

You have five minutes to discuss and come up with a plan,

你們有五分鐘來討論和想出計畫

and then I'll line you up, assign your hats, and we'll begin.

時間到之後我就會將你們排好，戴上帽子，然後開始

Can you think of a strategy guaranteed to save everyone?

你能想出一個保證能救出大家的策略嗎？

Pause the video now to figure it out for yourself.

現在請暫停影片然後自己想想看

Answer in: 3

公佈解答：3秒

Answer in: 2

公佈解答：2秒

Answer in: 1

公佈解答：1秒

The key is that the person at the back of the line

關鍵在於隊伍最後面的人

who can see everyone else's hats can use the words "black" or "white"

這位可以看到其他所有人的帽子的人，可以使用「黑色」或「白色」的詞語

to communicate some coded information.

來傳達一些秘密的資訊

So what meaning can be assigned to those words

所以這兩個單字可以代替什麼樣的意義

that will allow everyone else to deduce their hat colors?

來讓其他人推論他們的帽子顏色呢？

It can't be the total number of black or white hats.

那兩個詞所代表的意義不可能會是指黑色或白色的總數

There are more than two possible values,

不過有另外兩個可行的意思

but what does have two possible values is that number's parity,

這兩個可行的意思就是數字的奇偶性

that is whether it's odd or even.

也就是奇數或偶數

So the solution is to agree that whoever goes first will,

所以解決的方法就是和最先猜的人達成協議

for example, say "black" if he sees an odd number of black hats

例如，如果他看到奇數頂黑色帽子就說「黑色」

and "white" if he sees an even number of black hats.

如果看到偶數頂黑色帽子就說「白色」

Let's see how it would play out if the hats were distributed like this.

我們來看看如果帽子的分配是這樣的話，使用這個方法會是什麼樣子

The tallest captive sees three black hats in front of him,

最高的俘虜看到他眼前有三頂黑色帽子

so he says "black," telling everyone else he sees an odd number of black hats.

所以他說「黑色」來告訴大家他看到奇數頂黑帽

He gets his own hat color wrong, but that's okay

他猜錯了他自己的帽子顏色，不過沒關係

since you're collectively allowed to have one wrong answer.

因為你們被允許有一個錯誤的機會

Prisoner two also sees an odd number of black hats,

第二個俘虜也看到了奇數頂黑帽

so she knows hers is white, and answers correctly.

所以她知道自己的帽子是白色，答案對了

Prisoner three sees an even number of black hats,

第三個俘虜看到偶數頂黑帽

so he knows that his must be one of the black hats

所已他知道他必定是其中一個

the first two prisoners saw.

前兩人所看到的戴黑帽的人

Prisoner four hears that and knows

第四個俘虜聽到了，也知道

that she should be looking for an even number of black hats

她應該找出偶數頂黑帽

since one was behind her.

因為已有一頂黑帽在她後面

But she only sees one, so she deduces that her hat is also black.

但她只看到一頂，所以她推斷她自己的帽子也是黑的

Prisoners five through nine are each looking for an odd number of black hats,

俘虜五到九都在找尋奇數頂帽子

which they see, so they figure out that their hats are white.

他們都看到了奇數頂帽子，所以他們推論自己的帽子是白色的

Now it all comes down to you at the front of the line.

現在歸結到了隊伍最前方的你

If the ninth prisoner saw an odd number of black hats,

如果第九個俘虜看到的是奇數頂黑帽

that can only mean one thing.

這就代表了你的帽子只能是黑的

You'll find that this strategy works for any possible arrangement of the hats.

你會發現這個方法適用於任何可能的帽子顏色排列

The first prisoner has a 50% chance of giving a wrong answer about his own hat,

第一個俘虜有一半的機會猜錯他的帽子顏色

but the parity information he conveys

但是他傳達的奇偶性資料

allows everyone else to guess theirs with absolute certainty.

使得其他人都能有絕對的把握來猜出他們自己的帽子顏色

Each begins by expecting to see an odd or even number of hats

每個人都預期自己該看到奇數或偶數頂

of the specified color.

特定顏色的帽子

If what they count doesn't match, that means their own hat is that color.

如果他們數的數量和預期的不符，就表示他們的帽子就是那個顏色

And everytime this happens,

依次執行下去

the next person in line will switch the parity they expect to see.

隊伍中的下一個人就會改變他們預期看到的奇偶性

So that's it, you're free to go.

就是這樣，你們都自由了

It looks like these aliens will have to go hungry,

看起來這些外星人將會挨餓了

or find some less logical organisms to abduct.

或者他們可能尋找並綁走一些更沒邏輯性的生物來食用