Can you solve the prisoner hat riddle

你能解決囚帽之謎嗎

來(lái)源視頻

You and nine other individuals have been captured by super intelligent alien overlords.?

The aliens think humans look quite tasty, but their civilization forbids eating highly logical and cooperative beings.?

Unfortunately, they're not sure whether you qualify, so they decide to give you all a test.

你和其他九個(gè)人被高智商的外星人統(tǒng)治者俘虜了。

他們覺(jué)得地球人看起來(lái)很好吃，但是他們的文明禁止他們吃?有很強(qiáng)邏輯性和合作性的生物。

不幸的是，他們不確定你們是否合乎標(biāo)準(zhǔn)，所以他們決定給你們所有人一個(gè)測(cè)試。

Through its universal translator, the alien guarding you tells you the following:?You will be placed in a single-file line facing forward in size order so that each of you can see everyone lined up ahead of you.?

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

Each of you will have either a black or a white hat on your head assigned randomly, and I won't tell you how many of each color there are.

通過(guò)他們的“全宇宙通翻譯“軟件，外星守衛(wèi)告訴你以下信息：你們會(huì)被從高到矮排成一條直線，這樣每個(gè)人就可以看到站在前面的所有人，

?你不能往后看或者走到線外。

每個(gè)人的頭上會(huì)有一頂白色或者黑色的帽子。

帽子的顏色是隨機(jī)分配的，而且我不會(huì)告訴你 每種顏色的帽子總共有幾個(gè)。

When I say to begin, each of you must guess the color of your hat starting with the person in the back and moving up the line.

And don't even try saying words other than black or white or signaling some other way, like intonation or volume; you'll all be eaten immediately.?

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

You have five minutes to discuss and come up with a plan, and then I'll line you up, assign your hats, and we'll begin.?

Can you think of a strategy guaranteed to save everyone??

Pause the video now to figure it out for yourself.?

Answer in: 3

Answer in: 2

Answer in: 1

當(dāng)我說(shuō)“開(kāi)始”時(shí)， 每個(gè)人必須猜測(cè)自己帽子的顏色，從最后一個(gè)人開(kāi)始。

不要試圖說(shuō)除了黑或白以外的詞，或者通過(guò)聲調(diào)或音量等其他方式做出暗示，要不你們就會(huì)馬上被吃掉。

如果至少九個(gè)人能猜對(duì)，你們就會(huì)被釋放。

你們有五分鐘的時(shí)間來(lái)商量，想出一個(gè)方案，然后我會(huì)把你們排成一排， 分發(fā)帽子，然后就開(kāi)始。

你能想到一個(gè)絕對(duì)能救大家的計(jì)劃嗎？

暫停下視頻，好好想想。

倒計(jì)時(shí)：3、2、1。

The key is that the person at the back of the line who can see everyone else's hats can use the words "black" or "white" to communicate some coded information.?

So what meaning can be assigned to those words that will allow everyone else to deduce their hat colors?

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

There are more than two possible values, but what does have two possible values is that number's parity, that is whether it's odd or even.?

So the solution is to agree that whoever goes first will, for example, say "black" if he sees an odd number of black hats and "white" if he sees an even number of black hats.

其實(shí)重點(diǎn)在于排在隊(duì)尾的人，他在看到其他所有人的帽子后可以用黑白來(lái)傳遞加密信息。

那么我們應(yīng)當(dāng)在這些詞上附加什么含義，以使得其他人可以推測(cè)他們帽子的顏色呢？

首先不能是黑帽子或白帽子的總數(shù)，

那樣可能的值就會(huì)超過(guò)兩種。但是數(shù)字的奇偶性恰好只有兩種可能，那就是奇數(shù)，或偶數(shù)。

所以，解決方案就在于第一個(gè)說(shuō)的人——舉個(gè)例子，比如他看到了奇數(shù)個(gè)黑帽子， 他就要說(shuō)“黑色”，當(dāng)他看到了偶數(shù)個(gè)黑帽子時(shí)就要說(shuō)“白色”。

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

The tallest captive sees three black hats in front of him, so he says "black," telling everyone else he sees an odd number of black hats.?

He gets his own hat color wrong, but that's okay since you're collectively allowed to have one wrong answer.?

Prisoner two also sees an odd number of black hats, so she knows hers is white, and answers correctly.

Prisoner three sees an even number of black hats, so he knows that his must be one of the black hats the first two prisoners saw.

我們看下如果帽子顏色是這樣分配的話， 這個(gè)策略執(zhí)行起來(lái)如何。

最高的人看到前面有三個(gè)黑帽子，所以他說(shuō)“黑色”， 告訴其他所有人他看到的是奇數(shù)個(gè)黑帽子。

他沒(méi)有說(shuō)對(duì)自己帽子的顏色，但是沒(méi)關(guān)系，因?yàn)樗斜蛔サ娜丝偣部梢苑敢粋€(gè)錯(cuò)誤。

第二高的人也看到奇數(shù)個(gè)黑帽子，她就會(huì)知道她的是白色的，就答對(duì)了。

第三個(gè)人看到前面是偶數(shù)個(gè)黑帽子，所以他知道他的一定是前面兩個(gè)人看到的其中一頂黑帽子。

Prisoner four hears that and knows that she should be looking for an even number of black hats since one was behind her.?

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

Prisoners five through nine are each looking for an odd number of black hats, which they see, so they figure out that their hats are white.?

Now it all comes down to you at the front of the line. If the ninth prisoner saw an odd number of black hats, that can only mean one thing.?

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

第四個(gè)人聽(tīng)到后就知道她應(yīng)當(dāng)看到前面有偶數(shù)頂黑帽子，因?yàn)槠渲幸豁斣谒砗螅?/p>

但是她只看到了一個(gè)， 所以她推測(cè)出自己的也是黑帽子。

第五個(gè)人至第九個(gè)人每個(gè)都尋找奇數(shù)個(gè)黑帽子，他們找到了，所以他們推測(cè) 自己的帽子都是白色的。

現(xiàn)在到了站在最前面的你了，假如第九個(gè)人看到的是奇數(shù)個(gè)黑帽子的話，那就只有一種可能（最后一個(gè)人是黑帽子）。

你會(huì)發(fā)現(xiàn)這個(gè)策略 對(duì)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, but the parity information he conveys allows everyone else to guess theirs with absolute certainty.

Each begins by expecting to see an odd or even number of hats of the specified color.?

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

And everytime this happens, the next person in line will switch the parity they expect to see.

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

It looks like these aliens will have to go hungry, or find some less logical organisms to abduct.

最開(kāi)始的那個(gè)人有50%的幾率出錯(cuò)，但是他傳達(dá)的奇偶性的信息讓其他所有人都可以猜對(duì)自己帽子的顏色。

每個(gè)人在開(kāi)始時(shí)都假定自己 應(yīng)當(dāng)在身前看到奇數(shù)或偶數(shù)個(gè)特定顏色的帽子，如果他們的數(shù)字不對(duì)的話， 意味著他們自己的帽子就是那種特定的顏色。

每次這樣的情況發(fā)生后，下個(gè)人就知道他們需要看到 奇數(shù)還是偶數(shù)個(gè)特定顏色的帽子。

好了成功了，你們可以走了。

看起來(lái)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(lái)綁架。