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囚徒帽子的难题你能解开吗? – 译学馆
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囚徒帽子的难题你能解开吗?

Can you solve the prisoner hat riddle? - Alex Gendler

你和其他九个人
You and nine other individualshave been captured
被拥有高智商的外星统治者抓走了
by super intelligent alien overlords.
这些外星人觉得人类看起来非常美味
The aliens think humans look quite tasty,
但是他们的文明禁止他们食用逻辑思维强且懂得合作的生物
but their civilization forbids eatinghighly logical and cooperative beings.
不幸的是 他们不知道你们是否符合标准
Unfortunately, they’re not surewhether you qualify,
所以他们决定让你们做一个测试
so they decide to give you all a test.
这个领头的外星人使用宇宙翻译器
Through its universal translator,
告诉了你们如下信息:
the alien guarding you tells you the following:
你们会被按照身高依次排成一列纵队
You will be placed in a single-file line facing forward in size order
这样每个人都能看见站在自己前面的人
so that each of you can see everyone lined up ahead of you.
但你们不能往后看 或者是走出队列
You will not be able to look behind you or step out of line.
每个人头上都会随机地
Each of you will have either
戴一顶白色或者黑色的帽子
a black or a white hat on your head assigned randomly,
但你不会被告知每种颜色的帽子有多少
and I won’t tell you how many of each color there are.
当我说开始的时候
When I say to begin,
每个人都必须猜自己头上帽子是什么颜色
each of you must guess the color of your hat
从排在队列最后面的那个人开始一直到最前面
starting with the person in the back and moving up the line.
不准说“黑白”这两个字以外的词
And don’t even try saying wordsother than black or white
或者改变语调和声音大小等带有提示性的声音
or signaling some other way,like intonation or volume;
否则你们立刻就要被吃掉
you’ll all be eaten immediately.
如果你们中有九个都猜对的话 所有人都能幸免
If at least nine of you guess correctly, you’ll all be spared.
你们有五分钟的时间来讨论
You have five minutes to discuss
并想出解决问题的办法
and come up with a plan,
然后我会让你们排好队 分派你们帽子
and then I’ll line you up, assign your hats,
下面我们开始
and we’ll begin.
你能想到一个万全之策来保护每一个人吗?
Can you think of a strategy guaranteedto save everyone?
暂停视频 想一下你的对策
Pause the video nowto figure it out for yourself. Answer in: 3
三秒之内作答 三 二 一
Answer in: 3 2 1
解决问题的关键在于 站在队列中的最后一个人
The key is that the person at the back of the line
他能看到除自己以外的每一个人的帽子的颜色
who can see everyone else’s hatscan use the words”black” or”white”
并用”黑” “白”这两个字作为交流的密码信息
to communicate some coded information.
那么 这些词要被赋予什么样的涵义
So what meaning can beassigned to those words
才能让每一个人都猜出自己帽子的颜色呢
that will allow everyone elseto deduce their hat colors?
它不可能是黑色或者白色帽子的总数
It can’t be the total numberof black or white hats.
有超过两种以上的确切涵义
There are more than two possible values,
但确实包含两种可能涵义的就是 黑白帽子的奇偶性
but what does have two possible valuesis that number’s parity,
它不是奇数就是偶数
that is whether it’s odd or even.
所以解决的办法就是 无论谁做第一个
So the solution is to agreethat whoever goes first will,
例如 当他看到黑色帽子为奇数时就说”黑色”
for example, say”black” if he seesan odd number of black hats
而看到黑色帽子为偶数时就说”白色”
and”white” if he seesan even number of black hats.
我们来看看如果帽子是这样分派的
Let’s see how it would play out
这种方法能否行得通
if the hats were distributed like this.
个子最高的俘虏会看到他前面的三顶黑色的帽子
The tallest captive sees three blackhats in front of him,
所以他说”黑色” 来告诉每一个人他看到的黑色帽子数量是奇数
so he says”black,” telling everyone elsehe sees an odd number of black hats.
他猜错了自己所戴帽子的颜色 但没关系
He gets his own hat color wrong,but that’s okay
因为 你可以给出一次错误答案
since you’re collectively allowedto have one wrong answer.
第二个俘虏也知道黑色帽子是奇数
Prisoner two also sees an oddnumber of black hats,
所以 她知道自己的帽子是白色 并且答对了
so she knows hers is white,and answers correctly.
第三个俘虏看到的黑色帽子个数为偶数
Prisoner three seesan even number of black hats,
所以他肯定自己是 前两个俘虏看到的
so he knows that his must be one of the black hats
戴着黑色帽子人中的一个
the first two prisoners saw.
第四个俘虏听到并且知道
Prisoner four hears that and knows
她该看到的黑色帽子个数
that she should be looking
是一个偶数
for an even number of black hats
因为在她的后面人戴的是黑帽
since one was behind her.
但是她只看到了一个黑帽
But she only sees one,
所以她推测 自己戴的帽子也是黑色的
so she deduces that her hat is also black.
这九个人中有五个俘虏都
Prisoners five through nine are each looking
预测自己看到的黑色帽子个数会是个奇数
for an odd number of black hats,
所以他们知道自己戴的帽子是白色的
which they see, so they figure out that their hats are white.
现在 一切都取决于队伍中的第一个人
Now it all comes down to you at the front of the line.
如果第九个俘虏知道黑色帽子的个数是一个奇数
If the ninth prisoner sawan odd number of black hats,
那么就意味着一件事
that can only mean one thing.
你就会发现这种方法对猜出帽子的任意一种排列方式都很有效
You’ll find that this strategy works for any possible arrangement of the hats.
第一个俘虏有百分之五十的概率
The first prisoner has a 50 % chance
会猜错自己所戴帽子的颜色
of giving a wrong answer about his own hat,
但是他传递了帽子数量的奇偶性信息
but the parity information he conveys
使每个人都能确切的猜出自己帽子的颜色
allows everyone elseto guess theirs with absolute certainty.
每次开始 俘虏们都期待着看到
Each begins by expecting to see
有着规定的黑白颜色
an odd or even number of hats
帽子的奇偶性
of the specified color.
如果和他们预想之中的不相符
If what they count doesn’t match,
就意味着他们自己的帽子就是自己猜想的颜色
that means their own hat is that color.
且屡试不爽
And everytime this happens,
在行列之中的下一个俘虏会改变他们希望看到的奇偶性
the next person in line will switch the parity they expect to see.
就是这样 你们自由了
So that’s it, you’re free to go.
看起来这些外星人要饿肚子了
It looks like these alienswill have to go hungry,
或者是绑架一些逻辑性不强的生物
or find some less logicalorganisms to abduct.

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视频概述

这是一个非常有意思的逻辑推理小游戏,利用数字的奇偶性就能准确无误的推断出正确的答案。

听录译者

收集自网络

翻译译者

大可

审核员

审核团V

视频来源

https://www.youtube.com/watch?v=N5vJSNXPEwA

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