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三神谜题

Can you solve the three gods riddle? - Alex Gendler

Created by logician Raymond Smullyan
由哲学家Raymond Smullyan创作
and popularized by his colleague George Boolos,
并经他的同事George Boolos普及的
this riddle has been called the hardest logic puzzle ever.
这一谜题被称为有史以来最难的逻辑谜题
You and your team have crash-landed on an ancient planet.
你和你的队友在一个古老的星球上坠机了
The only way off is to appease its three alien overlords,
离开的唯一办法就是通过把正确的神器
Tee, Eff, and Arr,
拿给Tee Eff Arr三位君主
by giving them the correct artifacts.
让他们满意
Unfortunately, you don’t know who is who.
不幸的是 你不知道谁是谁
From an inscription,
从一块刻有铭文的石碑上
you learn that you may ask three “yes” or “no”questions
你明白自己可以问三个用“是”或“不是”回答的问题
each addressed to any one lord.
可以向任一君主提问
Tee’s answers are always true,
Tee的回答总是真实的
Eff’s are always false,
Eff的回答都是错的
and Arr’s answer is random each time.
Arr的答案每次都是随机的
But there’s a problem.
但还有一个问题
You’ve deciphered the language enough to ask any question,
你破解了他们的语言 可以问任何问题
but you don’t know which
但是你不知道
of the two words’ozo’ and’ulu’ means yes
ozo和ulu这两个单词哪个是“是”
and which means no.
哪一个是“否”
How can you still figure out which alien is which?
你还能分辨出来谁是谁吗
Pause here if you want to figure it out for yourself!
如果你需要思考一下可以在这里暂停
Answer in: 3 2 1
3 2 1 答案揭晓
At first, this puzzle seems not just hard,
首先 这个谜题看起来不仅难
but downright impossible.
而且似乎无解
What good is asking a question if you can neither
如果你既无法理解答案也不知道真假
understand the answer nor know if it’s true?
提问还有意义吗
But it can be done.
其实这个问题可以解决
The key is to carefully formulate our questions
关键在于小心提问
so that any answer yields useful information.
这样每个答案都可以给出必要的信息
First of all, we can get around to not knowing what’ozo’ and’ulu’ mean
首先 通过把ozo和ulu包含在问题里
by including the words themselves in the questions,
我们不需要知道ozo和ulu的具体意思也可以解答
and secondly, if we load each question with a hypothetical condition,
其次 我们要让问题里包含一个假设
whether an alien is lying or not won’t actually matter.
他们是否在撒谎就变得不重要了
To see how that could work,
让我们看看如何才能做到这一点
imagine our question is whether two plus two is four.
假设我们的问题是2+2是不是等于4
Instead of posing it directly,
不要直接提问
we say,” If I asked you whether two plus two is four,
我们可以说 “如果我问你2+2是不是4
would you answer’ozo’?”
你会回答‘ozo’吗?”
If’ozo’ means yes and the overlord is Tee,
如果ozo的意思是正确 并且我们提问的是Tee
it truthfully replies,”ozo.”
他会坦诚的回答ozo
But what if we ask Eff? Well,
如果我们提问的是Eff呢
it would answer”ulu,” or no to the embedded question,
他会对于嵌入的问题回答ulu 也就是“不”
so it lies and replies’ozo’ instead.
因此他会撒谎并回复ozo
And if’ozo’ actually means no,
如果ozo是“不”的意思
then the answer to our embedded question is’ulu,’
那么对于嵌入的问题答案应该是ulu
and both Tee and Eff still reply’ozo,’
Tee和Eff因为自身的秉性
each for their own reasons.
都会回答ozo
If you’re confused about why this works,
如果你搞不清楚这样怎么能解开谜题
the reason involves logical structure.
其实是因为这里有个逻辑关系
A double positive and a double negative
双重肯定和双重否定
both result in a positive.
都指向肯定
Now we can be sure
现在我们可以确定
that asking either Tee or Eff a question put this way
如果我们像之前说过的那样
will yield’ozo’
提问一个答案是正确的问题
if the hypothetical question is true.
Tee和Eff都会回答ozo
And ‘ulu’ if it’s false.
如果答案是不正确的 他们会回答ulu
Regardless of what each word actually means.
而不用去考虑这两个词的实际含义
Unfortunately, this doesn’t help us with Arr.
不幸的是 这个问题不能帮我们识别Arr
But don’t worry,
不过不用担心
we can use our first question to identify one alien lord
我们可以用第一个问题判断出
that definitely isn’t Arr.
一位肯定不是Arr的君主
Then we can use the second
然后我们可以用第二个问题
to find out whether its Tee or Eff.
来识别出谁是Tee和Eff
And once we know that,
一旦我们搞清楚了
we can ask it to identify one of the others.
我们可以通过提问他来确定其他人
So let’s begin.
我们开始吧
Ask the alien in the middle,
先提问中间的一位君主
If I asked you whether the overlord
如果我问你我左边的这位君主
on my left is Arr, would you answer’ozo’?”
是不是Arr 你会回答ozo吗
If the reply is’ozo,’
如果得到的回复是ozo
there are two possibilities.
那么有两种可能
You could already be talking to Arr,
你问的可能就是Arr
in which case the answer is meaningless.
这样他的回答就是没有意义的
But otherwise, you’re talking to either Tee or Eff,
或者你问及的人就是Tee或者Eff
and as we know,
我们已经知道
getting’ozo’ from either one
不管谁回答ozo
means your hypothetical question was correct,
都意味着你假设的问题是对的
and the left overlord is indeed Arr.
那么左边的君主一定是Arr
Either way, you can be sure
不管怎样 你都可以确定
the alien on the right is not Arr.
右边的那位一定不是Arr
Similarly, if the answer is’ulu’,
同理 如果我们得到的答案是ulu
then you know the alien on the left can’t be Arr.
你就会知道左边的君主一定不是Arr
Now go to the overlord you’ve determined
现在提问你已经确定
isn’t Arr, and ask:
不是Arr的君主
“If I asked’are you Eff?’
“如果我问你你是不是Eff
Would your answer ‘ozo’?”
你会回答ozo吗?”
Since you don’t have to worry
因为你不用担心
about the random possibility,
答案的不确定性
either answer will establish its identity.
不管他回答什么都可以确认他的身份
Now that you know whether its answers are true or false,
现在你知道他的回答是正确的还是错误的
ask the same alien
再问他一个问题
The process of elimination will identify the remaining one.
消除法可以让你确定最后一位君主的身份
The satisfied overlords help you repair your ship
满意的君主们帮你修好了飞船
and you prepare for takeoff.
你可以准备起飞了
Allowed one final question,
现在你还可以问一个问题
you ask Tee if it’s a long way to Earth,
你向Tee提问:回地球远不远
and he answers”ozo.”
他回答说ozo
Too bad you still don’t know what that means.
很不幸你还是不知道他说的是什么意思

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视频概述

怎样解答看似无解的三神谜题

听录译者

收集自网络

翻译译者

张总的小蜜

审核员

审核员 V

视频来源

https://www.youtube.com/watch?v=LKvjIsyYng8

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