Can you solve the three gods riddle? - Alex Gendler

翻译人员: Mingyu Cui 校对人员: Lipeng Chen

Created by logician Raymond Smullyan

由逻辑学家雷蒙德·斯穆里安设计，

and popularized by his colleague George Boolos,

并通过他的同事乔治·布罗斯为人熟知的这道题目，

this riddle has been called the hardest logic puzzle ever.

被称为史上最难的逻辑谜题。

You and your team have crash-landed on an ancient planet.

你和一行人迫降在了一个远古行星上。

The only way off is to appease its three alien overlords,

离开的唯一方法是把正确的工艺品，

Tee, Eff, and Arr,

给三个外星统治者T，F和R，

by giving them the correct artifacts.

从而取悦他们。

Unfortunately, you don't know who is who.

不幸的是，你不知道谁是谁。

From an inscription, you learn that you may ask three yes or no questions,

你从铭文上得知你可以问 每个统治者一个是或否问题，

each addressed to any one lord.

Tee's answers are always true,

T总说真话，

Eff's are always false,

F总说假话，

and Arr's answer is random each time.

R的答案是随机的。

But there's a problem.

但有一个麻烦。

You've deciphered the language enough to ask any question,

你已经掌握了足够的外星语言，可以问任何问题，

but you don't know which of the two words 'ozo' and 'ulu' means yes

但你不知道“哦”和“唔”这两个词，

哪个是“是”，哪个是“否”。

and which means no.

How can you still figure out which alien is which?

你怎么才能弄清楚谁是谁呢？

Pause here if you want to figure it out for yourself!

在这里暂停来思考答案！

Answer in: 3

答案：3

2

答案：2

1

答案：1

At first, this puzzle seems not just hard, but downright impossible.

最开始，你会觉得这个问题不只是难， 简直就是不可能的。

What good is asking a question

问一个问题，却理解不了答案，

if you can neither understand the answer nor know if it's true?

也不知道答案的真假，意义何在？

But it can be done.

但这个问题是有解的。

The key is to carefully formulate our questions

关键在于规范问题的问法，

so that any answer yields useful information.

从而让每种可能的回答都包含有效信息。

First of all, we can get around to not knowing what 'ozo' and 'ulu' mean

首先，我们把“哦”和“唔”放进问题中，

by including the words themselves in the questions,

就能绕过不知道“哦”和“唔”的意思的麻烦；

and secondly, if we load each question with a hypothetical condition,

其次，如果我们在每个问题前面加上假设条件，

whether an alien is lying or not won't actually matter.

那么回答者是否说谎就没关系了。

To see how that could work,

举个例子：

imagine our question is whether two plus two is four.

比如我们问2+2是不是4。

Instead of posing it directly,

我们不直接问，

we say, "If I asked you whether two plus two is four,

而是问，“如果我问你2+2是不是4，

would you answer 'ozo'?"

你的答案是不是‘哦’？”

If 'ozo' means yes and the overlord is Tee,

如果“哦”是“是”，而回答者是T，

it truthfully replies, "ozo."

他会诚实地说“哦”。

But what if we ask Eff?

但如果回答者是F呢？

Well, it would answer "ulu," or no to the embedded question,

他本来要回答“唔”（“否”） ，

so it lies and replies 'ozo' instead.

但是他说谎，还是回答了“哦”。

And if 'ozo' actually means no,

如果“哦”的意思是“否”，

then the answer to our embedded question is 'ulu,'

那么2+2=4问题的答案就本应是“唔”，

and both Tee and Eff still reply 'ozo,'

而T和F仍然都回答“哦”，

each for their own reasons.

两人原因不同。

If you're confused about why this works,

如果你对此有疑惑，

the reason involves logical structure.

是因为这涉及到逻辑结构。

A double positive and a double negative both result in a positive.

正正得正，负负也得正。

Now, we can be sure that asking either Tee or Eff a question put this way

现在，我们可以保证问T或F这样一个问题

will yield 'ozo' if the hypothetical question is true

如果问题为真，那么他们的回答一定是“哦”，

and 'ulu' if it's false

如果问题为假，那么他们的回答一定是“唔”，

regardless of what each word actually means.

这样就避开了“哦”和“唔”的意思。

Unfortunately, this doesn't help us with Arr.

但不幸的是，这个方法对R无效。

But don't worry, we can use our first question to identify one alien lord

别着急，我们可以用我们的第一个问题

判断出一个一定不是R的外星人。

that definitely isn't Arr.

Then we can use the second to find out whether its Tee or Eff.

然后在用第二个问题判断他是T还是F。

And once we know that,

知道了这些之后，

we can ask it to identify one of the others.

我们就可以问他来判断另两个外星人。

So let's begin.

咱们开始吧。

Ask the alien in the middle,

问中间的外星人，

"If I asked you whether the overlord on my left is Arr, would you answer 'ozo'?"

“如果我问你左边的外星人是不是R， 你会回答‘哦’吗？”

If the reply is 'ozo,' there are two possibilities.

如果回答是“哦”，那么有两种情况。

You could already be talking to Arr, in which case the answer is meaningless.

你可能就在跟R说话， 这样答案就毫无意义。

But otherwise, you're talking to either Tee or Eff,

也有可能，你正在和T或F说话，

and as we know,

那么可以知道，

getting 'ozo' from either one means your hypothetical question was correct,

如果答案是“哦”意味着我们的假设问题是对的，

and the left overlord is indeed Arr.

左边的外星人的确是R。

Either way, you can be sure the alien on the right is not Arr.

无论是哪种情况， 你都能确定右边的外星人不是R。

Similarly, if the answer is 'ulu,'

相似地，如果答案是“唔”，

then you know the alien on the left can't be Arr.

你就能知道左边的外星人一定不是R。

Now go to the overlord you've determined isn't Arr and ask,

第二个问题问向确定不是R的外星人，

"If I asked 'are you Eff?' would you answer 'ozo'?"

“如果我问‘你是F吗’，你会回答‘哦’吗？”

Since you don't have to worry about the random possibility,

既然对方的答案不会是随机的，

either answer will establish its identity.

从他的回答一定可以判断他的身份。

Now that you know whether its answers are true or false,

你现在知道他的答案是真是假，

ask the same alien whether the center overlord is Arr.

最后一个问题问他中间的外星人是不是R。

The process of elimination will identify the remaining one.

最后用排除法确定最后一个外星统治者。

The satisfied overlords help you repair your ship

满意的统治者帮你们修好了飞船，

and you prepare for takeoff.

你们将要离开了。

Allowed one final question, you ask Tee if it's a long way to Earth,

你被允许多问一个问题。

你问T，“从这到地球远吗？” T说，“哦。”

and he answers "ozo."

Too bad you still don't know what that means.

你还是不知道从这到地球远不远。