Can you solve the three gods riddle? - Alex Gendler

譯者: Mingyu Cui 審譯者: 庭芝 梁

Created by logician Raymond Smullyan

這一則謎題是由邏輯學家 雷蒙德．斯穆裏安所設計

and popularized by his colleague George Boolos,

並且由他的同事 喬治．布羅斯推廣而廣受歡迎

this riddle has been called the hardest logic puzzle ever.

被稱為「史上最難解的邏輯謎題」

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

你和隊友迫降在一個遠古行星上

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

離開這裡的唯一方法 是取悅三位外星統治者

Tee, Eff, and Arr,

Tee 、 Eff 和 Arr

by giving them the correct artifacts.

方法是把三件工藝品 正確地獻給他們

Unfortunately, you don't know who is who.

不幸的是，你不知道 他們到底誰是誰

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

你從銘文上得知 可以問每位統治者一個是非題

each addressed to any one lord.

Tee's answers are always true,

Tee 總是說真話

Eff's are always false,

Eff 總是說假話

and Arr's answer is random each time.

Arr 的答案則是隨機決定

But there's a problem.

但有一個麻煩之處

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

你已經掌握了足夠的外星語言 可以問任何問題

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

但你不知道 「哦」和「唔」這兩個詞

哪個代表「是」，哪個代表「否」

and which means no.

How can you still figure out which alien is which?

你如何才能弄清楚，到底誰是誰呢？

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

在這裏暫停一下，來思考答案！

Answer in: 3

倒數 3 秒

2

倒數 2 秒

1

倒數 1 秒

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

一開始，你會覺得這個問題 不只是難，簡直是無法回答

What good is asking a question

只能問一個問題

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

而且無法理解答案 也不知道答案的真假

But it can be done.

但這個謎題是有解的

The key is to carefully formulate our questions

關鍵在於規範問題的問法

so that any answer yields useful information.

並且讓各種可能的回答 都包含有用的資訊

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

首先把「哦」和「唔」放進問題中

by including the words themselves in the questions,

就算我們不知道 「哦」和「唔」意思也行

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

其次，如果我們在每個問題前面 加上假設條件

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

那麽回答者是否說謊就沒關係了

To see how that could work,

舉個例子：

imagine our question is whether two plus two is four.

例如我們問 2+2 是不是等於 4

Instead of posing it directly,

我們不直接問

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

而是問：「如果我問你 2+2 是不是等於 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」代表「是」 而回答者是 Tee

it truthfully replies, "ozo."

他會誠實地回答：「哦」

But what if we ask Eff?

但如果回答者是 Eff 呢？

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

他本來要回答「唔」(代表否)

so it lies and replies 'ozo' instead.

但是他會說謊，於是回答了「哦」

And if 'ozo' actually means no,

如果「哦」代表「否」

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

那麽 2+2=4 問題的答案 就應該是「唔」

and both Tee and Eff still reply 'ozo,'

而 Tee 和 Eff 仍然都會回答「哦」

each for their own reasons.

儘管兩人都有各自的原因

If you're confused about why this works,

如果你仍然不瞭解 為何這個方法可行

the reason involves logical structure.

其實這其中的原理涉及邏輯結構

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

就是「正正得正」而「負負也得正」

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

現在，我們可以確定 只要用上面的方式問 Tee 或 Eff

will yield 'ozo' if the hypothetical question is true

如果問題為真 那麽他們一定都回答「哦」

and 'ulu' if it's false

如果問題為假 那麽他們一定都回答「唔」

regardless of what each word actually means.

這樣就不必管 「哦」和「唔」代表什麼意思

Unfortunately, this doesn't help us with Arr.

但不幸的是，這個方法對 Arr 無效

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

別著急，我們可以用第一個問題

that definitely isn't Arr.

來判斷出哪一位外星人 一定不是 Arr

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

然後再用第二個問題 判斷他是 Tee 還是 Eff

And once we know that,

知道以後

we can ask it to identify one of the others.

我們就能分辨另外兩個外星人

So let's begin.

咱們開始吧

Ask the alien in the middle,

問中間的外星人

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

如果我問你「左邊的外星人是不是 Arr？」 你會回答「哦」嗎？

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

如果回答是「哦」，那麽有兩種情況

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

你可能正在跟 Arr 說話 那答案就毫無意義

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

也有可能 你正在和 Tee 或 Eff 說話

and as we know,

那麽我們可以知道

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

如果答案是「哦」 代表我們的假設問題是對的

and the left overlord is indeed Arr.

左邊的外星人的確是 Arr

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

無論是哪種情況 你都能確定右邊的外星人不是 Arr

Similarly, if the answer is 'ulu,'

相同的，如果答案是「唔」

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

你就能知道 左邊的外星人一定不是 Arr

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

第二個問題要詢問 「確定不是 Arr 的外星人」

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

如果我問：「你是不是 Eff ， 你會回答『哦』嗎？」

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

既然對方的答案不會是隨機決定的

either answer will establish its identity.

從他的回答一定可以判斷他的身份

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

你現在就可以知道 他的答案是真還是假

ask the same alien whether the center overlord is Arr.

最後一個問題問 「中間的外星人是不是 Arr？」

The process of elimination will identify the remaining one.

用消去法確認 最後一位外星統治者的身份

The satisfied overlords help you repair your ship

滿意的統治者幫你們修好了飛船

and you prepare for takeoff.

你們將要離開了

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

你被允許再問一個問題

你問 Tee：「從這到地球遠嗎？」 Tee 回答：「哦」

and he answers "ozo."

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

麻煩的是，你還是不懂 「哦」代表是或否。