and popularized by his colleague George Boolos,

並由他的同事George Boolos推廣

this riddle has been called the hardest logic puzzle ever.

這個謎題勘稱史上最難邏輯謎題

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

你和你的團隊墜落在一個古老的星球上

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

離開的唯一方法就是安撫三個外星神

Tee, Eff, and Arr,

T、F和R

by giving them the correct artifacts.

藉由給予祂們正確物品的方式

Unfortunately, you don't know who is who.

不幸的是，你不知道誰是誰

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

你從提示中知道，你可以問三個是非題

each addressed to any one lord.

一個問題問一個神

Tee's answers are always true,

T永遠回答「是」

Eff's are always false,

F永遠回答「否」

and Arr's answer is random each time.

R每次的答案是隨機的

But there's a problem.

但是，有個問題

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

你已經對這個語言有足夠的瞭解來提問

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

但是你不知道「ozo」和「ulu」這兩個字哪一個是「是」

and which means no.

哪一個是「否」

How can you still figure out which alien is which?

這樣的話 你如何得知哪一個外星人是哪一個神？

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

暫停一下，假如你想要整理一下你的思緒的話

Answer in: 3

答案將在3秒後解答

2

2秒

1

1秒

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

首先，這個謎題不只是難，而是完全不可能

What good is asking a question

重點在於問問題

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

如果你不知道答案也不知道答案是不是正確？

But it can be done.

但是，還是可以找到答案的

The key is to carefully formulate our questions

關鍵在於如何設計你的問題

so that any answer yields useful information.

讓對方的任何答案都是有用的資訊

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

第一，我們可以不知道「ozo」和「ulu」是什麼

by including the words themselves in the questions,

將這兩個字放在問題中

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

第二，如果我們每一個問題都用假設語氣

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

無論這個外星人是否說謊就不是那麼重要了

To see how that could work,

來試試看這個方法有沒有效

imagine our question is whether two plus two is four.

想像我們的問題是2+2是否等於4

Instead of posing it directly,

而非直接問答案

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

問題是：「如果問你2+2是否等於4

would you answer 'ozo'?"

你的答案是「ozo」嗎？

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

如果「ozo」代表「是」，那這個神就是T

it truthfully replies, "ozo."

T一定會直接回答「ozo」

But what if we ask Eff?

但是，如果問F呢？

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

嗯，F的答案會是「ulu」，也就是附加問句中的「否」

so it lies and replies 'ozo' instead.

所以這個神說謊，而不是回答「ozo」

And if 'ozo' actually means no,

如果，「ozo」意思是「否」的話

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

那麼附加問句的答案就是「ulu」

and both Tee and Eff still reply 'ozo,'

T和F都會回答「ozo」

each for their own reasons.

都有他們各自的原因

If you're confused about why this works,

如果你搞不懂這些問題如何運作的話

the reason involves logical structure.

這涉及了邏輯結構

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

雙重肯定與雙重否定的結果都是肯定

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

現在，我們可以確定，無論用什麼方式問T或F

will yield 'ozo' if the hypothetical question is true

都會得到「ozo」這個答案，假設問題答案是「是」

and 'ulu' if it's false

「ulu」如果答案是「否」

regardless of what each word actually means.

無論這兩個字的真正意思是什麼

Unfortunately, this doesn't help us with Arr.

不幸的是，這仍舊無法讓我們知道R是誰

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

但是，別擔心，我們可以使用第一個問題找出其中一個神

that definitely isn't Arr.

並且肯定那不是R

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

然後，我們可以用第二個問題找出T或F

And once we know that,

一旦知道T或F

we can ask it to identify one of the others.

我們可以問問題來確定另一個是誰

So let's begin.

那麼，我們就開始吧

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'?"

「如果我問你在我左邊的是R，你的答案是「ozo」嗎？」

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

如果答案是「ozo」，那是有兩個可能

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

你可能是在和R對話，這樣的話，答案是無意義的

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

但是，如果不是R，你的談話對象不是T就是F

and as we know,

我們可以知道

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

不管T或F，答案是「ozo」代表你的假設問句是正確的

and the left overlord is indeed Arr.

那麼左邊的神就是R

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

換句話說，你可以確定右邊的不是R

Similarly, if the answer is 'ulu,'

同樣，如果答案是「ulu」

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

你就知道左邊的不是R

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

現在，問你確定不是R的神

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

「如果我問『你是F嗎？』你會回答『ozo』嗎？」

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

因為你不必擔心答案是隨機的可能

either answer will establish its identity.

隨便一個答案都可以讓你知道你談話的對象是誰

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

現在，你知道，無論答是是「是」或「否」

ask the same alien whether the center overlord is Arr.

問同一個外星人中間的神是不是R

The process of elimination will identify the remaining one.

刪去法可以判斷出剩下的是誰

The satisfied overlords help you repair your ship

感到滿足的神會幫你修復你的太空船

and you prepare for takeoff.

你就可以準備起飛了

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

請容許最後一個問題，你問T回地球會不會很遙遠

and he answers "ozo."

他的答案是「ozo」

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

那麼你還是不知道「ozo」究竟是什麼意思，這真是太糟糕了