## 字幕列表 影片播放

• Created by logician Raymond Smullyan

邏輯學家Raymond Smullyan創造

• 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

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

Created by logician Raymond Smullyan

B1 中級 中文 美國腔 TED-Ed 問題 謎題 問句 外星人 回答

# 你能解開三神之謎嗎？- Alex Gendler (Can you solve the three gods riddle? - Alex Gendler)

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韓澐 發佈於 2021 年 01 月 14 日