Placeholder Image

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

  • 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

Created by logician Raymond Smullyan

邏輯學家Raymond Smullyan創造

字幕與單字

影片操作 你可以在這邊進行「影片」的調整,以及「字幕」的顯示

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)

  • 381 28
    韓澐 發佈於 2021 年 01 月 14 日
影片單字