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  • Once each year, thousands of logicians descend into the desert for Learning Man,

    每年一次,數以千計的邏輯學家都會來到沙漠,參加學習人。

  • a week-long event they attend to share their ideas,

    他們參加的為期一週的活動,分享他們的想法。

  • think through tough problems... and mostly to party.

    思考困難的問題... ...主要是為了聚會。

  • And at the center of that gathering is the world's most exclusive club,

    而在這個聚會的中心,是世界上最豪華的俱樂部。

  • where under the full moon, the annual logician's rave takes place.

    月圓之夜,一年一度的邏輯學家狂歡節在這裡舉行。

  • The entry is guarded by the Demon of Reason,

    入口處有理智之魔把守。

  • and the only way to get in is to solve one of his dastardly challenges.

    而唯一的辦法就是解決他的一個可怕的挑戰。

  • You're attending with 23 of your closest logician friends,

    你和23個最親密的邏輯學家朋友一起參加。

  • but you got lost on the way to the rave and arrived late.

    但你在去狂歡節的路上迷路了,到得很晚。

  • They're already inside, so you must face down the demon alone.

    他們已經進去了,所以你必須獨自面對惡魔。

  • He poses you the following question:

    他向你提出以下問題。

  • When your friends arrived, the demon put masks on their faces

    你的朋友來了之後,妖怪就給他們戴上了面具

  • and forbade them from communicating in any way.

    並禁止他們以任何方式進行交流。

  • No one at any point could see their own masks,

    在任何時候,沒有人能夠看到自己的面具。

  • but they stood in a circle where they could see everyone else's.

    但他們站在一個圓圈裡,可以看到其他人的。

  • The demon told the logicians that he distributed the masks in such a way

    惡魔告訴邏輯學家,他以這樣的方式分配面具

  • that each person would eventually be able to figure out their mask's color

    每個人最終都能弄清自己面具的顏色。

  • using logic alone.

    僅用邏輯。

  • Then, once every two minutes, he rang a bell.

    然後,每隔兩分鐘,他就按一次鈴。

  • At that point, anyone who could come to him

    那時候,誰都可以來找他。

  • and tell him the color of their mask would be admitted.

    並告訴他,他們的面具顏色會被錄取。

  • Here's what happened:

    事情是這樣的

  • Four logicians got in at the first bell.

    第一聲鐘聲響起,四位邏輯學家就進去了。

  • Some number of logicians, all in red masks, got in at the second bell.

    一些邏輯學家,都戴著紅色的面具,在第二聲鐘聲響起的時候就進去了。

  • Nobody got in when the third bell rang.

    第三次鈴聲響起時,沒有人進去。

  • Logicians wearing at least two different colors got in at the fourth bell.

    穿著至少兩種不同顏色的邏輯學家在第四個鐘聲時進了門。

  • All 23 of your friends played the game perfectly logically

    你的23個朋友都很有邏輯地玩了這個遊戲。

  • and eventually got inside.

    並最終進去了。

  • Your challenge, the demon explains,

    你的挑戰,惡魔解釋道。

  • is to tell him how many people gained entry when the fifth bell rang.

    就是告訴他,當第五次鐘聲響起時,有多少人獲得了進入。

  • Can you get into the rave?

    你能進入狂歡嗎?

  • Pause here to figure it out yourself.

    在這裡暫停一下,自己想辦法。

  • Answer in 3

    3個回答

  • Answer in 2

    答覆2

  • Answer in 1

    回答1

  • It's initially difficult to imagine how anyone could,

    最初很難想象怎麼會有人能。

  • using just logic and the colors they see on the other masks,

    只用邏輯和他們在其他面具上看到的顏色。

  • deduce their own mask color.

    推導出自己的面具顏色。

  • But even before the first bell, everyone will realize something critical.

    但即使在第一聲鐘聲之前,大家也會意識到一些關鍵的東西。

  • Let's imagine a single logician with a silver mask.

    讓我們想象一個帶著銀色面具的單身邏輯學家。

  • When she looks around, she'd see multiple colors, but no silver.

    當她環顧四周,她會看到多種顏色,但沒有銀色。

  • So she couldn't ever know that silver is an option,

    所以她永遠不可能知道,銀子是一種選擇。

  • making it impossible for her to logically deduce that she must be silver.

    使她無法從邏輯上推斷出自己一定是銀子。

  • That contradicts rule five, so there must be at least two masks of each color.

    這與規則五相矛盾,所以每種顏色至少要有兩個面具。

  • Now, let's think about what happens

    現在,讓我們想想會發生什麼

  • when there are exactly two people wearing the same color mask.

    當正好有兩個人戴著相同顏色的面具時。

  • Each of them sees only one mask of that color.

    他們每個人只看到一個該顏色的面具。

  • But because they already know that it can't be the only one,

    但因為他們已經知道,不可能是唯一的一個。

  • they immediately know that their own mask is the other.

    他們馬上知道自己的面具是另一個。

  • This must be what happened before the first bell:

    這一定是第一聲鐘聲之前發生的事情。

  • two pairs of logicians each realized their own mask colors

    兩對邏輯學家各自實現了自己的面具顏色。

  • when they saw a unique color in the room.

    當他們看到房間裡有一種獨特的顏色。

  • What happens if there are three people wearing the same color?

    如果有三個人穿同一種顏色的衣服會怎樣?

  • Each of them—A, B and C— sees two people with that color.

    他們每個人--A、B、C--看到的都是該顏色的兩個人。

  • From A's perspective, B and C would be expected to behave the same way

    從A的角度看,B和C的行為應該是一樣的。

  • that the orange and purple pairs did, leaving at the first bell.

    橙色和紫色的對子也是如此,在第一聲鈴響時就離開了。

  • When that doesn't happen,

    當這種情況沒有發生時。

  • each of the three realizes that they are the third person with that color,

    三人中的每一個人都意識到自己是第三種顏色的人。

  • and all three leave at the next bell.

    三人在下一個鐘聲時離開。

  • That was what the people with red masks did

    這就是那些帶著紅色面具的人所做的----------。

  • so there must have been three of them.

    所以肯定有三個人。

  • We've now established a basis for inductive reasoning.

    我們現在已經建立了一個歸納推理的基礎。

  • Induction is where we can solve the simplest case,

    歸納就是我們可以解決最簡單的情況。

  • then find a pattern that will allow the same reasoning

    然後再找一個同樣的模式,讓同樣的道理。

  • to apply to successively larger sets.

    以適用於連續較大的集。

  • The pattern here is that everyone will know what group they're in

    這裡的模式是,每個人都會知道自己是哪一組的人

  • as soon as the previously sized group has the opportunity to leave.

    一旦先前規模的集團有機會離開。

  • After the second bell, there were 16 people.

    第二次鐘聲過後,有16人。

  • No one left on the third bell,

    第三次鐘聲響起時,沒有人離開。

  • so everyone then knew there weren't any groups of four.

    所以大家就知道沒有什麼四人組。

  • Multiple groups, which must have been of five,

    多組,肯定是五人一組。

  • left on the fourth bell.

    在第四聲鐘聲中離開。

  • Three groups would leave a solitary mask wearer,

    三組會留下一個孤獨的面具佩戴者。

  • which isn't possible, so it must've been two groups.

    這是不可能的,所以一定是兩組。

  • And that leaves six logicians outside when the fifth bell rings:

    而當第五次鐘聲響起時,外面還剩下六個邏輯學家。

  • the answer to the demon's riddle.

    惡魔之謎的答案。

  • Nothing left to do but join your friends and dance.

    除了和你的朋友們一起跳舞,什麼都不用做了。

Once each year, thousands of logicians descend into the desert for Learning Man,

每年一次,數以千計的邏輯學家都會來到沙漠,參加學習人。

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B1 中級 中文 TED-Ed 面具 鐘聲 顏色 響起 惡魔

你能解開邏輯學家的狂歡之謎嗎?- Edwin Meyer (Can you solve the logician’s rave riddle? - Edwin Meyer)

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    林宜悉 發佈於 2021 年 02 月 23 日
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