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  • In this dystopian world, your resistance group is humanity's last hope.

    在這個反烏托邦的世界 你的對抗小組是人性最後一絲希望

  • Unfortunately, you've all been captured by the tyrannical rulers

    不幸的是 你們全被暴虐的統治者抓住

  • and brought to the ancient colosseum for their deadly entertainment.

    並且被帶到古羅馬競技場作為他們的娛樂消遣

  • Before you're thrown into the dungeon,

    在你被丟入地牢前

  • you see many numbered hallways leading outside.

    你看見很多通往外面的通道

  • But each exit is blocked by an electric barrier

    但是每個出口都被一個電子裝置鎖住

  • with a combination keypad.

    還有連著的數字鍵盤

  • You learn that one of you will be allowed to try to escape by passing a challenge

    你知道你們其中一人只要通過考驗就可以試著逃生

  • while everyone else will be fed to the mutant salamanders the next morning.

    但是剩下的人隔天早晨會被丟去餵食突變的火蜥蜴

  • With her perfect logical reasoning, Zara is the obvious choice.

    有著出色的邏輯思考能力的札拉是最好的選擇

  • You hand her a concealed audio transmitter so that the rest of you can listen along.

    你交給她一個隱藏的音頻傳輸裝置 這樣一來剩下的你們就可以竊聽

  • As Zara is led away,

    當札拉走了以後

  • you hear her footsteps echo through one of the hallways,

    你聽見她的腳步聲在其中一個通道發出回音

  • then stop.

    並且停下來

  • A voice announces that she must enter a code

    一個聲音告訴她 她一定要輸入一個密碼

  • consisting of three positive whole numbers in ascending order,

    包含三個以升冪排列的正整數

  • so the second number is greater than or equal to the first,

    所以第二個數字會比第一個數字大 或是和第一個數字一樣大

  • and the third is greater than or equal to the second.

    第三個數字會比第二個數字大或是和第二個一樣大

  • She may ask for up to three clues,

    她可以問三個問題以得到三個線索

  • but if she makes a wrong guess,

    但是一旦她猜錯了

  • or says anything else,

    或是說了一些不相干的話

  • she'll be thrown back into the dungeon.

    她就會被丟回地牢

  • For the first clue, the voice says the product of the three numbers is 36.

    第一個線索 這個聲音說三個數字相乘為三十六

  • When Zara asks for the second clue,

    當札拉詢問第二個線索的時候

  • it tells her the sum of the numbers

    它告訴她三個數字的總和

  • is the same as the number of the hallway she entered.

    和她所在之通道的編號相同

  • There's a long silence.

    一陣安靜後

  • You're sure Zara remembers the hallway number,

    你很確定札拉知道她從哪個通道進去

  • but there's no way for you to know it,

    但是你並不知道

  • and she can't say it outloud.

    而且她不能說出來

  • If Zara could enter the passcode at this point, she would,

    如果札拉這時候想輸入密碼 她可以直接輸入

  • but instead, she asks for the third clue,

    但是 她卻問了第三個問題

  • and the voice announces that the largest number appears only once

    然後這個聲音告訴她最大的數字只出現一次

  • in the combination.

    在這個密碼組合中

  • Moments later, the buzz of the electric barrier stops for a few seconds,

    不久後 電子裝置的雜訊安靜了幾秒鐘

  • and you realize that Zara has escaped.

    你知道札拉已經逃走了

  • Unfortunately, her transmitter is no longer in range,

    不幸的是 她的接收器已經離開有效的傳輸範圍

  • so that's all the information you get.

    所以你擁有的線索僅此而已

  • Can you find the solution?

    你能夠解出謎題嗎

  • Pause on the next screen to work out the solution.

    在下一個畫面按下「暫停鍵」 想想看答案是什麼

  • 3

  • 2

  • 1

  • You're worried about the fact that you don't know Zara's hallway number,

    你擔心你不知道札拉到底是進去了哪一個通道

  • but you decide to start from the beginning anyways.

    但是你仍決定從頭開始思考

  • From the first clue, you work out all of the eight possible combinations

    第一個線索 你找出了所有八個可能的組合

  • that come out to a product of 36.

    他們相乘的結果會是三十六

  • One of these must be right, but which one?

    其中一個一定是對的 但是到底是哪一個

  • Now comes the hard part.

    現在 最難的部分來了

  • Even though you don't know which number you're looking for,

    即便你不知道到底哪一個號碼才是正確的

  • you decide to work out the sum of each combination's three numbers.

    你決定將每一個可能的三個數字相加

  • That's when it hits you.

    突然 你想到了什麼

  • All but two of the sums are unique,

    八個組合中只有兩個總和相同

  • and if the hallway number had matched any of these,

    如果通道的號碼和其中任何一個相同

  • Zara would have known the correct combination right then and there

    札拉就知道正確的組合

  • without asking for the third clue.

    並不需要再問第三個問題

  • Since she did ask for the clue,

    既然她問了第三個問題

  • the hallway number must have matched the only sum

    通道的編號就一定和清單上

  • that appears more than once in the list:

    不只出現一次的總和相同

  • thirteen.

    也就是 十三

  • But which of the two combinations that add up to thirteen is correct:

    但是哪一個組合才是正確的呢

  • 1,6,6,

    一、六、六

  • or 2,2,9?

    還是 二、二、九?

  • That's where the third clue comes in.

    這就是為什麼需要第三個線索了

  • Since it tells us that the largest number must be unique,

    既然它告訴我們最大的數字只出現一次

  • 2,2,9 must be the code.

    二、二、九就絕對是密碼

  • When night falls, you and the others escape through hallway thirteen

    當夜晚降臨 你和其他人從第十三號通到逃跑

  • and rejoin Zara outside.

    和札拉在外面重逢

  • You've freed yourselves through math and logic.

    你透過數學和邏輯拯救了你自己

  • Now it's time to free the rest of the world.

    現在是時候拯救世界了

In this dystopian world, your resistance group is humanity's last hope.

在這個反烏托邦的世界 你的對抗小組是人性最後一絲希望

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B1 中級 中文 美國腔 TED-Ed 數字 通道 線索 密碼 組合

【TED-Ed】你能解出這密碼嗎? (Can you solve the passcode riddle? - Ganesh Pai)

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    Sh, Gang (Aaron) 發佈於 2016 年 07 月 27 日
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