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

三

2

二

1

一

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