Can you solve the riddle of Pandora’s box? - Alex Rosenthal

譯者: Lilian Chiu 審譯者: 麗玲 辛

Pandora was having a decisively bad day.

潘朵拉的這一天過得相當糟糕。

She didn’t set out to open the box;

她一開始並沒有打算打開盒子；

if anything, she’d resisted with every ounce of her will.

說真的，她曾經盡全力抗拒。

But her curiosity got the better of her,

但她的好奇心最終還是佔了上風，

and a cavalcade of evils of every shape and size spilled out.

萬惡如洪水般傾瀉而出， 無所不包、形態萬千。

By the time she'd slammed the front door of her home shut,

等到她趕快把前門關上時，

only 10 minor imps— of wrath, greed, gluttony, and sloth varieties—

屋裏只剩下十隻小惡魔——

分為憤怒、貪婪、暴食， 和懶惰四大類——

and three greater demons remained.

以及三隻大惡魔。

Pandora tried desperately to get them under control,

潘朵拉拼命想要控制住它們，

but they resisted and pounded at the windows.

但它們抵抗著，不斷猛拍窗戶。

“This is hopeless!” she cried.

她哭道：「沒希望了啊！」

The first greater demon turned to Pandora and said,

第一隻大惡魔轉向潘朵拉，說：

“Hope? Hope is still here. I just made her look like an imp.

「希望嗎？希望還在這裡。 我只是讓它看起來像個小惡魔。

Because that’s the kind of bad guy I am!”

因為我就是那種壞蛋！」

He whispered in the ears of the two other demons and continued.

它對另外兩隻大惡魔 耳語之後，繼續說：

“To make things interesting,

「為了增加樂趣，

I just told Abaddon which variety of imp Hope is,

我剛告訴阿班登 希望是哪一種小惡魔，

and Beelzebub how many eyes she has. Bye!”

然後告訴畢奧茲巴 它有多少個眼睛。拜拜！」

Abaddon taunted Beelzebub by saying,

阿班登嘲笑畢奧茲巴，說：

“I know you don’t know which one she is.”

「我知道你不知道它是哪一個。」

Beelzebub responded, “Well, I didn’t before, but now I know.”

畢奧茲巴回答：「嗯， 我原本不知道，但現在知道了。」

To which Abaddon replied in a huff, “Then I also know which one she is.”

阿班登對此的反應是惱火地說：

「那我也知道它是哪一個。」

And both left in a hurry, without so much as a farewell.

它們接著匆匆離去，連道別也沒有。

Pandora knows her only chance to fix this mess is to capture Hope

潘朵拉知道，她補救 這場災難的唯一機會

就是在小惡魔通通逃離 她家之前，抓到希望。

before the imps all escape her home.

But which one is she?

但希望是哪一個？

Pause here to figure it out yourself. Answer in 3

若要自行解題，在此暫停。 解答即將公佈：三。

Answer in 2

解答即將公佈：二。

Answer in 1

解答即將公佈：一。

This problem originally took the world by storm in 2015

這個問題最初 在 2015 年席捲世界，

when Dr. Joseph Yeo Boon Wooi posed it as Cheryl’s birthday problem,

那時，楊文偉博士

提出的「雪若的生日問題」 就是這個形式，

and for good reason.

它會爆紅是合情合理的，因為此邏輯 需要同時模擬三種不同的視角——

The logic requires simultaneously modeling three different perspectives—

ours, Abaddon’s and Beelzebub’s, whom we’ll call A and B from now on.

我們的視角、阿班登的視角， 和畢奧茲巴的視角，

後續簡稱這兩隻惡魔為 A 和 B。

This puzzle is much more approachable if we start by doing what Pandora could not:

要解這道謎，有個更容易的方法， 要從潘朵拉無法做到的事開始：

cramming all of these imps into a box...

把所有的小惡魔塞進一個盒子裡……

in this case, of the table variety.

在我們的例子中，盒子就是表格。

One key thing to note is that unlike many logic problems,

有一點要注意：與許多邏輯問題不同，

the order of statements matters here,

在這裡，陳述句的順序很重要，

because the two demons’ knowledge changes over the course of the dialogue.

因為在對話過程中， 兩隻小惡魔知道的資訊會有所變動。

So let's start with the first statement

咱們先從第一個陳述句開始，

and milk it for all it's worth before moving on.

先充份利用這句話，再繼續下去。

In it, A says to B, “I know you don’t know which one she is.”

第一個陳述句，A 對 B 說： 「我知道你不知道它是哪一個。」

At this point, A knows the imp type,

此時，A 知道希望 是哪種類型的小惡魔，

but since there are multiple imps of each type, A doesn’t know who Hope is.

但因為每種小惡魔都有好幾隻，

所以 A 並不知道希望是哪一隻。

The eyes, however, work differently;

然而，眼睛的作用不同；

if Hope had 3 or 5 eyes, B would know who she is.

如果希望有三隻或五隻眼睛， B 就會知道它是誰。

This step is where a lot of people succumb to a common pitfall.

在這一步，很多人 會落入一個常見陷阱。

Because the important takeaway here isn’t to just eliminate

因為這裡的重點

並不只是要排除 三眼和五眼的小惡魔。

the three- and five-eyed imps.

It’s to eliminate the entire rows of the table that they’re in.

重點是要把它們所在的整列 通通一併排除。

Why?

為什麼？密技在於

The trick is to think about B’s perspective from A’s perspective.

要從 A 的視角去思考 B 的視角。

Through A’s eyes, the entire table boils down to one of these four options,

對 A 來說，

整個表格可以精簡為 這四個選項之一，

because he knows which type the imp is.

因為它知道希望屬於哪一個種類。

If he knew Hope was a greed imp, she could have five eyes.

如果 A 知道希望是貪婪小惡魔，

那希望就有可能會有五隻眼睛。

There’s only one imp with five eyes, so B could know who Hope is.

所有的小惡魔中 只有一隻有五隻眼睛，

那麼 B 一定會知道希望是誰。

But A knows that B doesn’t know,

但 A 知道 B 不知道希望是誰，

so greed isn’t possible, nor, by the same reasoning, is wrath.

所以希望不可能是貪婪小惡魔， 同理，也不會是憤怒小惡魔。

Now we’re down to just five possible imps, and we can move on to the next statement,

現在只剩下五個可能性了，

我們可以進入到下一個陳述句，

which we have to consider through B’s eyes.

這一句就要從 B 的視角來考量。

Critically, B is an expert logician, so anything we’ve figured out—

重要的是， B 是邏輯高手， 所以我們剛才想通的一切——

like that wrath and greed are off the table—

比如憤怒和貪婪可以直接排除——

he’s also figured out.

它也都想到了。

That, plus knowing how many eyes Hope has,

此外，它也知道希望有幾隻眼睛，

allows him to figure out who she is.

這些資訊讓它能推斷出希望是誰。

So she must be in a column that has only one imp left,

所以，希望一定在 只有一隻小惡魔的那一欄，

meaning we can eliminate both one-eyed imps.

意即，兩隻只有一隻眼睛的 小惡魔也可以排除了。

Finally, let’s examine the last statement and switch back to A’s perspective.

最終，來看看最後一個陳述句，

並切換回 A 的視角。

For A to now know who Hope is,

若 A 知道希望是誰，

there must be only one option left in that row.

那一列肯定只剩下一隻小惡魔。

Therefore, Hope must be the six-eyed sloth imp.

因此，希望一定就是 六隻眼睛的懶惰小惡魔。

Before anyone else can escape,

在其他小惡魔逃走之前，

Pandora leaps into action and wrestles Hope to the ground.

潘朵拉立即採取行動，

將希望壓制在地上。

The world may be a mess,

世界可能還是一團糟，

but at least she’s got a glimmer of... well, you know.

但至少，仍有一線….，你知道的。