Can you solve the private eye riddle? - Henri Picciotto

譯者: 至磊Zi Le 黃Ng 審譯者: Bruce Sung

As Numberland’s best detective, you thought you’d seen it all.

身為數字國的最強偵探， 你覺得什麼大風大浪都見過了。

But the desiccated corpses of prominent natural numbers—

然而知名自然數的乾屍

whole numbers greater than 0—

——自然數是比 0 大的整數——

在過去幾週內遍布整座城市。

have been showing up all over the city for the past week.

All of Digitopolis is on lockdown from sundown to sunrise,

整座數字城邦 在日落到日出間實施宵禁，

and it’s still not enough to stop what can only be described

但仍不足以阻止吸血鬼的凶暴攻擊。

as a vampiric feeding frenzy.

The police are helpless, and have turned to you.

警方備感無助，於是找上了你。

You put the missing persons case you’ve been investigating on hold

你暫時放下手邊的人口失蹤案件，

and study the evidence.

先研究證據。

Here’s what you know:

這些是你所知道的：

most victims have been completely drained of their life’s essence.

多數被害人的身體被吸乾；

Some have a thin line of slime separating digits—

有些被一條條黏液切出不同的位數，

some of which were drained and others spared.

有些位數被吸乾，其他則沒有。

Which leads you to mystery one:

這讓你必須面對謎題一：

what’s the significance of the slime-lines,

黏液線段有什麼重要性，

and why are certain digits untouched?

而且為何特定位數毫髮無傷？

Pause here to figure it out yourself. Answer in 3

若想自己思考請按暫停。 三秒後公布答案。

Answer in 2

兩秒後公布答案。

Answer in 1

一秒後公布答案。

Let’s start by looking for a pattern in the victims.

我們先從觀察被害人的模式開始。

Why have some been fully drained, and some slimed?

為何有人被完全吸乾， 有人則有黏液？

Well, the slime-lined are in their prime—

黏液線段出現在質數——

which is to say they’re prime numbers, divisible only by 1 and themselves.

只能被 1 和自己整除的數。

Not a single one of the unslimed numbers, on the other hand, is.

另一方面，沒有一個 未被黏液切開的數是質數。

Furthermore, the drained parts of the slimed primes are not, themselves, prime.

而且，帶有黏液的質數中， 被吸乾的部分也並非質數。

When 71 got slimed, 7 was prime, but 1 was not.

71 有黏液， 7 是質數，但 1 不是。

If 461 had been split into 4 and 61, the right side would have been prime,

如果 461 被切成 4 和 61 ， 61 就會是質數，

but instead it was split further into non-prime digits.

但他被進一步切成不是質數的數。

And when 2099 got slimed, the attacker went with 20 and 99,

2099 有黏液， 攻擊者切成 20 和 99 ，

and was able to drain both.

如此便能兩者都吸乾。

So you have a big problem.

於是你遇到一個大問題。

There are infinite potential victims:

有無數個可能的被害人：

all non-prime numbers,

所有不是質數的整數、

and all prime numbers that can be slime-lined

所有可被黏液切割出 至少一個非質數的質數。

to reveal at least one non-prime number.

In fact, you can only think of a few numbers that aren't vulnerable.

事實上，你只想得到 少數幾個數不會被害。

First of all, the one digit primes: 2, 3, 5, and 7.

首先是一位數的質數： 2 、 3 、 5 、 7 。

Then primes like 23, which could only be split into 2 and 3, both prime.

然後是像 23 的質數， 只能切成 2 和 3 ，都是質數。

These numbers are familiar, but why?

這些數很眼熟，為什麼？

Aha! Your missing person’s case.

啊哈！你的失蹤人口案件。

Someone is kidnapping the numbers that can’t be drained:

有人在綁架不能被吸乾的數：

we’ll call them the immune.

我們稱其為「免疫數」。

If you can identify the four immune who remain,

如果你找得到 四個沒被綁架的免疫數，

perhaps you can get to them first and figure out what’s going on.

也許就可以先拜訪他們， 弄明白發生的事情。

Who are the immune? Pause here to figure it out yourself.

誰是免疫數？ 若想自己思考請按暫停。

Answer in 2

兩秒後公布答案。

Answer in 1

一秒後公布答案。

There are 4 one-digit immune: 2, 3, 5, and 7.

有四個一位數的免疫數： 2 、 3 、 5 、 7 ，

All have already been kidnapped.

全部都已被綁架。

But every digit in all of the immune must be one of those four numbers;

但所有免疫數的各位數 都必須是這四個數字之一，

otherwise there would be a non-prime split possible.

否則就可以切出一個非質數。

That means there are only these 16 candidates among the two-digit numbers.

這代表兩位數的免疫數 必然在這 16 位候選人之中，

The ones that are prime must be immune.

其中的質數一定是免疫數。

We can eliminate anything that ends in 2 or 5,

我們可以刪去 尾數是 2 或 5 的數，

as they’ll always be divisible by 2 and 5.

因為他們總會被 2 或 5 整除。

This diagonal is also out, as they’re divisible by 11.

這條斜線的數也都出局了， 因為會被 11 整除。

If the digits of a number add up to a multiple of 3,

若把某個數各個位數加總， 得出的是 3 的倍數，

it’s divisible by 3.

那他本身也會被 3 整除，

So that eliminates 57 and 27, leaving these numbers.

這樣就會刪去 57 和 27 ， 只留下這些數。

Which, upon double-checking, are, in fact, immune.

經過雙重檢查，他們確實是免疫數。

We now have a strong starting point for searching three-digit numbers:

我們現在站在很好的起點， 可以來搜尋三位數的免疫數：

any 2 consecutive digits must be on the list of the two-digit immune.

任兩個連續的位數必須位在 兩位數的免疫數清單中。

Those all end in 3 and 7,

他們的尾數都是 3 或 7 ，

so the only possibilities are these 8 options:

因此只有這八種可能性：

the two-digit immune with additional 3s or 7s on their ends.

在兩位數的免疫數 後面加上 3 或 7 。

3 can’t follow 3, nor 7 follow 7.

3 後面不能放 3， 7 後面也不能放 7 。

And once again, adding the digits reveals that 237 and 537

而且再一次，把各個位數相加

就會發現 237 和 537 可以被 3 整除。

are divisible by 3.

737 is 67 times 11, so that leaves just 373,

737 是 67 乘以 11 ， 這樣就只剩 373 了，

which is, in fact, prime, and therefore immune.

事實上 373 是質數， 因此也是免疫數。

Could a four-digit number be immune?

可以有四位數的免疫數嗎？

No, any consecutive three digits would have to be immune,

不行，任何連續的三個位數 都必須是免疫數，

and there’s no immune three digit number that starts with a 7.

但並沒有三位數的免疫數 第一個位數是 7 。

你衝了出去， 但還是太晚抵達他們家，

You rush out, but reach each home too late,

until the only immune left is 373.

只剩 373 一個免疫數了。

You’re in the nick of time to scare off her would-be kidnapper;

你在最後關頭嚇跑了想綁架她的人。

not the vampire itself but a minion.

不是吸血鬼本身，而是他的小嘍囉。

373 explains that she and the other immune are the subjects of an ancient prophecy

373 解釋說她和其他免疫數 是一個古老預言的主角，

that designated them as vampire slayers.

那個預言選定他們為殺吸血鬼者。

They’d sometimes gather and try to figure out what a vampire is,

他們有時會聚在一起， 試著弄清楚吸血鬼是誰，

but no one had the slightest idea.

但沒人有任何方向。

They found the idea of slaying things quite distasteful.

他們很厭惡殺人的想法。

You both trail her would-be kidnapper back to a foreboding castle.

你們兩個跟蹤試圖綁架她的人， 回到一座有著不祥預感的城堡。

There you release the other kidnapped numbers

在那裡，你釋放了其他被綁架的數，

and confront the vampire himself.

直接碰上了吸血鬼本人。

He’s powerless before the slayers, but ever the pacifists,

他在和平主義的殺吸血鬼者面前 表現得不堪一擊，

they round him up, return the lifeforce to his victims, and send him packing.

他們將他圍起來， 把生命力還給被害人，

並把他放逐。

Numberland is safe... for now.

數字國安全了……目前是如此。