Can you solve the sea monster riddle? - Dan Finkel

譯者: Clement Fu 審譯者: Helen Chang

According to legend, once every thousand years

傳說，每隔一千年

a host of sea monsters emerges from the depths to demand tribute

就會有一群海怪

從海上浮城亞特蘭提卡 四周環繞的萬丈深海冒出來，

from the floating city of Atlantartica.

要求進貢。

As the ruler of the city, you’d always dismissed the stories…

你身為邦主，不信這故事...

until today, when 7 Leviathan Lords rose out of the roiling waters

直到今天，7 隻利維坦巨龍王

從滔滔江水騰出水面，包圍你的城市。

and surrounded your city.

Each commands 10 giant kraken,

巨龍王各統御 10 隻克拉肯巨章領，

and each kraken is accompanied by 12 mermites.

巨章領又各率領 12 隻巨蟹兵。

Your city’s puny army is hopelessly outmatched.

護城軍寡不敵眾，無從匹敵。

You think back to the legends.

你沉思於傳說中，探尋指引。

In the stories, the ruler of the city saved his people

神話說

先王向怪力亂神進貢珍珠以示睦誼，

by feeding the creatures a ransom of pearls.

拯救了整個城市的子民。

The pearls would be split equally between the leviathans lords.

珍珠將平分給諸利維坦巨龍王。

Each leviathan would then divide its share into 11 equal piles, keeping one,

巨龍王把所得分成 11 份，

自己留一份，

and giving the other 10 to their kraken commanders.

其餘十份分派隸屬其下的 克拉肯巨章領。

Each kraken would then divide its share into 13 equal piles,

章魚將領又攤分 13 份，

keeping one, and distributing the other twelve to their mermite minions.

自己留一份，

其餘十二份配發屬下各巨蟹兵。

If any one of these divisions left an unequal pile or leftover pearl,

倘若攤分過程不均、有餘或不足，

the monsters would pull everyone to the bottom of the sea.

海怪就會把所有人都拉下水。

Such was the fate of your fabled sister city.

下場會跟傳說中的姊妹市一樣。

You rush to the ancient treasure room and find five chests,

你衝到先王藏寶庫找到五個寶箱，

each containing a precisely counted number of pearls

先王獨具慧眼，早已未雨綢繆，

prepared by your ancestors for exactly this purpose.

一箱箱珍珠分毫不差，有備無患。

Each of the chests bears a number telling how many pearls it contains.

每個寶箱都刻上一個數字。

表示載有多少珍珠。

Unfortunately, the symbols they used to write digits 1,000 years ago

可惜先王的慧眼趕不上時代的進化，

數字仍是以一千年前用的符號標示，

have changed with time,

and you don’t know how to read the ancient numbers.

記數寫法時移世易，今無人看得懂。

With hundreds of thousands of pearls in each chest, there’s no time to recount.

成千累萬的珍珠根本沒時間再點算。

One of these chests will save your city

其中一個寶箱能夠拯救城市，

and the rest will lead to its certain doom.

其他的就無力回天。

Which do you choose?

要怎麼選呢？

Pause the video to figure it out yourself.

「按下暫停自己想一想」

Answer in 3

[揭曉倒數 3]

Answer in 2

[揭曉倒數 2]

Answer in 1

[揭曉倒數 1]

There isn’t enough information to decode the ancient Atlantartican numeral system.

手上的資訊並不足以解碼

古代亞特蘭提卡的記數系統。

But all hope is not lost,

不過，希望在人間，

because there’s another piece of information those symbols contain:

這些符號其實蘊藏另一闋資訊：

patterns.

規律。

If we can find a matching pattern in arabic numerals,

如果在阿拉伯數字裡頭 找到對應的規律，

we can still pick the right chest.

我們按圖索驥 仍可挑到那個正確的箱子。

Let’s take stock of what we know.

好，我們盤點一下線索。

A quantity of pearls that can appease the sea monsters

珍珠的量剛好可安撫海怪，

must be divisible by 7, 11, and 13.

這個數須可以被 7、11、13 整除。

Rather than trying out numbers at random,

與其隨便嘗試不同的組合，

let’s examine ones that have this property

不如列舉一些符合特性的數目，

and see if there are any patterns that unite them.

看看它們有沒有如出一轍的規律。

Being divisible by 7, 11, and 13

一個數字可以被 7、11、13 整除

means that our number must be a multiple of 7, 11, and 13.

即是說它同時都是這三個數的倍數。

Those three numbers are all prime, so multiplying them together

7、11、13 都是質數，

乘出來的最小公倍數就是 1001。

will give us their least common multiple: 1001.

That’s a useful starting place

這是關鍵的起步點，

because we now know that any viable offering to the sea monsters

因為我們現在知道

奉獻給海怪要不得罪、不失禮，

must be a multiple of 1001.

必須是 1001 的倍數。

Let’s try multiplying it by a three digit number,

我們就隨便找一個三位數，

just to get a feel for what we might get.

乘一下，看看結果會是怎麼樣。

If we try 861 times 1001, we get 861,861,

譬如 861 乘 1001

得出 861,861。

and we see something similar with other examples.

其他的例子，也得出相似的結果。

It’s a peculiar pattern.

這是一個不同凡響的規律。

Why would multiplying a three-digit number by 1001

為什麼一個三位數 乘以 1001 得出來的數字

end up giving you two copies of that number,

看起來就像是把那個三位數 左右並排連寫兩次？

written one after the other?

Breaking down the multiplication problem can give us the answer.

把乘數題一分為二，就見到答案。

1001 times any number x is equal to 1000x + x.

1001 乘以任一數字 x

相等於 1000x + x。

For example, 725 times 1000 is 725,000, and 725 x 1 is 725.

舉例：725 乘 1000 得 725,000。

另 725 乘 1 得 725。

So 725 x 1001 will be the sum of those two numbers: 725,725.

725 乘 1001 就是兩個數字的總和：

725,725。

And there’s nothing special about 725.

725 不過是隨意的範例， 沒有什麼特殊的。

Pick any three-digit number,

信手拈來一個三位數，數字是多少，

and your final product will have that many thousands, plus one more.

最終乘積，就是多少千又多少。

Even though you don’t know how to read the numbers on the chests,

就算你不懂得解讀寶箱上的數字，

you can read which pattern of digits represents a number divisible by 1001.

你看得懂，什麼規律的數字。

表示那個數可以被 1001 整除。

As with many problems, trying concrete examples can give you an intuition

像許多問題一樣，看看實在的例子，

乍看之下神秘又飄渺的事情，

for behavior that may at first look abstract and mysterious.

也可找到一份直覺之下洞悉的覺察。

The monsters accept your ransom and swim back down to the depths

海怪很滿意你的獻禮，

又回到無底深海裡，再沉睡一千年。

for another thousand years.

With the proper planning,

就算是千載一逢的奇遇，

that should give you plenty of time to prepare for their inevitable return.

只要未雨綢繆，何時都總能化險為夷。