Can you solve the sea monster riddle? - Dan Finkel

翻译人员: Meng Ren 校对人员: Yanyan Hong

According to legend, once every thousand years

传说，每过一千年，

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

一群海怪就会从海底深处浮出水面，

向漂浮之城阿特兰蒂卡索要上贡。

from the floating city of Atlantartica.

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

作为全城的统治者， 你对传说总是不以为然……

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

直至今日，七条利维坦神兽 从滚滚的海浪里翻涌而出

and surrounded your city.

包围了你的城邦。

Each commands 10 giant kraken,

每条神兽指挥着十只北海巨怪，

and each kraken is accompanied by 12 mermites.

每只北海巨怪带领着十二只魔蟹。

Your city’s puny army is hopelessly outmatched.

而你城里的兵力远远不及。

You think back to the legends.

你回想起那个传说。

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

故事中提到， 城邦的统治者为了拯救子民，

by feeding the creatures a ransom of pearls.

向怪物们上贡珍珠作为赎金。

The pearls would be split equally between the leviathans lords.

珍珠必须能被 所有利维坦神兽均分。

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

而每条神兽将它所得的 分为十一等份，自留一份，

and giving the other 10 to their kraken commanders.

其余的分给十只北海巨怪。

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

每只北海巨怪又将 它的所得分为十三等份，

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

自留一份， 其余的分给十二只蟹卒。

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

若是任意一次分配不能被均分 或最后珍珠有剩余，

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

海怪们就会将整个城邦拖入海底。

Such was the fate of your fabled sister city.

传说中你的邻城就惨遭其毒手。

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

你赶紧跑去藏宝阁， 找到了五只大宝箱，

each containing a precisely counted number of pearls

每个箱子里装有特定数额的珍珠，

prepared by your ancestors for exactly this purpose.

这正是祖先们为今天准备的。

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

每个藏宝箱的铭牌上都刻着数字， 代表所装的珍珠数量。

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

但不巧的是，祖先的数字 是一千年前的古文字，

have changed with time,

如今时过境迁，

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

而你不认得这些古老的数字。

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

箱子里的珍珠成百上千， 根本没有再次清点的时间。

One of these chests will save your city

它们其中一只将会拯救你的城邦，

and the rest will lead to its certain doom.

而其余的则无力回天。

Which do you choose?

你要如何选择呢？

Pause the video to figure it out yourself.

[ 若要自己找到答案，就暂停一下视频 ]

Answer in 3

[ 答案 3 秒后揭晓 ]

Answer in 2

[ 答案 2 秒后揭晓 ]

Answer in 1

[ 答案 1 秒后揭晓 ]

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

虽然没有足够的信息去揭秘 古阿特兰蒂卡的计数系统。

But all hope is not lost,

但还是有一线希望，

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

因为那些符号包含着另一类信息：

patterns.

规律。

If we can find a matching pattern in arabic numerals,

如果我们能找到 相对应阿拉伯数字的规律，

we can still pick the right chest.

就能选出正确的箱子。

Let’s take stock of what we know.

我们先来总结一下已知的信息。

A quantity of pearls that can appease the sea monsters

能平息海怪的珍珠数量

must be divisible by 7, 11, and 13.

必须能被 7、11、和 13 整除。

Rather than trying out numbers at random,

与其随机地试不同的数字，

let’s examine ones that have this property

不如来研究一下 这些数字的特性，

and see if there are any patterns that unite them.

并找到它们共有的模式。

Being divisible by 7, 11, and 13

能被 7、11、和 13 整除，

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

说明这个数字必须 同时是 7、11、和 13 的倍数，

Those three numbers are all prime, so multiplying them together

这三个数字均为质数， 所以将它们相乘

will give us their least common multiple: 1001.

就得到了最小公倍数：1001。

That’s a useful starting place

这个信息非常重要，

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

现在我们知道任何一个 能满足海怪们要求的数字

must be a multiple of 1001.

必须是 1001 的倍数。

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

让我们来试一试 用它乘以一个三位数，

just to get a feel for what we might get.

看看能得到怎样的结果。

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

用 861 乘以 1001， 我们得到了 861861，

and we see something similar with other examples.

我们找到了所有数组 共有的规律。

It’s a peculiar pattern.

它们都有一个特定模式。

Why would multiplying a three-digit number by 1001

为什么用任意一个三位数乘以 1001，

end up giving you two copies of that number,

得到的结果从左到右读就是该三位数

written one after the other?

重复了两次？

Breaking down the multiplication problem can give us the answer.

分解这个乘式就能找到答案。

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

1001 乘以未知数 X 等于 1000 X + X 。

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

例如，725 乘 1000 是 725000 ， 725 乘 1 是 725，

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

所以，725 乘 1001 就是 两个数字总和：725725。

And there’s nothing special about 725.

我们可以把 725 换成任意一个三位数。

Pick any three-digit number,

随机选择一个三位数，

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

你得到的结果将会是 它的一千倍与它的一倍的和。

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

因此，即使你看不懂 宝箱上的古数字，

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

你仍然能找出符合 1001 整除规律的那一组。

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

许多问题是同一个道理。 面对抽象而神秘的表象时，

套入一个具体的例子， 能帮助我们洞察事物背后的规律。

for behavior that may at first look abstract and mysterious.

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

最后，海怪们接受了赎金， 潜回了海底深处，

for another thousand years.

等待下一个千年轮回。

With the proper planning,

经过周全地计划，

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

你将会有充裕的准备时间 迎接海怪们下一次不可避免的回归。