Can you solve the sea monster riddle

你能解決海怪之謎嗎

來源視頻

According to legend, once every thousand years a host of sea monsters emerges from the depths to demand tribute from the floating city of Atlantartica.?

As the ruler of the city, you’d always dismissed the stories… until today, when 7 Leviathan Lords rose out of the roiling waters and surrounded your city.?

Each commands 10 giant kraken, and each kraken is accompanied by 12 mermites.?

Your city’s puny army is hopelessly outmatched.

傳說，每過一千年，一群海怪就會從海底深處浮出水面，向漂浮之城阿特蘭蒂卡索要上貢。

作為全城的統(tǒng)治者，?你對傳說總是不以為然……直至今日，七條利維坦神獸 從滾滾的海浪里翻涌而出包圍了你的城邦。

每條神獸指揮著十只北海巨怪，每只北海巨怪帶領(lǐng)著十二只魔蟹。

而你城里的兵力遠(yuǎn)遠(yuǎn)不及。

You think back to the legends. In the stories, the ruler of the city saved his people by feeding the creatures a ransom of pearls.?

The pearls would be split equally between the leviathans lords.?

Each leviathan would then divide its share into 11 equal piles, keeping one, and giving the other 10 to their kraken commanders.?

Each kraken would then divide its share into 13 equal piles, keeping one, and distributing the other twelve to their mermite minions.?

If any one of these divisions left an unequal pile or leftover pearl, the monsters would pull everyone to the bottom of the sea.?

Such was the fate of your fabled sister city.

你回想起那個傳說。

故事中提到， 城邦的統(tǒng)治者為了拯救子民，向怪物們上貢珍珠作為贖金。

珍珠必須能被 所有利維坦神獸均分。而每條神獸將它所得的 分為十一等份，自留一份，其余的分給十只北海巨怪。

每只北海巨怪又將 它的所得分為十三等份，自留一份， 其余的分給十二只蟹卒。

若是任意一次分配不能被均分 或最后珍珠有剩余，海怪們就會將整個城邦拖入海底。

傳說中你的鄰城就慘遭其毒手。

You rush to the ancient treasure room and find five chests, each containing a precisely counted number of pearls prepared by your ancestors for exactly this purpose.?

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

Unfortunately, the symbols they used to write digits 1,000 years ago have changed with time, and you don’t know how to read the ancient numbers.?

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

One of these chests will save your city and the rest will lead to its certain doom.

Which do you choose??

Pause the video to figure it out yourself.?

Answer in 3?

Answer in 2

Answer in 1

你趕緊跑去藏寶閣， 找到了五只大寶箱，每個箱子里裝有特定數(shù)額的珍珠，這正是祖先們?yōu)榻裉鞙?zhǔn)備的。

每個藏寶箱的銘牌上都刻著數(shù)字， 代表所裝的珍珠數(shù)量。

但不巧的是，祖先的數(shù)字 是一千年前的古文字，如今時過境遷，而你不認(rèn)得這些古老的數(shù)字。

箱子里的珍珠成百上千， 根本沒有再次清點的時間。

它們其中一只將會拯救你的城邦，而其余的則無力回天。

你要如何選擇呢？

[?若要自己找到答案，就暫停一下視頻?]

[?答案?3?秒后揭曉?]

[?答案?2?秒后揭曉?]

[?答案?1?秒后揭曉?]

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

But all hope is not lost, because there’s another piece of information those symbols contain: patterns.?

If we can find a matching pattern in arabic numerals, we can still pick the right chest.?

Let’s take stock of what we know.?

A quantity of pearls that can appease the sea monsters must be divisible by 7, 11, and 13.

Rather than trying out numbers at random, let’s examine ones that have this property and see if there are any patterns that unite them.

雖然沒有足夠的信息去揭秘 古阿特蘭蒂卡的計數(shù)系統(tǒng)。

但還是有一線希望，因為那些符號包含著另一類信息：規(guī)律。

如果我們能找到 相對應(yīng)阿拉伯?dāng)?shù)字的規(guī)律，就能選出正確的箱子。

我們先來總結(jié)一下已知的信息。

能平息海怪的珍珠數(shù)量必須能被?7、11、和?13?整除。

與其隨機地試不同的數(shù)字，不如來研究一下 這些數(shù)字的特性，并找到它們共有的模式。

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

Those three numbers are all prime, so multiplying them together will give us their least common multiple: 1001.?

That’s a useful starting place because we now know that any viable offering to the sea monsters must be a multiple of 1001.?

Let’s try multiplying it by a three digit number, just to get a feel for what we might get.?

If we try 861 times 1001, we get 861,861, and we see something similar with other examples.?

It’s a peculiar pattern.

能被?7、11、和?13?整除，說明這個數(shù)字必須 同時是?7、11、和?13?的倍數(shù)，

這三個數(shù)字均為質(zhì)數(shù)， 所以將它們相乘就得到了最小公倍數(shù)：1001。

這個信息非常重要，現(xiàn)在我們知道任何一個 能滿足海怪們要求的數(shù)字必須是?1001?的倍數(shù)。

讓我們來試一試 用它乘以一個三位數(shù)，看看能得到怎樣的結(jié)果。

用?861?乘以?1001， 我們得到了?861861，我們找到了所有數(shù)組 共有的規(guī)律。

它們都有一個特定模式。

Why would multiplying a three-digit number by 1001 end up giving you two copies of that number, written one after the other?

Breaking down the multiplication problem can give us the answer.?

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

For example, 725 times 1000 is 725,000, and 725 x 1 is 725. So 725 x 1001 will be the sum of those two numbers: 725,725.

And there’s nothing special about 725.

Pick any three-digit number, and your final product will have that many thousands, plus one more.?

Even though you don’t know how to read the numbers on the chests, you can read which pattern of digits represents a number divisible by 1001.

為什么用任意一個三位數(shù)乘以?1001，得到的結(jié)果從左到右讀就是該三位數(shù)重復(fù)了兩次？

分解這個乘式就能找到答案。

1001?乘以未知數(shù)?X?等于?1000 X + X?。

例如，725?乘?1000?是?725000?，?725?乘?1?是?725，所以，725?乘?1001?就是 兩個數(shù)字總和：725725。

我們可以把?725?換成任意一個三位數(shù)。

隨機選擇一個三位數(shù)，你得到的結(jié)果將會是 它的一千倍與它的一倍的和。

因此，即使你看不懂 寶箱上的古數(shù)字，你仍然能找出符合?1001?整除規(guī)律的那一組。

As with many problems, trying concrete examples can give you an intuition for behavior that may at first look abstract and mysterious.?

The monsters accept your ransom and swim back down to the depths for another thousand years.?

With the proper planning, that should give you plenty of time to prepare for their inevitable return.

許多問題是同一個道理。 面對抽象而神秘的表象時，套入一個具體的例子， 能幫助我們洞察事物背后的規(guī)律。

最后，海怪們接受了贖金， 潛回了海底深處，等待下一個千年輪回。

經(jīng)過周全地計劃，你將會有充裕的準(zhǔn)備時間 迎接海怪們下一次不可避免的回歸。