Can you solve the locker riddle? - Lisa Winer

翻译人员: Mingyu Cui 校对人员: Zhenning YANG

Your rich, eccentric uncle just passed away,

你有钱又古怪的叔叔去世了，

and you and your 99 nasty relatives have been invited to the reading of his will.

你和你的99个恶心的亲戚 被邀请到他遗嘱的宣读会。

He wanted to leave all of his money to you,

他想要把所有钱留给你，

but he knew that if he did, your relatives would pester you forever.

但他知道如果他这么做了， 你的亲戚会永远缠着你。

So he is banking on the fact

所以他只能寄希望于

that he taught you everything you need to know about riddles.

他教给过你的所有猜谜技巧

Your uncle left the following note in his will:

你叔叔在遗嘱中写道：

"I have created a puzzle.

“我设计了一个谜题。

If all 100 of you answer it together, you will share the money evenly.

如果你们100个人一起回答， 就100个人均分我的钱。

However, if you are the first to find the pattern and solve the problem

但是，如果你是第一个 找到答案解决问题的人

without going through all of the leg work,

而没有用暴力跑腿法，

you will get the entire inheritance all to yourself.

你将会独享我的所有遗产。

Good luck."

祝你好运。”

The lawyer takes you and your 99 relatives to a secret room in the mansion

律师把你和99个亲戚 带到了宅第的密室。

that contains 100 lockers,

这有100个储藏柜，

each hiding a single word.

每个柜子里藏着一个词。

He explains:

他说：“

Every relative is assigned a number from 1 to 100.

每个亲戚被分发1到100里的一个数字。

Heir 1 will open every locker.

1号继承人要打开每个储藏柜。

Heir 2 will then close every second locker.

2号将关上偶数号码的储藏柜。

Heir 3 will change the status of every third locker,

3号改变整除3的储藏柜的状态，

specifically if it's open, she'll close it,

如果储藏柜开着，那就关上，

but if it's closed, she'll open it.

如果储藏柜关着，那就打开。

This pattern will continue until all 100 of you have gone.

100个人都按这个规律执行。

The words in the lockers that remain open at the end

最终开着的柜子里的词，

will help you crack the code for the safe.

会帮你打开保险箱。

Before cousin Thaddeus can even start down the line,

在1号继承人开始打开柜子之前，

you step forward and tell the lawyer you know which lockers will remain open.

你就大步向前告诉了律师哪些柜子会是开着的。

But how?

怎么做到的呢？

Pause the video now if you want to figure it out for yourself!

如果你想自己想，就暂停视频！

Answer in: 3

3秒后出答案

Answer in: 2

2秒后出答案

Answer in: 1

1秒后出答案

The key is realizing that the number of times a locker is touched

关键是算出每个柜子被改变状态的次数

is the same as the number of factors in the locker number.

是和柜子号码的因子数相同的。

For example, in locker #6,

比如对于6号柜子，

Person 1 will open it,

1号继承人把它打开，

Person 2 will close it,

2号把它关上，

Person 3 will open it,

3号把它打开，

and Person 6 will close it.

最后6号把它关上。

The numbers 1, 2, 3, and 6 are the factors of 6.

1，2，3，6就是6的四个因数。

So when a locker has an even number of factors

所以如果一个柜子有偶数个因数，

it will remain closed,

它最后就是关着的，

and when it has an odd number of factors,

如果一个柜子有奇数个因数，

it will remain open.

它就是开着的。

Most of the lockers have an even number of factors,

大多数柜子有偶数个因子因数，

which makes sense because factors naturally pair up.

因为因数自然是成对出现的。

In fact, the only lockers that have an odd number of factors

实际上，仅有的几个有奇数个因数的柜子

are perfect squares

是完全平方柜^_^

because those have one factor that when multiplied by itself equals the number.

因为它们有一个因数自己乘自己得到柜号

For Locker 9, 1 will open it,

对于9号柜子，1号继承人把它打开，

3 will close,

3号把它关上，

and 9 will open it.

最后9号把它打开。

3 x 3 = 9,

3 x 3 = 9,

but the 3 can only be counted once.

但是3只能算一个因数。

Therefore, every locker that is a perfect square will remain open.

因此，每个完全平方柜最后是开着的。

You know that these ten lockers are the solution,

你知道了这十个柜子就是答案，

so you open them immediately and read the words inside:

所以你立刻打开了它们。里面写着：

"The code is the first five lockers touched only twice."

“保险箱的密码是前五个只被碰了两次的柜子。”

You realize that the only lockers touched twice have to be prime numbers

你发现满足条件的是质数柜

since each only has two factors:

因为它们每个只有两个因数：

1 and itself.

1和它本身。

So the code is 2-3-5-7-11.

所以密码是2-3-5-7-11。

The lawyer brings you to the safe,

律师把你带到保险箱前，

and you claim your inheritance.

你获得了你叔叔的遗产。

Too bad your relatives were always too busy being nasty to each other

你的亲戚光顾着互相恶心了

to pay attention to your eccentric uncle's riddles.

没注意你的怪叔叔出的题