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 that he taught you everything you need to know about riddles.
所以他只能寄希望于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. If all 100 of you answer it together, you will share the money evenly.
“我设计了一个谜题。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 without going through all of the leg work,
但是，如果你是第一个找到答案解决问题的人而没有用暴力跑腿法，
you will get the entire inheritance all to yourself. Good luck.'
你将会独享我的所有遗产。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, each hiding a single word.
这有100个储藏柜，每个柜子里藏着一个词。
He explains: Every relative is assigned a number from 1 to 100.
他说：“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, but if it's closed, she'll open it.
如果储藏柜开着，那就关上，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 will help you crack the code for the safe.
最终开着的柜子里的词，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. But how?
你就大步向前告诉了律师哪些柜子会是开着的。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！
The key is realizing that the number of times a locker is touched is the same as the number of factors in the locker number.
关键是算出每个柜子被改变状态的次数是和柜子号码的因子数相同的。
For example, in locker #6, Person 1 will open it, Person 2 will close it, Person 3 will open it, and Person 6 will close it.
比如对于6号柜子，1号继承人把它打开，2号把它关上，3号把它打开，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 it will remain closed,
所以如果一个柜子有偶数个因数，它最后就是关着的，
and when it has an odd number of factors, it will remain open.
如果一个柜子有奇数个因数，它就是开着的。
Most of the lockers have an even number of factors, which makes sense because factors naturally pair up.
大多数柜子有偶数个因子因数，因为因数自然是成对出现的。
In fact, the only lockers that have an odd number of factors are perfect squares
实际上，仅有的几个有奇数个因数的柜子是完全平方柜，
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, 3 will close, and 9 will open it.
对于9号柜子，1号继承人把它打开，3号把它关上，最后9号把它打开。
3x3=9, but the 3 can only be counted once.
3x3=9，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, so you open them immediately and read the words inside:
你知道了这十个柜子就是答案，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 since each only has two factors: 1 and itself.
你发现满足条件的是质数柜，因为它们每个只有两个因数：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, and you claim your inheritance.
律师把你带到保险箱前，你获得了你叔叔的遗产。
Too bad your relatives were always too busy being nasty to each other to pay attention to your eccentric uncle's riddles.
你的亲戚光顾着互相恶心了，没注意你的怪叔叔出的题。