Can you solve the locker riddle? - Lisa Winer

譯者: Rowena Lee 審譯者: Max Chern

Your rich, eccentric uncle just passed away,

你那個富有、古怪的叔叔剛去世，

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

你和你 99 個卑劣的親戚 被邀請去聽他的遺囑宣讀。

He wanted to leave all of his money to you,

他想把所有的錢都留給你，

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

可是，他知道如果這樣做， 你的親戚們會一直騷擾你。

So he is banking on the fact

因此，他指望

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

他教過你所有你需要知道 關於謎語的資訊。

Your uncle left the following note in his will:

你的叔叔在遺囑留下了以下註記：

"I have created a puzzle.

「我設計了一個謎題，

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

如果你們 100 個人能一起解答， 你們就平均分配我的遺產。

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

但是，如果你是第一個找到模式， 並解開謎語，

without going through all of the leg work,

而不是經由一個個慢慢細算，

you will get the entire inheritance all to yourself.

你將會得到全部的遺產。

Good luck."

祝你好運。」

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

律師帶你和你的 99 個親戚 去一座公寓裡的密室，

that contains 100 lockers,

裡面有 100 個櫃子，

each hiding a single word.

每個藏有一個字。

He explains:

他解釋：

Every relative is assigned a number from 1 to 100.

「每個親戚會分配到 1 至 100 中一個數字。

Heir 1 will open every locker.

一號繼承人會打開所有櫃子，

Heir 2 will then close every second locker.

之後，二號繼承人會把 每個 2 的倍數的櫃子關上。

Heir 3 will change the status of every third locker,

三號繼承人會把 每個 3 的倍數的櫃子的狀態反轉，

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

明確地說， 如果本來是開著，她會關上它，

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

但如果本來是關著，她會打開它。

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

這方式會繼續，直到你們 100 個人都做完。

The words in the lockers that remain open at the end

最後保持開著的櫃子裡的字

will help you crack the code for the safe.

會幫助你破解保險箱密碼。」

Before cousin Thaddeus can even start down the line,

在你表哥 Thaddeus 開始排隊之前，

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

你驅前告訴律師 你知道哪幾個櫃子最後仍然開著。

But how?

但是，如何知道的？

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

如果你想自己找出答案， 你可以現在暫停影片！

Answer in: 3

答案揭曉：3

Answer in: 2

答案揭曉：2

Answer in: 1

答案揭曉：1

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

關鍵是要瞭解一個櫃子被觸碰的次數

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

等於櫃子編號的因子數目。

For example, in locker #6,

例如，在 6 號櫃子，

Person 1 will open it,

第 1 個人會打開，

Person 2 will close it,

第 2 個人會把它關上，

Person 3 will open it,

第 3 個人會再打開，

and Person 6 will close it.

第 6 個人會把它關上。

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

數字 1、2、3、6 都是 6 的因子，

So when a locker has an even number of factors

所以當櫃子編號有偶數個因子時，

it will remain closed,

最後會保持關著，

and when it has an odd number of factors,

而當它有奇數個因子時，

it will remain open.

它會保持開著。

Most of the lockers have an even number of factors,

大部分的櫃子編號都有偶數個因子，

which makes sense because factors naturally pair up.

這是合理的，因為因子本來就是配對。

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

事實上，只有奇數個因子的櫃子編號

are perfect squares

都是完全平方數，

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

因為那些有一個因子是自己相乘等於櫃子編號。

For Locker 9, 1 will open it,

以 9 號櫃子為例，一號繼承人會打開它，

3 will close,

三號會關上它，

and 9 will open it.

而九號會打開它。

3 x 3 = 9,

3 x 3 = 9,

but the 3 can only be counted once.

但 3 只能被算一次。

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

所以，完全平方數的櫃子 最後都會保持打開。

You know that these ten lockers are the solution,

你知道這 10 個櫃子就是答案，

so you open them immediately and read the words inside:

所以你立刻打開它們，並讀裡面的字：

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

「密碼是首五個只被觸碰兩次的櫃子。」

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

你知道只被觸碰兩次的櫃子 必須是質數，

since each only has two factors:

因為每個只有兩個因子：

1 and itself.

1 和那數字本身。

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

所以密碼是 2 - 3 - 5 - 7 - 11。

The lawyer brings you to the safe,

那個律師帶你到保險箱，

and you claim your inheritance.

你聲明了你的遺產權。

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

可惜你的親戚 一直忙於惡劣地彼此對待，

to pay attention to your eccentric uncle's riddles.

以致無法專注於你古怪叔叔的謎語。

翻譯：Wing Kiu Lee