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你能解开这个锁的难题吗？

Can you solve the locker riddle? - Lisa Winer

Your rich, eccentric uncle just passed away,

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

He wanted to leave all of his money to you,

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

So he is banking on the fact

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

Your uncle left the following note in his will:
“我设计了一个迷题
“I have created a puzzle.

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

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

without going through all of the leg work,

you will get the entire inheritance all to yourself.

Good luck.”

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

that contains 100 lockers,

each hiding a single word.

He explains:

Every relative is assigned a number from 1 to 100.

Heir 1 will open every locker.

Heir 2 will then close every second locker.

Heir 3 will change the status of every third locker,

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

but if it’s closed, she’ll open it.

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

The words in the lockers that remain open at the end

Before cousin Thaddeus can even start down the line,

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

But how?

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

2
1

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.

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.

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

So when a locker has an even number of factors

it will remain closed,

and when it has an odd number of factors,

it will remain open.

Most of the lockers have an even number of factors,

which makes sense because factors naturally pair up.

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

are perfect squares

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

For Locker 9, 1 will open it,
3会锁上它
3 will close,
9会打开它
and 9 will open it.
3乘3等于9
3 x 3 = 9,

but the 3 can only be counted once.

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

You know that these ten lockers are the solution,

so you open them immediately and read the words inside:
“密码是被触碰两次的前五把锁”
“The code is the first five lockers touched only twice.”

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

since each only has two factors:
1和它本身
1 and itself.

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

The lawyer brings you to the safe,

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

to pay attention to your eccentric uncle’s riddles.