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:

"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

will help you crack the code for the safe.

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!

Answer in: 3

Answer in: 2

Answer in: 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 will close,

and 9 will open it.

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:

"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 and itself.

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

The lawyer brings you to the safe,

and you claim your inheritance.

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

to pay attention
to your eccentric uncle's riddles.