WEBVTT

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Your rich, eccentric uncle 
just passed away,

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

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He wanted to leave 
all of his money to you,

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

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So he is banking on the fact

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

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Your uncle left the following 
note in his will:

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"I have created a puzzle.

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

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

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without going through all of the leg work,

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you will get the entire inheritance 
all to yourself.

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Good luck."

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

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that contains 100 lockers,

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each hiding a single word.

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He explains:

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Every relative is assigned a number
from 1 to 100.

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Heir 1 will open every locker.

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Heir 2 will then 
close every second locker.

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Heir 3 will change the status
of every third locker,

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

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

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

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The words in the lockers that remain
open at the end

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will help you crack the code for the safe.

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Before cousin Thaddeus can even start
down the line,

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

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But how?

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

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Answer in: 3

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Answer in: 2

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Answer in: 1

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

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

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For example, in locker #6,

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Person 1 will open it,

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Person 2 will close it,

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Person 3 will open it,

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and Person 6 will close it.

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

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So when a locker has an even number
of factors

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it will remain closed,

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and when it has an odd number of factors,

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it will remain open.

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Most of the lockers 
have an even number of factors,

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which makes sense because factors
naturally pair up.

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

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are perfect squares

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

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For Locker 9, 1 will open it,

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3 will close,

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and 9 will open it.

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3 x 3 = 9,

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but the 3 can only be counted once.

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

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You know that these ten lockers 
are the solution,

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so you open them immediately
and read the words inside:

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

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

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since each only has two factors:

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1 and itself.

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

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The lawyer brings you to the safe,

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and you claim your inheritance.

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

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to pay attention 
to your eccentric uncle's riddles.