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Your rich, eccentric uncle [br]just passed away,

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

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He wanted to leave [br]all of his money to you,

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but he knew that if he did,[br]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 [br]you need to know about riddles.

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Your uncle left the following [br]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,[br]you will share the money evenly.

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However, if you are the first to find[br]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 [br]all to yourself.

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Good luck."

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The lawyer takes you and your 99 relatives[br]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[br]from 1 to 100.

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Heir 1 will open every locker.

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Heir 2 will then [br]close every second locker.

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Heir 3 will change the status[br]of every third locker,

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specifically if it's open, [br]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[br]all 100 of you have gone.

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The words in the lockers that remain[br]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[br]down the line,

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

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But how?

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Pause the video now if you want[br]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[br]of times a locker is touched

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is the same as the number of factors[br]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 [br]are the factors of 6.

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So when a locker has an even number[br]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 [br]have an even number of factors,

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which makes sense because factors[br]naturally pair up.

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

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are perfect squares

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because those have one factor that when[br]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 [br]a perfect square will remain open.

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You know that these ten lockers [br]are the solution,

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so you open them immediately[br]and read the words inside:

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

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You realize that the only lockers [br]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[br]too busy being nasty to each other

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to pay attention [br]to your eccentric uncle's riddles.