WEBVTT

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In this dystopian world, your resistance
group is humanity's last hope.

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Unfortunately, you've all been captured
by the tyrannical rulers

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and brought to the ancient colosseum
for their deadly entertainment.

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Before you're thrown into the dungeon,

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you see many numbered hallways
leading outside.

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But each exit is blocked by 
an electric barrier

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with a combination keypad.

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You learn that one of you will be allowed
to try to escape by passing a challenge

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while everyone else will be fed to
the mutant salamanders the next morning.

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With her perfect logical reasoning,
Zara is the obvious choice.

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You hand her a concealed audio transmitter
so that the rest of you can listen along.

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As Zara is led away,

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you hear her footsteps echo 
through one of the hallways,

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then stop.

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A voice announces 
that she must enter a code

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consisting of three positive whole numbers
in ascending order,

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so the second number is greater than
or equal to the first,

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and the third is greater than
or equal to the second.

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She may ask for up to three clues,

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but if she makes a wrong guess,

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or says anything else,

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she'll be thrown back into the dungeon.

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For the first clue, the voice says
the product of the three numbers is 36.

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When Zara asks for the second clue,

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it tells her the sum of the numbers

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is the same as the number 
of the hallway she entered.

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There's a long silence.

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You're sure Zara remembers 
the hallway number,

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but there's no way for you to know it,

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and she can't say it outloud.

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If Zara could enter the passcode 
at this point, she would,

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but instead, she asks for the third clue,

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and the voice announces that the largest
number appears only once

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in the combination.

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Moments later, the buzz of the electric
barrier stops for a few seconds,

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and you realize that Zara has escaped.

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Unfortunately, her transmitter 
is no longer in range,

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so that's all the information you get.

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Can you find the solution?

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Pause on the next screen
to work out the solution.

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3

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2

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1

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You're worried about the fact that you
don't know Zara's hallway number,

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but you decide to start 
from the beginning anyways.

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From the first clue, you work out all of
the eight possible combinations

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that come out to a product of 36.

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One of these must be right,
but which one?

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Now comes the hard part.

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Even though you don't know which number
you're looking for,

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you decide to work out the sum
of each combination's three numbers.

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That's when it hits you.

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All but two of the sums are unique,

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and if the hallway number had matched
any of these,

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Zara would have known the correct
combination right then and there

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without asking for the third clue.

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Since she did ask for the clue,

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the hallway number must have 
matched the only sum

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that appears more than once in the list:

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thirteen.

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But which of the two combinations
that add up to thirteen is correct:

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1,6,6,

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or 2,2,9?

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That's where the third clue comes in.

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Since it tells us that the largest
number must be unique,

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2,2,9 must be the code.

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When night falls, you and the others
escape through hallway thirteen

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and rejoin Zara outside.

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You've freed yourselves through 
math and logic.

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Now it's time to free 
the rest of the world.