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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 we 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 hallways 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.