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

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

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and brought to the ancient colosseum[br]for their deadly entertainment.

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Before you're thrown into the dungeon,

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you see many numbered hallways[br]leading outside.

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But each exit is blocked by [br]an electric barrier

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with a combination keypad.

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

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

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

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You hand her a concealed audio transmitter[br]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 [br]through one of the hallways,

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then stop.

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A voice announces [br]that she must enter a code

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consisting of three positive whole numbers[br]in ascending order,

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

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and the third is greater than[br]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[br]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 [br]of the hallway she entered.

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There's a long silence.

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You're sure Zara remembers [br]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 [br]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[br]number appears only once

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in the combination.

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

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and you realize that Zara has escaped.

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Unfortunately, her transmitter [br]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[br]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[br]don't know Zara's hallway number,

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but you decide to start [br]from the beginning anyways.

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From the first clue, you work out all of[br]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,[br]but which one?

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Now comes the hard part.

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

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you decide to work out the sum[br]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[br]any of these,

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Zara would have known the correct[br]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 [br]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[br]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[br]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[br]escape through hallway thirteen

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and rejoin Zara outside.

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You've freed yourselves through [br]math and logic.

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