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

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

  • and brought to the ancient colosseum for their deadly entertainment.

  • Before you're thrown into the dungeon,

  • you see many numbered hallways leading outside.

  • But each exit is blocked by an electric barrier

  • with a combination keypad.

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

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

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

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

  • As Zara is led away,

  • you hear her footsteps echo through one of the hallways,

  • then stop.

  • A voice announces that she must enter a code

  • consisting of three positive whole numbers in ascending order,

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

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

  • She may ask for up to three clues,

  • but if she makes a wrong guess,

  • or says anything else,

  • she'll be thrown back into the dungeon.

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

  • When Zara asks for the second clue,

  • it tells her the sum of the numbers

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

  • There's a long silence.

  • You're sure Zara remembers the hallway number,

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

  • and she can't say it outloud.

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

  • but instead, she asks for the third clue,

  • and the voice announces that the largest number appears only once

  • in the combination.

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

  • and you realize that Zara has escaped.

  • Unfortunately, her transmitter is no longer in range,

  • so that's all the information you get.

  • Can you find the solution?

  • Pause on the next screen to work out the solution.

  • 3

  • 2

  • 1

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

  • but you decide to start from the beginning anyways.

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

  • that come out to a product of 36.

  • One of these must be right, but which one?

  • Now comes the hard part.

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

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

  • That's when it hits you.

  • All but two of the sums are unique,

  • and if the hallway number had matched any of these,

  • Zara would have known the correct combination right then and there

  • without asking for the third clue.

  • Since she did ask for the clue,

  • the hallway number must have matched the only sum

  • that appears more than once in the list:

  • thirteen.

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

  • 1,6,6,

  • or 2,2,9?

  • That's where the third clue comes in.

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

  • 2,2,9 must be the code.

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

  • and rejoin Zara outside.

  • You've freed yourselves through math and logic.

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

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

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B1 US TED-Ed zara hallway clue combination transmitter

【TED-Ed】Can you solve the passcode riddle? - Ganesh Pai

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    Sh, Gang (Aaron) posted on 2016/07/27
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