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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

• 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,

• 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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