1
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In this dystopian world, your resistance
group is humanity's last hope.

2
00:00:15,345 --> 00:00:19,359
Unfortunately, you've all been captured
by the tyrannical rulers

3
00:00:19,359 --> 00:00:23,527
and brought to the ancient colosseum
for their deadly entertainment.

4
00:00:23,527 --> 00:00:25,382
Before you're thrown into the dungeon,

5
00:00:25,382 --> 00:00:28,964
you see many numbered hallways
leading outside.

6
00:00:28,964 --> 00:00:31,942
But each exit is blocked by 
an electric barrier

7
00:00:31,942 --> 00:00:34,506
with a combination keypad.

8
00:00:34,506 --> 00:00:39,541
You learn that one of you will be allowed
to try to escape by passing a challenge

9
00:00:39,541 --> 00:00:44,852
while everyone else will be fed to
the mutant salamanders the next morning.

10
00:00:44,852 --> 00:00:48,631
With her perfect logical reasoning,
Zara is the obvious choice.

11
00:00:48,631 --> 00:00:54,466
You hand her a concealed audio transmitter
so that the rest of you can listen along.

12
00:00:54,466 --> 00:00:56,058
As Zara is led away,

13
00:00:56,058 --> 00:00:58,942
you hear her footsteps echo 
through one of the hallways,

14
00:00:58,942 --> 00:01:00,694
then stop.

15
00:01:00,694 --> 00:01:03,659
A voice announces 
that she must enter a code

16
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consisting of three positive whole numbers
in ascending order,

17
00:01:08,166 --> 00:01:11,466
so the second number is greater than
or equal to the first,

18
00:01:11,466 --> 00:01:15,254
and the third is greater than
or equal to the second.

19
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She may ask for up to three clues,

20
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but if she makes a wrong guess,

21
00:01:19,026 --> 00:01:20,966
or says anything else,

22
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she'll be thrown back into the dungeon.

23
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For the first clue, the voice says
the product of the three numbers is 36.

24
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When Zara asks for the second clue,

25
00:01:33,092 --> 00:01:35,092
it tells her the sum of the numbers

26
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is the same as the number 
of the hallway she entered.

27
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There's a long silence.

28
00:01:41,682 --> 00:01:44,317
You're sure Zara remembers 
the hallway number,

29
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but there's no way for you to know it,

30
00:01:46,809 --> 00:01:50,002
and she can't say it outloud.

31
00:01:50,002 --> 00:01:53,422
If Zara could enter the passcode 
at this point, she would,

32
00:01:53,422 --> 00:01:57,215
but instead, she asks for the third clue,

33
00:01:57,215 --> 00:02:01,811
and the voice announces that the largest
number appears only once

34
00:02:01,811 --> 00:02:04,117
in the combination.

35
00:02:04,117 --> 00:02:08,931
Moments later, the buzz of the electric
barrier stops for a few seconds,

36
00:02:08,931 --> 00:02:11,766
and you realize that Zara has escaped.

37
00:02:11,766 --> 00:02:15,002
Unfortunately, her transmitter 
is no longer in range,

38
00:02:15,002 --> 00:02:17,507
so that's all the information you get.

39
00:02:17,507 --> 00:02:19,849
Can you find the solution?

40
00:02:19,849 --> 00:02:27,280
Pause on the next screen
to work out the solution.

41
00:02:27,280 --> 00:02:28,451
3

42
00:02:28,451 --> 00:02:29,394
2

43
00:02:29,394 --> 00:02:30,401
1

44
00:02:30,401 --> 00:02:33,829
You're worried about the fact that you
don't know Zara's hallway number,

45
00:02:33,829 --> 00:02:37,140
but you decide to start 
from the beginning anyways.

46
00:02:37,140 --> 00:02:41,170
From the first clue, you work out all of
the eight possible combinations

47
00:02:41,170 --> 00:02:43,911
that come out to a product of 36.

48
00:02:43,911 --> 00:02:45,972
One of these must be right,
but which one?

49
00:02:45,972 --> 00:02:48,371
Now comes the hard part.

50
00:02:48,371 --> 00:02:51,313
Even though you don't know which number
you're looking for,

51
00:02:51,313 --> 00:02:55,782
you decide to work out the sum
of each combination's three numbers.

52
00:02:55,782 --> 00:02:57,564
That's when it hits you.

53
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All but two of the sums are unique,

54
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and if the hallway number had matched
any of these,

55
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Zara would have known the correct
combination right then and there

56
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without asking for the third clue.

57
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Since she did ask for the clue,

58
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the hallway number must have 
matched the only sum

59
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that appears more than once in the list:

60
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thirteen.

61
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But which of the two combinations
that add up to thirteen is correct:

62
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1,6,6,

63
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or 2,2,9?

64
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That's where the third clue comes in.

65
00:03:27,594 --> 00:03:30,465
Since it tells us that the largest
number must be unique,

66
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2,2,9 must be the code.

67
00:03:33,152 --> 00:03:37,449
When night falls, you and the others
escape through hallway thirteen

68
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and rejoin Zara outside.

69
00:03:39,785 --> 00:03:42,293
You've freed yourselves through 
math and logic.

70
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Now it's time to free 
the rest of the world.