1
00:00:06,720 --> 00:00:10,354
Your rich, eccentric uncle 
just passed away,

2
00:00:10,354 --> 00:00:16,854
and you and your 99 nasty relatives have
been invited to the reading of his will.

3
00:00:16,854 --> 00:00:19,374
He wanted to leave 
all of his money to you,

4
00:00:19,374 --> 00:00:24,805
but he knew that if he did,
your relatives would pester you forever.

5
00:00:24,805 --> 00:00:27,062
So he is banking on the fact

6
00:00:27,062 --> 00:00:32,660
that he taught you everything 
you need to know about riddles.

7
00:00:32,660 --> 00:00:35,558
Your uncle left the following 
note in his will:

8
00:00:35,558 --> 00:00:37,777
"I have created a puzzle.

9
00:00:37,777 --> 00:00:42,028
If all 100 of you answer it together,
you will share the money evenly.

10
00:00:42,028 --> 00:00:46,185
However, if you are the first to find
the pattern and solve the problem

11
00:00:46,185 --> 00:00:48,721
without going through all of the leg work,

12
00:00:48,721 --> 00:00:52,521
you will get the entire inheritance 
all to yourself.

13
00:00:52,521 --> 00:00:54,098
Good luck."

14
00:00:54,098 --> 00:00:58,929
The lawyer takes you and your 99 relatives
to a secret room in the mansion

15
00:00:58,929 --> 00:01:01,795
that contains 100 lockers,

16
00:01:01,795 --> 00:01:04,270
each hiding a single word.

17
00:01:04,270 --> 00:01:05,440
He explains:

18
00:01:05,440 --> 00:01:09,805
Every relative is assigned a number
from 1 to 100.

19
00:01:09,805 --> 00:01:12,705
Heir 1 will open every locker.

20
00:01:12,705 --> 00:01:16,702
Heir 2 will then 
close every second locker.

21
00:01:16,702 --> 00:01:20,879
Heir 3 will change the status
of every third locker,

22
00:01:20,879 --> 00:01:23,775
specifically if it's open, 
she'll close it,

23
00:01:23,775 --> 00:01:26,580
but if it's closed, she'll open it.

24
00:01:26,580 --> 00:01:31,179
This pattern will continue until
all 100 of you have gone.

25
00:01:31,179 --> 00:01:34,462
The words in the lockers that remain
open at the end

26
00:01:34,462 --> 00:01:38,037
will help you crack the code for the safe.

27
00:01:38,037 --> 00:01:42,644
Before cousin Thaddeus can even start
down the line,

28
00:01:42,644 --> 00:01:49,012
you step forward and tell the lawyer
you know which lockers will remain open.

29
00:01:49,012 --> 00:01:51,366
But how?

30
00:01:51,366 --> 00:01:54,332
Pause the video now if you want
to figure it out for yourself!

31
00:01:54,332 --> 00:01:55,421
Answer in: 3

32
00:01:55,421 --> 00:01:56,577
Answer in: 2

33
00:01:56,577 --> 00:01:58,248
Answer in: 1

34
00:01:58,248 --> 00:02:02,151
The key is realizing that the number
of times a locker is touched

35
00:02:02,151 --> 00:02:06,427
is the same as the number of factors
in the locker number.

36
00:02:06,427 --> 00:02:09,064
For example, in locker #6,

37
00:02:09,064 --> 00:02:10,708
Person 1 will open it,

38
00:02:10,708 --> 00:02:12,602
Person 2 will close it,

39
00:02:12,602 --> 00:02:14,316
Person 3 will open it,

40
00:02:14,316 --> 00:02:17,212
and Person 6 will close it.

41
00:02:17,212 --> 00:02:22,332
The numbers 1, 2, 3, and 6 
are the factors of 6.

42
00:02:22,332 --> 00:02:25,165
So when a locker has an even number
of factors

43
00:02:25,165 --> 00:02:26,812
it will remain closed,

44
00:02:26,812 --> 00:02:28,833
and when it has an odd number of factors,

45
00:02:28,833 --> 00:02:30,962
it will remain open.

46
00:02:30,962 --> 00:02:33,953
Most of the lockers 
have an even number of factors,

47
00:02:33,953 --> 00:02:37,713
which makes sense because factors
naturally pair up.

48
00:02:37,713 --> 00:02:41,475
In fact, the only lockers that have
an odd number of factors

49
00:02:41,475 --> 00:02:43,774
are perfect squares

50
00:02:43,774 --> 00:02:48,952
because those have one factor that when
multiplied by itself equals the number.

51
00:02:48,952 --> 00:02:51,334
For Locker 9, 1 will open it,

52
00:02:51,334 --> 00:02:52,818
3 will close,

53
00:02:52,818 --> 00:02:54,934
and 9 will open it.

54
00:02:54,934 --> 00:02:57,094
3 x 3 = 9,

55
00:02:57,094 --> 00:02:59,379
but the 3 can only be counted once.

56
00:02:59,379 --> 00:03:04,529
Therefore, every locker that is 
a perfect square will remain open.

57
00:03:04,529 --> 00:03:07,426
You know that these ten lockers 
are the solution,

58
00:03:07,426 --> 00:03:11,285
so you open them immediately
and read the words inside:

59
00:03:11,285 --> 00:03:17,043
"The code is the first five lockers
touched only twice."

60
00:03:17,043 --> 00:03:21,881
You realize that the only lockers 
touched twice have to be prime numbers

61
00:03:21,881 --> 00:03:24,454
since each only has two factors:

62
00:03:24,454 --> 00:03:26,508
1 and itself.

63
00:03:26,508 --> 00:03:30,835
So the code is 2-3-5-7-11.

64
00:03:30,835 --> 00:03:33,209
The lawyer brings you to the safe,

65
00:03:33,209 --> 00:03:35,045
and you claim your inheritance.

66
00:03:35,045 --> 00:03:38,527
Too bad your relatives were always
too busy being nasty to each other

67
00:03:38,527 --> 00:03:41,344
to pay attention 
to your eccentric uncle's riddles.