Can you solve the giant cat army riddle? - Dan Finkel

3,543,099 views ใƒป 2018-06-11

TED-Ed


ืื ื ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ืœืžื˜ื” ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ.

ืชืจื’ื•ื: Ido Dekkers ืขืจื™ื›ื”: Roni Ravia
00:07
The villainous Dr. Schrรถdinger has developed a growth ray
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ื“ืจ' ืฉืจื•ื“ื™ื ื’ืจ ื”ืžืจื•ืฉืข ืคื™ืชื— ืงืจืŸ ืžื’ื“ื™ืœื”
00:10
and intends to create an army of giant cats
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ื•ืžืชื›ื•ื•ืŸ ืœื™ืฆื•ืจ ืฆื‘ื ืฉืœ ื—ืชื•ืœื™ ืขื ืง
00:13
to terrorize the city.
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ื•ืœื”ื˜ื™ืœ ื˜ืจื•ืจ ืขืœ ื”ืขื™ืจ.
00:16
Your team of secret agents
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ื”ืฆื•ื•ืช ืฉืœื›ื ืฉืœ ืกื•ื›ื ื™ื ื—ืฉืื™ื™ื
00:17
has tracked him to his underground lab.
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ืขืงื‘ ืื—ืจื™ื• ืœืžืขื‘ื“ื” ื”ืชืช ืงืจืงืขื™ืช ืฉืœื•.
00:20
You burst in to findโ€ฆ that itโ€™s a trap!
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ืืชื ืคื•ืจืฆื™ื ืคื ื™ืžื” ื•ืžื’ืœื™ื.... ืฉื–ื• ืžืœื›ื•ื“ืช!
00:23
Dr. Schrรถdinger has slipped into the next room to activate his device
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ื“ืจ' ืฉืจื•ื“ื™ื ื’ืจ ื—ืžืง ืœื—ื“ืจ ื”ืกืžื•ืš ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืžื›ืฉื™ืจ ืฉืœื•
00:27
and disabled the control panel on the way out.
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ื•ื ื™ื˜ืจืœ ืืช ืœื•ื— ื”ื‘ืงืจื” ื‘ื“ืจืš ื”ื—ื•ืฆื”.
00:30
Fortunately, your teammates are masters of spy-craft.
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ืœืžืจื‘ื” ื”ืžื–ืœ, ื—ื‘ืจื™ ื”ืฆื•ื•ืช ืฉืœื›ื ื”ื ืืฉืคื™ ืจื™ื’ื•ืœ.
00:34
Agent Delta has hacked into the control panel
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ื”ืกื•ื›ืŸ ื“ืœืชื ืคืจืฅ ืœืœื•ื— ื”ื‘ืงืจื”
00:37
and managed to reactivate some of its functionality.
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ื•ื”ืฆืœื™ื— ืœืฉื—ื–ืจ ื—ืœืง ืžื”ืฉื™ืžื•ืฉื™ื•ืช ืฉืœื•.
00:41
Meanwhile, Agent Epsilon has searched through surveillance
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ื‘ื™ื ืชื™ื™ื, ื”ืกื•ื›ืŸ ืืคืกื™ืœื•ืŸ ื ืขื–ืจ ื‘ืžืฆืœืžื•ืช ื”ืื‘ื˜ื—ื”
00:44
to find the code for the door:
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ื›ื“ื™ ืœื’ืœื•ืช ืืช ื”ืงื•ื“ ืœื“ืœืช:
00:46
2,
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2,
00:47
10,
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767
10,
00:48
14.
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14.
00:49
All you have to do is enter those numbers and youโ€™ll be free.
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ื›ืœ ืžื” ืฉืืชื ืฆืจื™ื›ื™ื ืœืขืฉื•ืช ื–ื” ืœื”ื›ื ื™ืก ืืช ื”ืžืกืคืจื™ื ื”ืืœื” ื•ืชื”ื™ื• ื—ื•ืคืฉื™ื™ื.
00:53
But thereโ€™s a problem.
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ืื‘ืœ ื™ืฉ ื‘ืขื™ื”.
00:54
The control panel has only three buttons:
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ื‘ืœื•ื— ื”ื‘ืงืจื” ื™ืฉ ืจืง ืฉืœื•ืฉื” ื›ืคืชื•ืจื™ื:
00:57
one which adds 5 to the display number,
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ืื—ื“ ืฉืžื•ืกื™ืฃ 5 ืœืžืกืคืจ ื”ืžื•ืฆื’,
01:00
one which adds 7,
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ืื—ื“ ืฉืžื•ืกื™ืฃ 7,
01:01
and one which takes the square root.
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ื•ืื—ื“ ืฉืžื•ืฆื™ื ืฉื•ืจืฉ ืจื™ื‘ื•ืขื™.
01:04
You need to make the display output the numbers
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ืืชื ืฆืจื™ื›ื™ื ืฉืขืœ ื”ืžืกืš ื™ื•ืคื™ืขื• ื”ืžืกืคืจื™ื
01:07
2, 10, and 14, in that order.
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2, 10 ื• 14 ื‘ืกื“ืจ ื”ื–ื”.
01:10
Itโ€™s okay if it outputs different numbers in between,
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ื–ื” ื‘ืกื“ืจ ืื ืžื•ืคื™ืขื™ื ืžืกืคืจื™ื ืื—ืจื™ื ื‘ื™ื ื”ื,
01:13
but thereโ€™s no way to reset the display,
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ืื‘ืœ ืื™ืš ื“ืจืš ืœืืคืก ืืช ื”ืชืฆื•ื’ื”,
01:16
so once you get to 2,
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ืื– ื‘ืจื’ืข ืฉืืชื ืžื’ื™ืขื™ื ืœ 2,
01:17
youโ€™ll have to continue on to 10 and 14 from there.
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ืืชื ืชื”ื™ื• ื—ื™ื™ื‘ื™ื ืœื”ืžืฉื™ืš ืœ 10 ื•ืœ 14 ืžืฉื.
01:22
Not only that, Agent Delta explains
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ืœื ืจืง ื–ื”, ื”ืกื•ื›ืŸ ื“ืœืชื ืžืกื‘ื™ืจ
01:24
that there are other traps built into the panel.
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ืฉืœืคืื ืœ ื™ืฉ ืžืœื›ื•ื“ื•ืช ื ื•ืกืคื•ืช.
01:27
If it ever shows the same number more than once,
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ืื ื”ื•ื ืื™ ืคืขื ืžืจืื” ืืช ืื•ืชื• ืžืกืคืจ ืคืขืžื™ื™ื,
01:30
a number greater than 60,
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ืื• ืžืจืื” ืžืกืคืจ ื”ื’ื“ื•ืœ ืž 60,
01:32
or a non-whole number,
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ืื• ืžืกืคืจ ืœื ืฉืœื,
01:34
the room will explode.
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ื”ื—ื“ืจ ื™ืชืคื•ืฆืฅ.
01:37
Right now, the display reads zero, and time is running out.
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ืขื›ืฉื™ื•, ื”ืชืฆื•ื’ื” ืžืจืื” ืืคืก, ื•ื”ื–ืžืŸ ื”ื•ืœืš ื•ืื•ื–ืœ.
01:42
Thereโ€™s only one way to solve the puzzle, with a few small variations.
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ื™ืฉ ืจืง ื“ืจืš ืื—ืช ืœืคืชื•ืจ ืืช ื”ืคืื–ืœ, ืขื ืžืกืคืจ ื•ืืจื™ืืฆื™ื•ืช ื“ื•ืžื•ืช.
01:45
How will you input the code to escape from Dr. Schrรถdingerโ€™s lair
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ืื™ืš ืชื›ื ื™ืกื• ืืช ื”ืงื•ื“ ื›ื“ื™ ืœื‘ืจื•ื— ืžื”ืžืื•ืจื” ืฉืœ ื“ืจืณ ืฉืจื•ื“ื™ื ื’ืจ
01:49
and save the day?
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ื•ืœื”ืฆื™ืœ ืืช ื”ืžืฆื‘?
01:51
Pause the video now if you want to figure it out for yourself!
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ืขืฆืจื• ืืช ื”ืกืจื˜ื•ืŸ ืคื” ืื ืืชื ืจื•ืฆื™ื ืœื”ื‘ื™ืŸ ื‘ืขืฆืžื›ื!
01:58
Answer in: 3
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ืชืฉื•ื‘ื” ื‘ืขื•ื“: 3
02:00
2
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02:00
1.
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ืชืฉื•ื‘ื” ื‘ืขื•ื“: 2
ืชืฉื•ื‘ื” ื‘ืขื•ื“: 1.
02:02
You look over your options.
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ืืชื ื—ื•ืฉื‘ื™ื ืขืœ ื”ืื•ืคืฆื™ื•ืช ืฉืœื›ื.
02:03
Adding 5 or 7 increases the number,
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ื”ื•ืกืคืช 5 ืื• 7 ืชื’ื“ื™ืœ ืืช ื”ืžืกืคืจ,
02:07
and the square root button will make it smaller.
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ื•ื›ืคืชื•ืจ ื”ืฉื•ืจืฉ ื”ืจื™ื‘ื•ืขื™ ื™ืงื˜ื™ืŸ ืื•ืชื•.
02:09
But there are only a few options where you can use that button:
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ืื‘ืœ ื™ืฉ ืจืง ื›ืžื” ืื•ืคืฆื™ื•ืช ื‘ื”ืŸ ืืชื ื™ื›ื•ืœื™ื ืœื”ืฉืชืžืฉ ื‘ื›ืคืชื•ืจ ื”ื–ื”:
02:13
4
46
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716
02:13
9
47
133748
782
4
9
02:14
16
48
134530
716
16
02:15
25,
49
135246
813
25,
02:16
36,
50
136059
883
02:16
and 49.
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36,
ื• 49.
02:18
Youโ€™d love to make 4 or 16.
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ืืชื ืžืžืฉ ืจื•ืฆื™ื ืœื™ืฆื•ืจ 4 ืื• 16.
02:20
Then you could hit the square root button once or twice to get 2.
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ืื– ืชื•ื›ืœื• ืœืœื—ื•ืฅ ืขืœ ื”ืฉื•ืจืฉ ืคืขื ืื• ืคืขืžื™ื™ื ื•ืœื”ื’ื™ืข ืœ 2.
02:24
But you canโ€™t make either with just the 5 and 7 buttons.
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ืื‘ืœ ืืชื ืœื ื™ื›ื•ืœื™ื ืœื”ื’ื™ืข ืœืืฃ ืื—ื“ ืจืง ืขื ื” 5 ื•ื” 7.
02:27
What will you do?
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ืžื” ืชืขืฉื•?
02:29
You look at the other possible options for numbers you could take the square root of.
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ืืชื ืžื‘ื™ื˜ื™ื ื‘ืืคืฉืจื•ื™ื•ืช ื”ืื—ืจื•ืช ืœืžืกืคืจื™ื ืฉืืคืฉืจ ืœืงื—ืช ืžื”ื ืฉื•ืจืฉ.
02:33
Nine you canโ€™t reach.
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ืœืชืฉืข ืื™ ืืคืฉืจ ืœื”ื’ื™ืข.
02:35
Twenty-five and 49 would take you back to 5 or 7,
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ื• 25 ื• 49 ื™ืงื—ื• ืืชื›ื ื—ื–ืจื” ืœ 5 ืื• 7,
02:39
and you can already get to each of those.
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ื•ืืชื ื›ื‘ืจ ื™ื›ื•ืœื™ื ืœื”ื’ื™ืข ืœื›ืœ ืื—ื“ ืžืืœื”.
02:41
Thirty-six is your only option.
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ืฉืœื•ืฉื™ื ื•ืฉืฉ ื”ื™ื ื”ืื•ืคืฆื™ื” ื”ื™ื—ื™ื“ื” ืฉืœื›ื.
02:44
You add 5,
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ืืชื ืžื•ืกื™ื™ืคื™ื 5,
02:45
7,
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7,
02:46
5,
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5,
02:47
7,
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755
02:47
5,
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718
7,
5,
02:48
7,
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1038
7,
02:49
and then hit the square root button.
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ื•ืื– ืœื•ื—ืฆื™ื ืขืœ ื”ืฉื•ืจืฉ ื”ืจื™ื‘ื•ืขื™.
02:51
Why that series of 5s and 7s?
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ืœืžื” ื”ืกื“ืจื” ื”ื–ื• ืฉืœ 5 ื• 7?
02:53
Itโ€™s somewhat arbitrary,
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ื–ื” ื“ื™ ืฉืจื™ืจื•ืชื™,
02:55
but you know that you want to avoid 10, 14, and perfect squares,
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ืื‘ืœ ืืชื ื™ื•ื“ืขื™ื ืฉืืชื ืจื•ืฆื™ื ืœื”ืžื ืข ืž 10, 14, ื•ืจื™ื‘ื•ืขื™ื ืžื•ืฉืœืžื™ื,
02:59
since youโ€™ll need them later.
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ืžืื—ืจ ื•ืชืฆื˜ืจื›ื• ืื•ืชื ืžืื•ื—ืจ ื™ื•ืชืจ.
03:01
This gets you to 6.
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ื–ื” ืžื‘ื™ื ืืชื›ื ืœ 6.
03:03
Does that help?
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ื”ืื ื–ื” ืขื•ื–ืจ?
03:04
Looking at your options, you see that 16 is now in your sights.
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ืื ืžื‘ื™ื˜ื™ื ื‘ืืคืฉืจื•ื™ื•ืช, ืืชื ืชืจืื• ืฉ 16 ืขื‘ืฉื™ื• ื‘ืจ ื”ืฉื’ื”.
03:08
You add 5 twice more to reach it.
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ืืชื ืžื•ืกื™ืคื™ื 5 ืคืขืžื™ื™ื ื›ื“ื™ ืœื”ื’ื™ืข ืืœื™ื•.
03:11
Then hit square root twice.
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ืื– ืœื•ื—ืฆื™ื ืขืœ ืฉื•ืจืฉ ืจื™ื‘ื•ืขื™ ืคืขืžื™ื.
03:14
That gets you to 2.
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ื–ื” ืžื‘ื™ื ืืชื›ื ืœ 2.
03:15
Youโ€™re on your way!
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ืืชื ื‘ื“ืจืš!
03:17
Now to 10.
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ืขื›ืฉื™ื• ืœ 10.
03:18
You canโ€™t get straight there through addition alone,
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ืืชื ืœื ื™ื›ื•ืœื™ื ืœื”ื’ื™ืข ื™ืฉื™ืจื•ืช ืœืฉื ื“ืจืš ื”ื•ืกืคื” ื‘ืœื‘ื“,
03:21
so youโ€™re going to have to reach another square.
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ืื– ืืชื ืชืฆื˜ืจื›ื• ืœื”ื’ื™ืข ืœืจื™ื‘ื•ืข ื ื•ืกืฃ.
03:23
Taking the square root of 9 or 25 would get you to a good place,
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ืื ื ื™ืงื— ืฉื•ืจืฉ ืฉืœ 9 ืื• 25 ื–ื” ื™ื‘ื™ื ืื•ืชื ื• ืœืžืงื•ื ื˜ื•ื‘.
03:28
but it turns out that 25 is unreachable from 2.
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ืืš ืžืกืชื‘ืจ ืฉ 25 ืœื ื ื™ืชืŸ ืœื”ื’ืขื” ืž 2.
03:32
So you add 7 to get to 9,
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ืื– ืืชื ืžื•ืกื™ืคื™ื 7 ื›ื“ื™ ืœื”ื’ื™ืข ืœ 9,
03:35
then take the square root again.
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ื•ืื– ืœื•ืงื—ื™ื ืฉื•ืจืฉ ืฉื•ื‘.
03:36
That gets you to 3.
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ื•ืžื’ื™ืขื™ื ืœ 3.
03:38
Adding 7 again makes 10.
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ื”ื•ืกืคืช 7 ืชื‘ื™ื ืืชื›ื ืœ 10.
03:41
Finally, you need to reach 14.
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ืœื‘ืกื•ืฃ, ืืชื ืฆืจื™ื›ื™ื ืœื”ื’ื™ืข ืœ 14.
03:43
Thinking backwards, you imagine where you could be before 14:
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ืื ื—ื•ืฉื‘ื™ื ืื—ื•ืจื”, ืืชื ืžื“ืžื™ื™ื ื™ื ืื™ืคื” ืืชื ื™ื›ื•ืœื™ื ืœื”ื™ื•ืช ืœืคื ื™ 14.
03:48
7 or 9.
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7 ืื• 9.
03:50
But 9 wonโ€™t work because youโ€™ve already used 9.
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ืื‘ืœ 9 ืœื ื™ืขื‘ื•ื“ ื‘ื’ืœืœ ืฉื›ื‘ืจ ื”ืฉืชืžืฉืชื ื‘ 9.
03:53
However, you could get to 7 by reaching 49 first.
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ืื‘ืœ, ืืชื ื™ื›ื•ืœื™ื ืœื”ื’ื™ืข ืœ 7 ืขืœ ื™ื“ื™ ื”ื’ืขื” ืœ 49.
03:58
You add your way towards it,
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ืืชื ืžื•ืกื™ืคื™ื ืžืกืคืจื™ื ื‘ื“ืจืš ืœืžื˜ืจื”,
04:00
being careful not to hit any of the numbers youโ€™ve hit so far.
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ื ื–ื”ืจื™ื ืœื ืœื”ื’ื™ืข ืœืืฃ ืžืกืคืจ ืฉื›ื‘ืจ ื”ื’ืขืชื ืืœื™ื•.
04:03
You thread your way carefully,
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ืืชื ื ื•ืงื˜ื™ื ื‘ื–ื”ื™ืจื•ืช,
04:05
adding five 5s and two 7s.
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ืžื•ืกื™ืคื™ื ื—ืžื™ืฉื” 5 ื•ืฉื ื™ 7.
04:08
Then, square root to 7, and add 7 more.
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ืื–, ืœื•ืงื—ื™ื ืฉื•ืจืฉ ืจื™ื‘ื•ืขื™ ืฉื™ื•ื‘ื™ืœ ืœ 7, ึฟื•ืžื•ืกื™ืคื™ื ืขื•ื“ 7.
04:12
The door opens, and youโ€™re out of the trap.
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ื”ื“ืœืช ื ืคืชื—ืช, ื•ืืชื ื™ื•ืฆืื™ื ืžื”ืžืœื›ื•ื“ืช.
04:15
Thanks to your problem-solving skills,
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ื”ื•ื“ื•ืช ืœื™ื›ื•ืœื•ืช ืคืชืจื•ืŸ ื”ื‘ืขื™ื•ืช ืฉืœื›ื,
04:17
your team gets Schrรถdingerโ€™s cats out of the box in the nick of time.
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ื”ืฆื•ื•ืช ืฉืœื›ื ืžื•ืฆื™ื ืืช ื”ื—ืชื•ืœื™ื ืฉืœ ืฉืจื•ื“ื™ื ื’ืจ ืžื”ืงื•ืคืกื” ื‘ืจื’ืข ื”ืื—ืจื•ืŸ.
04:21
As for Schrรถdinger, you can be certain of one thing:
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ื•ื‘ื ื•ื’ืข ืœืฉืจื•ื“ื™ื ื’ืจ, ืืชื ื™ื›ื•ืœื™ื ืœื”ื™ื•ืช ื‘ื˜ื•ื—ื™ื ื‘ื“ื‘ืจ ืื—ื“:
04:24
heโ€™ll be spending quite some time in a box of his own.
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ื”ื•ื ื™ื‘ืœื” ื“ื™ ื”ืจื‘ื” ื–ืžืŸ ื‘ืงื•ืคืกื” ืžืฉืœื•.
ืขืœ ืืชืจ ื–ื”

ืืชืจ ื–ื” ื™ืฆื™ื’ ื‘ืคื ื™ื›ื ืกืจื˜ื•ื ื™ YouTube ื”ืžื•ืขื™ืœื™ื ืœืœื™ืžื•ื“ ืื ื’ืœื™ืช. ืชื•ื›ืœื• ืœืจืื•ืช ืฉื™ืขื•ืจื™ ืื ื’ืœื™ืช ื”ืžื•ืขื‘ืจื™ื ืขืœ ื™ื“ื™ ืžื•ืจื™ื ืžื”ืฉื•ืจื” ื”ืจืืฉื•ื ื” ืžืจื—ื‘ื™ ื”ืขื•ืœื. ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ื”ืžื•ืฆื’ื•ืช ื‘ื›ืœ ื“ืฃ ื•ื™ื“ืื• ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ ืžืฉื. ื”ื›ืชื•ื‘ื™ื•ืช ื’ื•ืœืœื•ืช ื‘ืกื ื›ืจื•ืŸ ืขื ื”ืคืขืœืช ื”ื•ื•ื™ื“ืื•. ืื ื™ืฉ ืœืš ื”ืขืจื•ืช ืื• ื‘ืงืฉื•ืช, ืื ื ืฆื•ืจ ืื™ืชื ื• ืงืฉืจ ื‘ืืžืฆืขื•ืช ื˜ื•ืคืก ื™ืฆื™ืจืช ืงืฉืจ ื–ื”.

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