Can you solve the unstoppable blob riddle? - Dan Finkel

7,999,340 views ใƒป 2019-03-18

TED-Ed


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

ืชืจื’ื•ื: Ido Dekkers
00:07
A shooting star crashes on Earth,
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ืžื˜ืื•ืจ ืžืชืจืกืง ืขืœ ื›ื“ื•ืจ ื”ืืจืฅ,
00:10
and a hideous blob emerges.
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ื•ื‘ืœื•ื‘ ืžื—ืจื™ื“ ืžื•ืคื™ืข.
00:13
It creeps and leaps, it glides and slides.
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ื”ื•ื ื–ื•ื—ืœ, ื•ืงื•ืคืฅ, ื”ื•ื ื’ื•ืœืฉ ื•ืžื—ืœื™ืง.
00:17
Itโ€™s also unstoppable:
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ื”ื•ื ื’ื ื‘ืœืชื™ ื ื™ืชืŸ ืœืขืฆื™ืจื”:
00:19
weapons, fire, extreme temperaturesโ€ฆ
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ื ืฉืงื™ื, ืืฉ, ื˜ืžืคืจื˜ื•ืจื•ืช ืงื™ืฆื•ื ื™ื•ืช...
00:21
no matter what you throw at it,
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ืœื ืžืฉื ื” ืžื” ืืชื ืžืฉืœื™ื›ื™ื ืขืœื™ื•,
00:23
it just regrows and continues its rampage.
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ื”ื•ื ืจืง ื’ื“ืœ ืžื—ื“ืฉ ื•ืžืžืฉื™ืš ื‘ื”ืจืก.
00:27
Its expansion is breathtaking;
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ื”ื”ืชืจื—ื‘ื•ืช ืฉืœื• ืขื•ืฆืจืช ื ืฉื™ืžื”;
00:29
it doubles in size every hour.
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ื”ื•ื ืžื›ืคื™ืœ ืืช ื’ื•ื“ืœื• ื›ืœ ืฉืขื”.
00:32
But thereโ€™s one opportunity:
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ืื‘ืœ ื™ืฉ ื”ื–ื“ืžื ื•ืช ืื—ืช:
00:34
after each hour, it goes to sleep,
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ืื—ืจื™ ื›ืœ ืฉืขื”, ื”ื•ื ื”ื•ืœืš ืœื™ืฉื•ืŸ,
00:37
forming itself into a flat triangle
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ื•ื”ื•ืคืš ืืช ืขืฆืžื• ืœืžืฉื•ืœืฉ ืฉื˜ื•ื—
00:39
and resting for a few minutes
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ื•ื ื— ืœื›ืžื” ื“ืงื•ืช
00:41
before it begins eating and growing again.
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ืœืคื ื™ ืฉื”ื•ื ืžืชื—ื™ืœ ืœืื›ื•ืœ ื•ืœื’ื“ื•ืœ ืฉื•ื‘.
00:45
Your only chance to save the planet
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ื”ื”ื–ื“ืžื ื•ืช ื”ื™ื—ื™ื“ื” ืฉืœื›ื ืœื”ืฆื™ืœ ืืช ื”ืคืœื ื˜ื”
00:47
involves a satellite-mounted nano-fission ray that can cut through the blob.
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ื›ื•ืœืœืช ืงืจืŸ ื ื ื• ื”ื™ืชื•ืš ืœื•ื•ื™ื ื™ืช ืฉื™ื›ื•ืœื” ืœื—ืชื•ืš ืืช ื”ื‘ืœื•ื‘.
00:53
When the blog is active
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ื›ืฉื”ื‘ืœื•ื‘ ืืงื˜ื™ื‘ื™
00:54
it heals itself within seconds.
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ื”ื•ื ืžืจืคื ืืช ืขืฆืžื• ืชื•ืš ืฉื ื™ื•ืช.
00:57
However, when you break the sleeping blob into two triangles,
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ืขื ื–ืืช, ื›ืฉืืชื ื—ื•ืชื›ื™ื ืืช ื”ื‘ืœื•ื‘ ื”ื™ืฉืŸ ืœืžืฉื•ืœืฉื™ื,
01:00
you make a critical discovery.
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ืืชื ืžื’ืœื™ื ื’ื™ืœื•ื™ ื—ืฉื•ื‘.
01:03
The acute triangle portion,
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ื—ืœืง ื”ืžืฉื•ืœืฉ ื”ื—ื“,
01:05
with all angles less than 90 degrees, is inert.
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ืขื ื›ืœ ื”ื–ื•ื™ื•ืช ืคื—ื•ืช ืž 90 ืžืขืœื•ืช, ื”ื•ื ืœื ืคืขื™ืœ.
01:09
It never โ€œwakes up.โ€
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ื”ื•ื ืœืขื•ืœื ืœื "ืžืชืขื•ืจืจ."
01:11
The obtuse triangle,
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ื”ืžืฉื•ืœืฉ ื›ื”ื” ื”ื–ื•ื™ืช,
01:12
which has an angle greater than 90 degrees,
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ืฉื™ืฉ ืœื• ื–ื•ื™ืช ืฉืœ ื™ื•ืชืจ ืž 90 ืžืขืœื•ืช,
01:15
wakes up as usual and keeps growing.
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ืžืชืขื•ืจืจ ื›ืจื’ื™ืœ ื•ืžืžืฉื™ืš ืœื’ื“ื•ืœ.
01:18
Similar experiments show that all shapes other than acute triangles,
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ื ื™ืกื•ื™ื ื“ื•ืžื™ื ืžืจืื™ื ืฉื›ืœ ื”ืฆื•ืจื•ืช ืฉื”ืŸ ืœื ืžืฉื•ืœืฉ ื—ื“ ื–ื•ื™ืช,
01:22
including right triangles, will also wake up.
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ื›ื•ืœืœ ืžืฉื•ืœืฉื™ื ื™ืฉืจื™ ื–ื•ื™ืช ื’ื ืžืชืขื•ืจืจื™ื.
01:26
For the next few minutes,
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ื‘ื“ืงื•ืช ื”ื‘ืื•ืช,
01:27
the blob is sleeping in its obtuse triangle form.
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ื”ื‘ืœื•ื‘ ื™ืฉืŸ ื‘ืฆื•ืจืช ืžืฉื•ืœืฉ ื›ื”ื” ื–ื•ื™ืช.
01:31
You can make clean, straight-line cuts
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ืืชื ื™ื›ื•ืœื™ื ืœืขืฉื•ืช ื—ื™ืชื•ื›ื™ื ื™ืฉืจื™ื ื•ื ืงื™ื™ื
01:34
between any two points on or inside the triangle.
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ื‘ื™ืŸ ื›ืœ ืฉืชื™ ื ืงื•ื“ื•ืช ืขืœ ืื• ื‘ืชื•ืš ื”ืžืฉื•ืœืฉ.
01:37
But youโ€™ll only have time to make 7 cuts while the satellite is above you.
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ืื‘ืœ ื™ื”ื™ื” ืœื›ื ื–ืžืŸ ืœืขืฉื•ืช ืจืง 7 ื—ื™ืชื•ื›ื™ื ื›ืฉื”ืœื•ื•ื™ืŸ ืžืขืœื™ื™ื›ื.
01:42
By the time it completes its orbit and returns,
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ืขื“ ืฉื”ื•ื ื™ืฉืœื™ื ื”ืงืคื” ื ื•ืกืคืช ื•ื™ื—ื–ื•ืจ,
01:45
the blob will have consumed the entire world,
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ื”ื‘ืœื•ื‘ ื™ื‘ืœืข ืืช ื›ืœ ื”ืขื•ืœื,
01:48
if even a single portion that will wake up remains.
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ืื ืืคื™ืœื• ื—ืœืง ืื—ื“ ืฉื™ืชืขื•ืจืจ ื™ืฉืืจ.
01:52
How can you cut the blob entirely into acute triangles
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ืื™ืš ืืชื ื™ื›ื•ืœื™ื ืœื—ืชื•ืš ืืช ื”ื‘ืœื•ื‘ ืœื’ืžืจื™ ืœืžืฉื•ืœืฉื™ื ื—ื“ื™ ื–ื•ื™ืช
01:56
and stop it from destroying the planet?
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ื•ืœืขืฆื•ืจ ืื•ืชื• ืžืœื”ืจื•ืก ืืช ื›ืœ ื”ืคืœื ื˜ื”?
01:59
Pause the video now to figure out for yourself
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ืขืฆืจื• ืคื” ืื ืืชื ืจื•ืฆื™ื ืœื”ื‘ื™ืŸ ื‘ืขืฆืžื›ื
02:01
Answer in 3
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ืชืฉื•ื‘ื” ืขื•ื“ 3
02:02
Answer in 2
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ืชืฉื•ื‘ื” ืขื•ื“ 2
02:05
Answer in 1
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1
02:07
While this seems doable at first,
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ื‘ืขื•ื“ ื ืจืื” ืฉื–ื” ืืคืฉืจื™ ื‘ืชื—ื™ืœื”,
02:09
thereโ€™s a hidden difficulty when it comes to avoiding obtuse and right angles.
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ื™ืฉ ืงื•ืฉื™ ื—ื‘ื•ื™ ื›ืฉื–ื” ืžื’ื™ืข ืœื”ืžื ืข ืžืžืฉื•ืœืฉื™ื ื›ื”ื™ ื–ื•ื™ืช ื•ื™ืฉืจื™ ื–ื•ื™ืช.
02:14
Every time you make a cut that reaches an edge,
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ื›ืœ ืคืขื ืฉืืชื ืขื•ืฉื™ื ื—ื™ืชื•ืš ืฉืžื’ื™ืข ืœืงืฆื”,
02:17
it either makes an acute and an obtuse angle, or two right angles.
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ื”ื•ื ื™ื•ืฆืจ ื–ื•ื™ืช ื—ื“ื” ื•ื›ื”ื”, ืื• ืฉืชื™ ื–ื•ื™ื•ืช ื™ืฉืจื•ืช.
02:22
That makes it seems like youโ€™re doomed to keep creating obtuse angles.
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ื–ื” ื’ื•ืจื ืœื–ื” ืœื”ืจืื•ืช ื›ืื™ืœื• ื ื™ื“ื•ื ืชื ืœื”ืžืฉื™ืš ืœื™ืฆื•ืจ ืžืฉื•ืœืฉื™ื ื›ื”ื™ ื–ื•ื™ืช.
02:27
But as with so many of lifeโ€™s problems,
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ืื‘ืœ ื›ืžื• ืขื ื›ืœ ื›ืš ื”ืจื‘ื” ื‘ืขื™ื•ืช ื‘ื—ื™ื™ื,
02:30
we can look to pizza for inspiration.
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ืื ื—ื ื• ื™ื›ื•ืœื™ื ืœืงื‘ืœ ื”ืฉืจืื” ืžืคื™ืฆื”.
02:33
Imagine squaring off the outside of a pizza,
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ื“ืžื™ื™ื ื• ืฉืืชื ืžื™ื™ืฉืจื™ื ืืช ื”ื—ืœืง ื”ื—ื™ืฆื•ื ื™ ืฉืœ ืคื™ืฆื”,
02:36
so that instead of a circle, itโ€™s an octagon.
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ื›ืš ืฉื‘ืžืงื•ื ืขื™ื’ื•ืœ, ื”ื™ื ืžืชื•ืžืŸ.
02:39
When we cut it into slices,
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ื›ืฉืื ื—ื ื• ื—ื•ืชื›ื™ื ืื•ืชื” ืœืจืฆื•ืขื•ืช,
02:41
each of the eight triangles is acute.
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ื›ืœ ืื—ื“ ืžื”ืžืฉื•ืœืฉื™ื ื—ื“ ื–ื•ื™ืช.
02:44
This works with larger polygons too.
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ื–ื” ืขื•ื‘ื“ ื’ื ืขื ืคื•ืœื™ื’ื•ื ื™ื ื’ื“ื•ืœื™ื ื™ื•ืชืจ.
02:46
Importantly, it also works for some polygons with fewer sides,
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ื•ื—ืฉื•ื‘ ื™ื•ืชืจ, ื–ื” ื’ื ืขื•ื‘ื“ ืขื ืคื•ืœื™ื’ื•ื ื™ื ืขื ืคื—ื•ืช ืคืื•ืช,
02:51
including heptagons, hexagons, and pentagons.
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ื›ื•ืœืœ ืžืฉื•ื‘ืขื™ื, ืžืฉื•ืฉื™ื, ื•ืžื—ื•ืžืฉื™ื.
02:55
Thatโ€™s good news,
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ืืœื” ื—ื“ืฉื•ืช ื˜ื•ื‘ื•ืช,
02:56
because if you cut off the sharp corners of the blob triangle,
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ื‘ื’ืœืœ ืฉืืชื ื™ื›ื•ืœื™ื ืœื—ืชื•ืš ืืช ื”ืงืฆื•ื•ื•ืช ื”ื—ื“ื™ื ืฉืœ ื”ื‘ืœื•ื‘ ื”ืžืฉื•ืœืฉ,
03:00
a pentagon is exactly what youโ€™ll be left with.
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ืžื—ื•ืžืฉ ื”ื•ื ื‘ื“ื™ื•ืง ืžื” ืฉื ืฉืืจ ืœื›ื.
03:04
And just like a pizza,
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ื•ืžืžืฉ ื›ืžื• ืคื™ืฆื”,
03:06
you can cut the blob pentagon into five acute triangles.
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ืืชื ื™ื›ื•ืœื™ื ืœื—ืชื•ืš ืืช ื”ื‘ืœื•ื‘ ื”ืžื—ื•ืžืฉ ืœื—ืžื™ืฉื” ืžืฉื•ืœืฉื™ื ื—ื“ื™ ื–ื•ื™ืช.
03:10
Thatโ€™s 7 cuts, and it renders the blob completely inert.
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ื–ื” 7 ื—ืชื›ื™ื, ื•ื–ื” ื”ื•ืคืš ืื•ืชื• ืœืœื ืคืขื™ืœ ืœื’ืžืจื™.
03:15
Youโ€™ve saved the day!
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ื”ืฆืœืชื ืืช ื”ื™ื•ื!
03:17
Now you just need to figure out what to do
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ืขื›ืฉื™ื• ืืชื ืจืง ืฆืจื™ื›ื™ื ืœื”ื‘ื™ืŸ ืžื” ืœืขืฉื•ืช
03:19
with all of these giant, practically indestructible triangles.
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ืขื ื”ืžืฉื•ืœืฉื™ื ื”ืขืฆื•ืžื™ื ื”ืืœื” ืฉื‘ืœืชื™ ื ื™ืชื ื™ื ืœื”ืฉืžื“ื”.
ื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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