Can you solve the sea monster riddle? - Dan Finkel
-
0:07 - 0:10According to legend,
once every thousand years -
0:10 - 0:15a host of sea monsters emerges
from the depths to demand tribute -
0:15 - 0:19from the floating city of Atlantartica.
-
0:19 - 0:22As the ruler of the city,
you’d always dismissed the stories… -
0:22 - 0:28until today, when 7 Leviathan Lords
rose out of the roiling waters -
0:28 - 0:30and surrounded your city.
-
0:30 - 0:33Each commands 10 giant kraken,
-
0:33 - 0:37and each kraken
is accompanied by 12 mermites. -
0:37 - 0:42Your city’s puny army
is hopelessly outmatched. -
0:42 - 0:43You think back to the legends.
-
0:43 - 0:47In the stories, the ruler of the city
saved his people -
0:47 - 0:51by feeding the creatures
a ransom of pearls. -
0:51 - 0:55The pearls would be split equally
between the leviathans lords. -
0:55 - 1:01Each leviathan would then divide its share
into 11 equal piles, keeping one, -
1:01 - 1:05and giving the other 10
to their kraken commanders. -
1:05 - 1:10Each kraken would then divide its share
into 13 equal piles, -
1:10 - 1:15keeping one, and distributing the other
twelve to their mermite minions. -
1:15 - 1:20If any one of these divisions left
an unequal pile or leftover pearl, -
1:20 - 1:24the monsters would pull everyone
to the bottom of the sea. -
1:24 - 1:28Such was the fate
of your fabled sister city. -
1:28 - 1:33You rush to the ancient treasure room
and find five chests, -
1:33 - 1:36each containing a precisely counted number
of pearls -
1:36 - 1:40prepared by your ancestors
for exactly this purpose. -
1:40 - 1:45Each of the chests bears a number
telling how many pearls it contains. -
1:45 - 1:50Unfortunately, the symbols they used
to write digits 1,000 years ago -
1:50 - 1:51have changed with time,
-
1:51 - 1:54and you don’t know how
to read the ancient numbers. -
1:54 - 2:00With hundreds of thousands of pearls
in each chest, there’s no time to recount. -
2:00 - 2:03One of these chests will save your city
-
2:03 - 2:06and the rest will lead
to its certain doom. -
2:06 - 2:08Which do you choose?
-
2:08 - 2:10Pause the video to figure it out yourself.
-
2:10 - 2:10Answer in 3
-
2:10 - 2:13Answer in 2
-
2:13 - 2:15Answer in 1
-
2:15 - 2:20There isn’t enough information to decode
the ancient Atlantartican numeral system. -
2:20 - 2:23But all hope is not lost,
-
2:23 - 2:27because there’s another piece
of information those symbols contain: -
2:27 - 2:28patterns.
-
2:28 - 2:31If we can find a matching pattern
in arabic numerals, -
2:31 - 2:34we can still pick the right chest.
-
2:34 - 2:36Let’s take stock of what we know.
-
2:36 - 2:39A quantity of pearls that can appease
the sea monsters -
2:39 - 2:44must be divisible by 7, 11, and 13.
-
2:44 - 2:46Rather than trying out numbers
at random, -
2:46 - 2:48let’s examine ones that have this property
-
2:48 - 2:51and see if there are any
patterns that unite them. -
2:51 - 2:55Being divisible by 7, 11, and 13
-
2:55 - 3:00means that our number must
be a multiple of 7, 11, and 13. -
3:00 - 3:04Those three numbers are all prime,
so multiplying them together -
3:04 - 3:09will give us their least
common multiple: 1001. -
3:09 - 3:10That’s a useful starting place
-
3:10 - 3:14because we now know that any viable
offering to the sea monsters -
3:14 - 3:17must be a multiple of 1001.
-
3:17 - 3:20Let’s try multiplying it by a three digit
number, -
3:20 - 3:22just to get a feel for what we might get.
-
3:22 - 3:30If we try 861 times 1001, we get 861,861,
-
3:30 - 3:34and we see something similar
with other examples. -
3:34 - 3:35It’s a peculiar pattern.
-
3:35 - 3:40Why would multiplying a three-digit
number by 1001 -
3:40 - 3:42end up giving you two copies
of that number, -
3:42 - 3:44written one after the other?
-
3:44 - 3:48Breaking down the multiplication
problem can give us the answer. -
3:48 - 3:541001 times any number x is equal
to 1000x + x. -
3:54 - 4:03For example, 725 times 1000 is 725,000,
and 725 x 1 is 725. -
4:03 - 4:13So 725 x 1001 will be the sum of
those two numbers: 725,725. -
4:13 - 4:16And there’s nothing special about 725.
-
4:16 - 4:18Pick any three-digit number,
-
4:18 - 4:23and your final product will have
that many thousands, plus one more. -
4:23 - 4:26Even though you don’t know how
to read the numbers on the chests, -
4:26 - 4:32you can read which pattern of digits
represents a number divisible by 1001. -
4:32 - 4:38As with many problems, trying concrete
examples can give you an intuition -
4:38 - 4:42for behavior that may at first look
abstract and mysterious. -
4:42 - 4:47The monsters accept your ransom
and swim back down to the depths -
4:47 - 4:48for another thousand years.
-
4:48 - 4:50With the proper planning,
-
4:50 - 4:54that should give you plenty of time
to prepare for their inevitable return.
- Title:
- Can you solve the sea monster riddle? - Dan Finkel
- Speaker:
- Dan Finkel
- Description:
-
View full lesson: https://ed.ted.com/lessons/can-you-solve-the-sea-monster-riddle-dan-finkel
According to legend, once every thousand years a host of sea monsters emerges from the depths to demand tribute from the floating city of Atlantartica. As the ruler of the city, you'd always dismissed the stories... until today, when they rose out of the roiling waters, surrounded your city and demanded a ransom of pearls. Can you figure out which chest of pearls is the ransom? Dan Finkel shows how. \
Lesson by Dan Finkel, directed by Artrake Studio.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 04:55
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Tara Ahmadinejad edited English subtitles for Can you solve the sea monster riddle? | ||
Tara Ahmadinejad edited English subtitles for Can you solve the sea monster riddle? |