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According to legend, once
every thousand years
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a host of sea monsters emerges from the
depths to demand tribute
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from the floating city of Atlantartica.
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As the ruler of the city, you’d always
dismissed the stories…
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until today, when 7 Leviathan Lords
rose out of the roiling waters
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and surrounded your city.
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Each commands 10 giant kraken, and
each kraken is accompanied by 12 mermites.
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Your city’s puny army is
hopelessly outmatched.
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You think back to the legends.
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In the stories, the ruler of the city
saved his people
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by feeding the creatures
a ransom of pearls.
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The pearls would be split equally between
the leviathans lords.
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Each leviathan would then divide its share
into 11 equal piles, keeping one,
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and giving the other 10 to their kraken
commanders.
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Each kraken would then divide its share
into 13 equal piles,
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keeping one, and distributing the other
twelve to their mermite minions.
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If any one of these divisions left an
unequal pile or leftover pearl,
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the monsters would pull everyone to the
bottom of the sea.
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Such was the fate of your
fabled sister city.
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You rush to the ancient treasure room and
find five chests,
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each containing a precisely counted number
of pearls
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prepared by your ancestors
for exactly this purpose.
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Each of the chests bears a number
telling how many pearls it contains.
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Unfortunately, the symbols they used
to write digits 1000 years ago
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have changed with time,
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and you don’t know how to
read the ancient numbers.
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With hundreds of thousands of pearls
in each chest, there’s no time to recount.
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One of these chests will save your city
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and the rest will lead
to its certain doom.
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Which do you choose?
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Pause the video to figure it out yourself.
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Answer in 3
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Answer in 2
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Answer in 1
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There isn’t enough information to decode
the ancient Atlantartican numeral system.
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But all hope is not lost,
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because there’s another piece of
information those symbols contain:
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patterns.
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If we can find a matching pattern
in arabic numerals,
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we can still pick the right chest.
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Let’s take stock of what we know.
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A quantity of pearls that can appease
the sea monsters
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must be divisible by 7, 11 and 13.
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Rather than trying out numbers
at random,
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let’s examine ones that have this property
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and see if there are any
patterns that unite them.
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Being divisible by 7, 11 and 13
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means that our number must
be a multiple of 7, 11, and 13.
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Those three numbers are all prime,
so multiplying them together
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will give us their least
common multiple: 1001.
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That’s a useful starting place
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because we now know that any viable
offering to the sea monsters
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must be a multiple of 1001.
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Let’s try multiplying it by a three digit
number,
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just to get a feel for what happens.
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If we try 861 times 1001, we get 861,861,
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and we see something similar
with other examples.
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It’s a peculiar pattern.
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Why would multiplying a three-digit
number by 1001
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end up giving you two copies of
the that number,
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written one after the other?
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Breaking down the multiplication
problem can give us the answer.
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1001 times any number x is equal to
1000x + x.
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For example, 725 times 1000 is 725,000,
and 725 x 1 is 725.
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So 725 x 1001 will be the sum of
those two numbers: 725,725.
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And there’s nothing special about 725.
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Pick any three-digit number,
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and your final product will have
that many thousands, plus one more.
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Even though you don’t know how to
read the numbers on the chests,
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you can read which pattern of digits
represents a number divisible by 1001.
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As with many problems, trying concrete
examples
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can give you an intuition for behavior
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that may at first look
abstract and mysterious.
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The monsters accept your ransom
and swim back down to the depths
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for another thousand years.
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With the proper planning,
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that should give you plenty of time
to prepare for their inevitable return.