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

100 thoughts on “Can you solve the sea monster riddle? – Dan Finkel

  1. Visit https://brilliant.org/TedEd/ to check out Brilliant’s 60+ courses in math, logic, science, and computer science. They feature storytelling, code-writing, interactive challenges, and plenty of puzzles for you to solve. And as an added bonus, the first 833 of you to use that link will receive 20% off the annual premium subscription fee.

  2. I am disappointed. This had nothing to do with sea monsters. This was a word math problem. We are not in school anymore.

  3. King: "No problem. I just need my calculator which is in my … Uh … airplane. Yeah, that's right. Wait for me here, I'll be right back."

  4. Some folks said they should remember how to read the 1,000 year old numbers. You still gotta do the math to know what is the base number that is a divisor of the number of pearls in the chests. Once you know that, the symbols are easy to work out. You don't know how many groups of monsters will show up next time, anyway.
    What is really tough, however, is planning how to communicate to people 1,000 years into the future. Sheese, we can't even agree on what the writers of the Constitution meant, and that was only about 200 years ago. Also look into the methods they are trying to devise to communicate to people in the far, far future that nuclear waste is buried in certain locations and that people should stay away, and read, "A Canticle for Leibowitz."

  5. Plot twist: The monsters aren't patient and attack the city of Atlantartica before you finish solving the math, thus making Atlantartica non existant. Atlanartica is too far away from land for it to be recorded, so it is lost from history.

  6. Ok. Here is my reasoning
    7x11x13=1001

    Since 1001 multiplied by any number have the same start and end. Ex. 1001×24= 24024. Then the Ill choose the one where the chest has the same symbols in the beginning and end which means the right chest is the one above the timer

    Edit: Oh my gosh. This is the first time I got a ted ed riddle right on the first try. Yay

  7. I would have solved this with ease if I was informed that the ancient numeric system was a decimal system. I was very confused as I was unaware if this was decimal or if it was binary or hexadecimal

  8. TED-Ed: Can you solve the riddle?

    Me: Well seeing how the symbols are in the same three symbol sequence, my ancestor must have meant that that chest is the one to be divided in equal parts, much like the serpents' culture.

    Ted-Ed: Actually, its math.

    Me:…

  9. Moral learnt…

    VISIT THE TREASURY AT LEAST ONCE A YEAR OR YOU ARE GOING TO GET KILLED BY SEA CRACKERS OR WHATEVER

  10. Idk if the math is done right though. The amount the biggest monster receives is different from the kraken because the kraken has to redistribute their earnings after the big one redistributed. Same with the kraken with the smallest monster. Correct me if I'm wrong, it's a hunch

  11. Because that chest follows the repeating pattern you are 100% sure it is a multiple of 1001. I think I get it. Now I need some rest and an aspirin.

  12. As soon as I had 7x11x13 = 1001, it was so easy to solve. Choose the chest with its first three digits being the same in order as the next three digits.

  13. I'm sorry, but before delving into the mathematical process, my first thought was take the unopened chest, because if your ancestors truly prepared for this, all the chests should hold the necessary amount of pearls. But since you, the ruler didn't believe in the myth, it's likely your treasurer didn't either. So all the opened chests will have an amount of missing pearls, because someone opened them and took them to do other useful stuff than feeding monsters. Only the unopened chest can save you. ?

  14. I solved this is by assigning each symbol with a letter. Then I replaced each letter with one of 3 shapes. Square, triangle, and circle. Square for the first number and ones alike. Triangle for the second number and ones alike. And Circle for the third. Finally, I replaced each shape with any number from 1-9 and divided each set by 7,11, and 13 ??

  15. Wait…if the city is floating (not anchored) can't they just float where it's inhabitable for monsters in the next thousand years?

  16. I was able to get the answer, however, I used a somewhat different method. I would like to know if my method just happened to work in this lone case, or would this also work in any case? And Warning! If you didn't solve it yet, and want to, don't read ahead!

    What I did was just randomly assign a number to each symbol, and then I would divide by 7, then by 11, then by 13. I tested each chest. Only one of the chests didn't have any remainders, so that was the answer, and I chose that chest with that pattern. Is that also an ok way to do it? Or does that seem like it works just in this one case?

  17. 1:55 how does the second chest have more than the first but less than the third? The first and third start with the same digit but the second does not. There’s no possible number that could fall between the first and third without also having the same starting digit. This means the numbering system from long ago was much more complicated and the selected chest might not be correct.

  18. Holy cow I actually got it right? I thought the same if you can't read the number symbol but it is a even divide the symbols would've to repeat itself.

  19. But if you aren't suppose to give mermaids three digit number of pearls? For example the should get only 3 pearls per mermaid, so than you are looking for 3003 chest, and this is not the one we have picked in the riddle.

  20. Answer:
    Dump the contents of the chests onto the floor and pick however many pearls you want.
    13x11x7=1001 pearls
    Each creature gets 1 pearl.

  21. At 3:00, you say that because 7, 11, and 13 are all prime, the answer must be a multiple of 1001. That's correct; however, since the piles must be subdivided, the primeness of the numbers doesn't matter. For instance, if it were 2 piles, divided into 5 piles, divided into 10 piles, the answer would have to be a multiple of 2*5*10=100, not just 2*5=10.

    Love this video series!

  22. "Can you solve the…"

    No. I can't. We've been through this. Tens of times. I Cannot. Stop asking.

    Still gonna watch the video though lol

  23. I would give them all 5 chests and while they spent a very long time doing all the math my measly army would paddle us to safty somplace not in the middle of an ocean full of extortionist lizard monsters. Beach my city on a real landmass and be forever remebered as the king who solved the problem for eternity

  24. These riddles are not meant to be solved – a key piece of information was given after the (pause to solve). Furthermore, they don’t give you the pattern until the end

  25. It would have been helpful to include that each chest has exactly 6 markings. I don’t assume that the animations are 100% accurate

  26. These riddles have been easy af. None hold a candle to the three gods riddle or even Einstein's riddle.

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