According to an ancient legend, every thousand years, a group of sea monsters rises from the ocean to demand a tribute from the floating city of Atlantartica. As the city’s ruler, you always thought these were just stories—until today. Seven massive sea creatures, known as Leviathan Lords, have surrounded your city. Each Leviathan commands ten giant krakens, and each kraken is followed by twelve smaller creatures called mermites. Your city’s army is no match for them.
In the legends, the city’s ruler saved everyone by offering the sea monsters a ransom of pearls. The pearls had to be divided equally among the Leviathan Lords. Each Leviathan would then split its share into eleven equal parts, keeping one and giving the rest to their krakens. Each kraken would then divide its share into thirteen equal parts, keeping one and giving the rest to their mermites. If any division left an uneven pile or leftover pearl, the monsters would drag everyone to the ocean floor. This was the fate of a sister city long ago.
You rush to the ancient treasure room and find five chests filled with pearls, each chest marked with a number. Unfortunately, the numbers are written in an ancient script you can’t read. With no time to count the pearls, you must choose the right chest to save your city. But how?
There’s not enough information to decode the ancient numbers, but there’s still hope. The key is in the patterns. If we can find a pattern that matches our modern numbers, we can choose the right chest.
Here’s what we know: the pearls must be divisible by 7, 11, and 13. Instead of guessing, let’s find numbers that meet this requirement. A number divisible by 7, 11, and 13 is a multiple of their least common multiple, which is 1001. So, any number that can appease the sea monsters must be a multiple of 1001.
Let’s try multiplying 1001 by a three-digit number to see what happens. For example, if we multiply 861 by 1001, we get 861,861. This pattern repeats with other numbers too. But why does multiplying by 1001 create this pattern?
Here’s the trick: multiplying any number by 1001 is like multiplying it by 1000 and then adding the number again. For instance, 725 times 1000 is 725,000, and 725 times 1 is 725. So, 725 times 1001 equals 725,725. This works for any three-digit number, creating a pattern where the number repeats itself.
Even if you can’t read the numbers on the chests, you can spot the pattern of digits that shows a number is divisible by 1001. By trying out examples, you can understand how this works, even if it seems mysterious at first.
Thanks to your clever thinking, the sea monsters accept your ransom and return to the depths for another thousand years. With this knowledge, you’ll have plenty of time to prepare for their next visit.
Try multiplying different three-digit numbers by 1001. Write down the results and observe the patterns. Can you see how the original number repeats itself? Discuss why this happens with your classmates.
Design a set of symbols to represent numbers 1 to 10. Use these symbols to write a message or a number on a piece of paper. Exchange with a partner and try to decode each other’s script. This will help you understand the challenge of decoding ancient numbers.
Work in groups to find numbers that are divisible by 7, 11, and 13. Use a calculator to check your answers. Discuss why these numbers are important in the context of the sea monster riddle.
In groups, act out the story of the sea monsters and the ruler of Atlantartica. Assign roles such as the ruler, Leviathan Lords, krakens, and mermites. Use props to represent pearls and demonstrate how they must be divided equally.
Create a game where you and your classmates identify patterns in numbers. Use cards with different numbers and challenge each other to find which ones are divisible by 1001. This will reinforce your understanding of the pattern recognition needed to solve the riddle.
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 had always dismissed the stories…until today, when seven Leviathan Lords rose out of the roiling waters and surrounded your city. Each commands ten giant kraken, and each kraken is accompanied by twelve mermites. Your city’s 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 Leviathan Lords. Each Leviathan would then divide its share into eleven equal piles, keeping one and giving the other ten to their kraken commanders. Each kraken would then divide its share into thirteen 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.
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 times 1 is 725. So 725 times 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 recognize 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.
Divisible – A number is divisible by another if you can divide them without a remainder. – Example sentence: The number 24 is divisible by 6 because 24 divided by 6 equals 4 with no remainder.
Multiple – A multiple of a number is the product of that number and an integer. – Example sentence: The number 20 is a multiple of 5 because 5 times 4 equals 20.
Pattern – A sequence or arrangement that follows a particular rule or formula. – Example sentence: The pattern in the sequence 2, 4, 6, 8 is that each number increases by 2.
Number – A mathematical object used to count, measure, and label. – Example sentence: The number 7 is a prime number because it has no divisors other than 1 and itself.
Ancient – Relating to a time long past, often used to describe old mathematical concepts or discoveries. – Example sentence: The ancient Greeks were among the first to study geometry systematically.
