Is it magic... or math?
A magician asks you to think of a number, do a few steps, and then... reveals your secret! How? Great "mind-reading" tricks work by collecting just enough information and then using the unstoppable logic of math to figure out the rest.
In this lesson you'll learn 4 tricks. For each one, you'll see the trick, try it yourself, then uncover why it works.
🔒 Earn all 4 badges to unlock the Magician's Exam.
Puzzles inspired by "The Secret Math Behind Mind-Reading Magic Tricks" by Pradeep Mutalik (Quanta Magazine, 2022), retold for kids.
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The 1,001 Trick
Multiply by 7, then 11, then 13... and watch what happens!
Try it!
🔍 Why does it work?
Here's the secret: 7 × 11 × 13 = 1,001. So multiplying by 7, then 11, then 13 is exactly the same as multiplying by 1,001 all at once!
And multiplying by 1,001 is the same as multiplying by 1,000 (which adds three zeros) and then adding the number one more time:
🧩 The trick only works because the number has exactly 3 digits. That's the secret information! For a 4-digit number, you'd need to multiply by 10,001 instead (which is 73 × 137).
🔮 Now YOU be the magician!
A friend did the trick and shows you their final answer. Quickly reveal their secret number! Get 5 right.
Check your understanding
The Sum & Product Detectives
Two detectives. Two clues. One conversation.
A magician picks two secret numbers from 2 to 9. (They might even be the same number!) She whispers the SUM to Sally and the PRODUCT to Pete. Both detectives know all these rules. Then they have this conversation:
It seems like they've said nothing useful... but each sentence is a clue! Can you figure out the two numbers?
Each box shows S = sum and P = product for a pair. Tap any box to see all the boxes with the same sum (🟨) and same product (🟦).
The "Impossible" Puzzle
The same game with MUCH bigger numbers, and an unsolved mystery!
Now the two secret numbers can be anything from 2 to 70. Again, Sally knows the sum and Pete knows the product. This time the conversation goes:
There are way too many pairs to check with a table. So mathematicians use a shortcut... and it involves one of the most famous unsolved questions in math!
🔢 Goldbach's Conjecture
In 1742, a mathematician named Christian Goldbach guessed that every even number bigger than 2 can be made by adding two prime numbers. (A prime number can only be divided evenly by 1 and itself, like 2, 3, 5, 7, 11, 13...)
Computers have checked this for every even number up to 4,000,000,000,000,000,000... and it always works! But nobody has ever PROVED it works for every even number. It's still a mystery!
🗝️ How Sally knew
Sally said "I knew you couldn't figure it out." How could she be so sure? If her sum were even, it could be two primes added together (thanks, Goldbach!). And if Pete's product came from two primes, he'd know the numbers instantly, because a product of two primes can only be split one way. Sally was certain Pete couldn't know, so her sum must be odd and not a prime plus 2.
Using clever rules like this, mathematicians narrow it down to just a few sums, check those carefully, and find the one answer: 4 and 13! (Sum 17, product 52.)
Brain buster check
The Red Card Mind Reader
Name 5 people's cards just by knowing who has RED ones!
🎭 Watch the trick
The magician uses a deck of 32 cards. Anyone can cut the deck as many times as they want. Then 5 volunteers each take the next card from the top. The magician says, "The colors are fuzzy today... will everyone with a RED card please stand up?" And then she names ALL FIVE cards!
🔍 The secret: a very special order
The deck isn't really shuffled! The cards are arranged in a clever order called a de Bruijn sequence (say "duh BROIN"). Look at this tiny version with just 8 cards, using 0 for black and 1 for red:
If you read any 3 cards in a row (wrapping around from the end back to the start), you get a different pattern every time. All 8 possible patterns appear exactly once! Tap a starting card to see:
🔑 The 32-card deck works the same way with 5 cards in a row. There are 2 × 2 × 2 × 2 × 2 = 32 possible red/black patterns, and each one appears exactly once in the deck. Cutting the deck doesn't change the order around the circle, so once the magician knows which people have red, she knows exactly where in the deck they are!
🔮 Now YOU be the magician!
Here's the magician's secret deck in order (it goes around in a circle). The volunteers' red/black pattern is shown below. Tap the card in the deck where the 5 volunteers' cards START. Solve 3 tricks!
Check your understanding
The Magician's Exam
Prove you know the secrets!
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