The Nine Trick: How to Read Minds with a Calculator

I promise there is nothing tricky about this trick. If you can add two and two, you can amaze people the same way you were amazed. You don’t even need to know how to multiply three times seven. Adding is all you need.

Here’s what happened when we chatted at the conference:

You made a number using the red and blue blocks. I added another block.

You put that number in your calculator. You multiplied it by a random number — the last two digits of your phone number, your friend’s birthday, whatever secret number you chose.

You read me the result, leaving out one of the digits.

I told you the missing digit. Extraordinary! Amazing! Wonderful!

Here’s how I did it. Like any magic trick, it’s obvious once you know the secret. But first, a few warm-up questions. Go ahead and use the calculator on your phone — I promised you don’t even need to know how to multiply.

The Strange Behavior of Nine

What is 3 × 9? Three times nine is 27. How much is two plus seven? Nine.

What is 7 × 9? Seven times nine is 63. How much is six plus three? Also nine.

What is 12 × 9? Twelve times nine is 108. One plus zero plus eight? Nine again.

No matter what number you start with, when you multiply it by nine, the digits of the answer add up to a multiple of nine — and if you keep summing those digits, you eventually land back on nine itself.

It even keeps working when the numbers get silly:

What is 1,357 × 9? 1,357 times nine is 12,213. One plus two plus two plus one plus three is nine.

What is 9,788,917 × 9? That’s 88,100,253. Eight + eight + one + zero + zero + two + five + three = 27. And two plus seven is — say it with me — nine.

This isn’t a coincidence. It’s a quiet rule of arithmetic: the digits of any multiple of nine always add up to a multiple of nine. Mathematicians call it casting out nines, and it has been hiding in plain sight inside every calculator since the abacus.

The Secret of the Extra Block

Remember when I said “I added another block”? That was the whole trick.

When you laid out your number with the red and blue blocks, I quietly added one more block — the exact one needed to make the sum of your digits a multiple of nine. From that moment on, no matter what you multiplied your number by, the answer was guaranteed to be a multiple of nine. And every multiple of nine has digits that add up to a multiple of nine.

So when you read me your answer with one digit missing, all I had to do was add up the digits you did tell me, and figure out what was needed to round the sum up to the next multiple of nine. That was your missing digit.

A Worked Example

Let’s do the trick from the beginning. This time, you’re in control.

You: Pick a number. Any number at all!

Your friend: Okay. I pick 736.

You: Great number! Plug 7,362 into the calculator on your phone.

(You added a 2, because 7 + 3 + 6 = 16, and 16 + 2 = 18, which is a multiple of nine. Your friend has no idea.)

You: Now multiply 7,362 by any number you like — but don’t tell me what it is.

Your friend: Okay. (They multiply by 13. You don’t know that, and you don’t care.)

You: Read me the result, but leave out one of the digits.

Your friend: Nine, five, seven, zero.

You think to yourself: 9 + 5 + 7 + 0 = 21. Two plus one is three. What do I need to add to three to get nine? Six.

You: You left out a six.

Your friend: That’s incredible! How did you know?

A Quick Recipe

Want to try it tonight at dinner? Here’s the cheat sheet:

Ask your friend to pick a number.
Secretly tack on a digit so the digits add up to a multiple of nine.
Have them multiply by anything they like.
Have them read the answer aloud, skipping one digit.
Add up the digits they read. Whatever you need to reach the next multiple of nine — that’s the digit they hid.

A small word of warning: if their digits already add up to a multiple of nine, the missing digit is either 0 or 9. Smile mysteriously and ask, “Was the missing digit a zero, or a nine?” They’ll be even more impressed that you narrowed it down.

Why Mathematicians Love This

The nine trick feels like sleight of hand, but it’s really a window into one of the deepest ideas in number theory: modular arithmetic. When you “cast out nines,” you’re working with the remainder a number leaves when divided by nine — and that remainder behaves beautifully under addition and multiplication.

The same idea, scaled up, is how computers check that data hasn’t been corrupted, how banks validate credit card numbers, and how cryptography keeps your messages safe. A trick you can do with a calculator at a kitchen table is the same family of math that keeps the internet running.

Math, it turns out, was magic all along. We just stopped being surprised.

A mathe-magician never reveals their secrets — except, apparently, in articles like this one.