How to do the magic number nine trick
Learn the magic number nine trick: a spectator hides one digit of a secret calculation and you name it, using a simple rule about multiples of nine.
By The Online Magic Store
· 3 min read
In this story 8 sections
A spectator writes a number, scrambles its digits, subtracts the smaller number from the larger, and circles one digit of the answer. They read out the other digits and you name the circled one. It works because the answer is always a multiple of nine, and the digits of a multiple of nine always add up to a multiple of nine. You only need simple addition.
What does the audience see?
You turn your back while someone works with a pen and paper. They choose any number, mix up its digits, do one subtraction and secretly circle one digit of the result. They read the remaining digits to you in any order. You concentrate for a moment and name the digit they circled.
How do you do it?
- A secret number. Ask the spectator to write any four- or five-digit number, without letting you see it.
- Scramble it. Have them write the same digits in a different order underneath.
- Subtract. They subtract the smaller number from the larger one.
- Circle a digit. They circle any digit of the answer that isn’t a zero.
- Read out the rest. They call out the digits they didn’t circle, in any order.
- Add as they read. Add those digits in your head.
- Find the gap. Work out how far your total is from the next multiple of nine (9, 18, 27, 36 and so on). That difference is the circled digit.
Example: they write 5,281 and scramble it to 1,825. The difference is 3,456. They circle the 4 and read out 3, 5 and 6. Those add up to 14. The next multiple of nine is 18, and 18 minus 14 is 4.
If the digits they read out already add up to a multiple of nine, the circled digit is 9. That is why you ask them not to circle a zero: a zero would give the same result.
Why does it work?
A number and the sum of its digits leave the same remainder when divided by nine. This is the rule known as “casting out nines”. Scrambling the digits doesn’t change their sum, so the original number and the scrambled number leave the same remainder. When you subtract one from the other, the remainders cancel, and the difference is a multiple of nine.
The digits of any multiple of nine add up to a multiple of nine. So when one digit is hidden, the visible digits fall short of the next multiple of nine by exactly the hidden digit.
How do you make it feel like mind reading?
- Stay far away. Turn your back or leave the room for the writing. The less you seem to be involved, the stronger the ending.
- Let them use a calculator. A phone calculator makes the subtraction fast and removes mistakes.
- Don’t rush. Ask them to picture the circled digit, and reveal it slowly, perhaps as “something round… no, a 6.”
- Repeat with someone else. Because every number is different, it doesn’t look like the same trick twice.
- Build a set. Follow it with the 1089 number trick or the age cards for a short, prop-free mind-reading routine.
What are the common mistakes?
- Subtraction errors. One slip by the spectator and the method fails. Offer a calculator, or ask them to check their subtraction.
- Circling a zero. Always say “any digit except zero.”
- Repeating the same digit. If they read out the same digit twice, add it twice. Every digit they read counts.
- Answering too fast. An instant answer looks like arithmetic. A pause looks like mind reading.
Where does the trick come from?
We haven’t found a reliable earliest source for this exact trick. W. W. Rouse Ball’s Mathematical Recreations and Essays (first published 1892) includes digit restorations among its miscellaneous problems.
What helps you take it further?
- Mathematical Recreations and Essays by W. W. Rouse Ball, free from our public-domain library. Arithmetical recreations, magic squares, digit restorations and more, and a favourite source for number-based effects.
- Philosophical Amusements by Henri Decremps, also free. Number tricks such as a number thought of and the magical century, set out step by step.
- How to Read Minds Kit by Peter Turner. Over 20 techniques with special props, including how to correctly predict the total of randomly generated numbers.
Find more in our easy mentalism collection.
Frequently asked questions
Why does the magic number nine trick work?
A number and any rearrangement of its digits leave the same remainder when divided by nine, so their difference is always a multiple of nine. The digits of a multiple of nine add up to a multiple of nine.
Why can’t the spectator circle a zero?
If they circle a zero, the remaining digits already add up to a multiple of nine, so your method would give 9 instead of 0. Asking for a non-zero digit removes the problem.
Does it work with numbers of any length?
Yes. The rule holds for any number of digits. Four or five digits is a good size because the sums stay easy.
Do I have to add the digits in my head?
Yes, but it is simple addition. You can add the digits as they are read out and keep reducing the total until you know the next multiple of nine.
