🔢 The Missing Digit

The Missing Digit for kids: the whole trick

A friend writes any big number, does a quick sum with it, and crosses out one digit of the answer while your back is turned. They add up the digits that are left and tell you only that total. You name the digit they crossed out. It's a level 2 conjurer trick for ages 9 to 13 (grades 4th–7th), takes 15 minutes to learn, and needs 3 things you already have. Flick, the shop's rabbit, reads every step aloud with a picture, so a child can follow it alone.

The secret

A number take away the sum of its own digits always leaves a number whose digits add up to a multiple of 9. So the digits left over always fall short of a multiple of 9 by exactly the digit that was crossed out.

What you need

• A sheet of paper
• A wooden pencil
• A calculator, or a calculator app (optional)

How to do it

1. Turn your back. Ask your friend to write any number with four or five digits on the paper.
2. Ask them to add up its digits, then take that total away from the big number.
3. They can use the calculator for the take-away if they like.
4. Ask them to cross out any one digit of the answer, except a 0.
5. They add up the digits that are left, and tell you only that total.
6. Add the digits of their total until you have one digit: 20 is 2 + 0, which is 2.
7. Take that from 9. 9 − 2 = 7, so they crossed out a 7. If you get 0, it was a 9.
8. Name the digit slowly, as if it is coming to you from far away.

Magic words to say

“Numbers leave footprints. You can cross one out, but the others still remember where it was standing.”

Pro tips

• Ask them to check the take-away twice, or to use a calculator. One slip in the sum and the trick can't work.
• Take your time over the answer. An instant answer looks like maths; a slow one looks like mind reading.
• Once you know it, let them pick a six-digit number. Bigger numbers make it look harder, and the secret is just the same.

If something goes wrong

If they say you're wrong, ask to see the sum: nearly always the take-away has a slip. Fix it together and do it again.

Safety notes

• Needs a helper.
• No fire, no flames and nothing sharp in a child's hand anywhere in the Magic Shop. Nothing ever goes in a mouth, a nose or an ear.

Why it works

A number and the sum of its digits always leave the same remainder when you divide by 9 (that is the old "casting out nines" check). So a number take away its digit sum is an exact multiple of 9, and the digits of a multiple of 9 always add up to a multiple of 9. Hide one digit, and the rest fall short of the next multiple of 9 by exactly that digit.

What kind of trick is this?

🔮 Prediction. You knew all along, or you read their mind. Almost every trick ever invented is one of eight kinds, and knowing which one you're watching is how magicians work out how a new trick is done.

The skill it teaches: Practise like a pro. Ready means ten times in a row without looking at your hands. Perform it and it counts towards the Mind Reader badge.

Questions about the missing digit

Are there magic tricks with a calculator or phone?

Yes. The Calculator Prediction fills a whole screen with your friend's favourite digit, nine times over, after a single multiplication. Any calculator works, including the app on a grown-up's phone.

How do magicians read minds?

They don't hear your thoughts. Mind-reading tricks use maths that always lands on the same answer, a secret peek, or a code agreed with a partner beforehand. Magicians who do mind tricks are called mentalists.

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