The Phone Number Trick
Eight steps on a calculator, and the display shows a phone number you were never told.
Run it on a number
Any number of any length. Nothing is sent anywhere.
The right-hand column is the calculator display. The line under each step is what that display actually is, written in terms of A, the front of the number, and B, the last four digits. Watch the two 250s and one of the two Bs disappear: when they have all gone, what is left is the number itself.
Nothing is hidden and nothing is guessed. Every step is one you say out loud, and the person doing the typing is the only one who ever sees a digit.
Also called the calculator phone number trick, the phone number math trick, or the mobile number trick. It is the same arithmetic in each case.
How to perform it
- Hand them a calculator and turn away, or just do not look. They are about to type their own number into it.
- Key in everything except the last four digits. For 555‑1234 that is 555. For a ten-digit number it is the first six. This is the step the usual instructions get wrong — see below.
- Multiply by 80.
- Add 1.
- Multiply by 250.
- Add the last four digits.
- Add the last four digits again.
- Subtract 250.
- Divide by 2. Ask them to look at the display and read it out.
The one thing that can go wrong
Splitting in the wrong place. The last four digits have to be exactly four — that is the only part of this the arithmetic actually cares about. Everything in front of them can be any length you like.
Does it work with 10 or 11 digits?
Yes, and nothing about the method changes. Every page that teaches this says to key in the first three digits, not the area code. That is not a rule. It is a description of one American phone number written before mobiles.
The arithmetic requires exactly one thing: that the number added at steps 6 and 7 is four digits. What sits in front of those four is multiplied by 10,000 and shifted out of the way, and it does not matter whether that is three digits or eight. So for a ten-digit number, key in the first six at step 2. For eleven, the first seven. Then carry on exactly as written.
You can check that rather than take it from me: put a ten- or eleven-digit number into the tool above and watch it come back.
Why does the phone number trick work?
Call the front of the number A and the last four digits B. The number itself is 10000A + B — that is what a written number means, four places for B and everything above it for A.
| Step | The display is | What it does |
|---|---|---|
| Key in the front | A | — |
| × 80 | 80A | — |
| + 1 | 80A + 1 | parks a 1 |
| × 250 | 20000A + 250 | the 1 becomes 250 |
| + B | 20000A + 250 + B | — |
| + B | 20000A + 250 + 2B | doubles B on purpose |
| − 250 | 20000A + 2B | the 250 cancels |
| ÷ 2 | 10000A + B | the doubling cancels |
The three moves, one at a time
The two multiplications are really one. 80 × 250 is 20,000, and halving it at the end gives 10,000 — which is what pushes A four places left and leaves exactly four empty places for B to sit in. The whole trick is a way of multiplying by 10,000 without ever saying so.
The add 1 is misdirection with a job. It looks like the strangest instruction on the list. All it does is survive the next multiplication as a 250, so that the − 250 later has something to cancel. Take out both and the trick still works — it just looks like arithmetic instead of a mystery.
B is added twice because it is about to be halved. The divide by 2 is there for the 20,000; it would halve B as well. Adding B twice first means halving hands it back whole.
What the numbers could have been
None of 80, 250 or 1 is special on its own. What matters is that the two multipliers come to 2 × 10,000, because the halving turns that into the 10,000 the trick needs. 8 × 2,500 works. 40 × 500 works. And if you use a different pair, the number you subtract changes with it — it is always the second multiplier, not always 250, which is the trap in trying to improvise this at a table.
Splitting off a different number of digits
Multipliers that come to 2 × 1,000 — 8 × 250, or 40 × 50 — split off the last three digits instead of four. 2 × 100,000 splits off five. The pattern is the same every time: the two multipliers multiply to twice the place value you want, and you subtract the second one.
Questions people ask
What is the phone number trick?
Somebody keys their own number into a calculator through eight steps you dictate, and the display shows their phone number back. You never see a digit of it. It is arithmetic, not mind reading.
Does the phone number trick work with 10 or 11 digits?
Yes, with no change at all. Key in everything except the last four at step 2 — six digits for a ten-digit number, seven for eleven — and carry on. The famous first three digits is a description of an old seven-digit American number, not a requirement.
Why do you add the last four digits twice?
Because of the divide by 2 at the end. That halving is there to turn 20,000 into 10,000, and it would halve the last four digits along with everything else. Adding them twice first means halving gives them back intact.
Why does the calculator not run out of room?
The largest the display gets is a little over 20,000 times the front of the number. For an eleven-digit number that is around two hundred billion, which is twelve digits — inside what a phone calculator shows exactly. Past about fifteen digits a calculator starts rounding, and a rounded step gives a wrong answer rather than a near one.
Can they use somebody else's number?
Yes. Nothing in the method knows or cares whose number it is, which is worth remembering if you are performing for somebody who would rather not type their own.
More
The forces on what people pick are the other half of this: arithmetic makes an answer certain, and a force makes a free choice predictable. How magicians read minds covers where both of them sit among the methods.
Harrison Alley
Hobbyist · Writes Sleightless
A hobbyist, not a professional. I write up the self-working end of card magic, because it is the door I would point a beginner at, and every trainer here is played through and checked before it ships.