Magic Number Cards
A step-by-step guide for every Magic Number Cards kit.
How to use this guide
Six cards, one secret number, and a trick that looks like mind reading. Learn how to play, how the magician reads the cards, and why it always works.
The math behind the magic
Why does this work?
The trick works because of binary numbers. Binary uses only two digits, 0 and 1, instead of the ten digits we usually count with. Computers use binary because their electronic circuits understand two states, on and off, which stand for 1 and 0.
How binary works
In binary, each place is worth double the one to its right: 1, 2, 4, 8, 16, 32 and so on. These are the powers of 2, and they are the numbers in the corners of the six cards.
- 32
- 16
- 8
- 4
- 2
- 1
Every number from 1 to 63 can be made by adding some of these corner numbers, and there is only one way to do it.
Why the trick works
Say the secret number is 19. 19 = 16 + 2 + 1, so it is on the cards with 16, 2 and 1 in the corner, and not on the 32, 8 or 4 cards.
| Corner number | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|
| Is 19 on the card? | No | Yes | No | No | Yes | Yes |
| Binary digit | 0 | 1 | 0 | 0 | 1 | 1 |
Write 1 for every Yes and 0 for every No, and you get 010011: 19 in binary.
Each card holds exactly the numbers that have a 1 in its place when they are written in binary. So when the player says Yes to a card, they are telling you a 1, and No is a 0. Add up the corner numbers of the Yes cards and you have their number.
Why it never goes wrong
Each corner number is bigger than all the smaller ones added together: 1 + 2 + 4 + 8 + 16 is only 31, less than 32. So two different numbers can never land on the same set of cards.
