Mind Reading

The volunteer calls out numbers of the cards containing their birthday. If the birthday falls on the 22nd the person will chose cards 4, 2 and 1. You add up the first number printed on each of those cards. In this example the numbers are 16 (card 4), 4 (card 2) and 2 (card 1) yielding 16 + 4 + 2 = 22, the birthday.

Note that the first number on cards 0 to 4 are in order: 1, 2, 4, 8 and 16, notice the doubling pattern. Such numbers are also called powers of two.
This technique works for any number between 1 and 31. If you want to perform this trick download the card and print it double sided.

Tip: if you want to remember the first number on each card note that
22= 2x2 = 4 (card 2)
23= 2x2x2 = 8 (card 3)
24= 2x2x2x2 = 16 (card 4).
Also: 21 = 2, and 20= 1 (for cards 1 and 0).

Why does it work?

When you select cards containing your birthday you are in fact writing the date in binary. Surprised?
The numbers we use in day-to-day life are written using ten digits from 0 to 9. This is called 'decimal' where each place in the number is worth units, tens, hundreds, thousands and so on, these numbers are powers of 10, 1, 10, 10², 10³, .... So for example 546 in decimal stands for 6 units, 4 tens and 5 hundreds.
In binary we use 0s and 1s only and each place in a number is worth units, twos, fours, eights and so on, doubling every time. For example the number 1011 in binary is (from right to left):
1 unit plus 1 two plus 0 fours plus 1 eight, so 1+2+8 =11.
The fundamental thing here is that any number between 1 and 31 has a unique sequence of 0s and 1s in binary. Since we are using five places to write a number, all possible strings of 0s and 1s from 00001 to 11111 give you 31 different possibilities (try!).

Binary is also called base two, decimal base ten. There are other number bases, a very famous one being base 16 or hexadecimal used to code colours for webpages, see
http://en.wikipedia.org/wiki/Hexadecimal
There is version of this game for numbers between 1 and 100 in
http://www.cut-the-knot.org/blue/Cards.shtml
For more "magic tricks" involving mathematics go to http://www.mathematicalmagic.com/ or http://www.cs4fn.org/magic/

Download the cards (PDF file)