I'll quote Mike since the thread isn't visible to everyone.
Nah, you're not nuts. It's just a mathematical trick.
The trick can be explained algebraically if you know that you can expand any decimal number using powers of ten, like this:
Say you have the number 7,463.
You can write it in expanded powers of ten form this way:
7(10^3) + 4(10^2) + 6(10^1) + 3(10^0)
Since:
10^3 = 1000
10^2 = 100
10^1 = 10
and,
10^0 = 1
When you multiply it out you get:
7000 + 400 + 60 + 3
Which, when added, is 7463.
So…
The site asks you to pick any two digit number.
If you use a as the first digit (tens place), and b as the second digit (one’s place), with a and b each being a number between 1 and 9, you can write your two digit number in generic, expanded form:
a(10^1) + b(10^0)
(So if your number was 34, then a=3 and b=4, so 3(10^1) + 4(10^0) = 3(10) + 4(1) = 34)
Now the site asks you to add the digits of the number together, and then subtract this total from the original number. Mathematically you can represent this like:
a(10^1) + b(10^0) – (a + b) =
Which means:
(Original number): a(10^1) + b(10^0)
(minus): –
(the two digits of the number added together): (a + b)
Now work it algebraically…
Clear the second set of parentheses and you get:
a(10^1)+b(10^0) – a – b =
Simplify the powers of ten parts:
a(10) + b(1) – a – b =
10a + b – a – b
Combine like terms and the b’s cancel out leaving just:
9a
Since the first digit of your original number was a, and the original number had to be a two digit number (any number from 10 to 99), a has to be between 1 and 9. So no matter what number you pick in the beginning, the number that you get in the end will always be a multiple of 9 (and what multiple of 9 depends only on the value of the tens place digit (the a) of your original two digit number):
(9*1) = 9
(9*2) = 18
(9*3) = 27
(9*4) = 36
(9*5) = 45
(9*6) = 54
(9*7) = 63
(9*Cool = 72
(9*9) = 81
Look at the symbol for each multiple of nine on the last page:
