How does this work?

Originally posted by masscat
http://trunks.secondfoundation.org/files/psychic.swf

Somebody explain how this works, please.

The link takes you to a "mind reading crystal ball" and a list of the numbers 0-99 with a concurrent list of symbols. Then it asks you to pick a two-digit number, add the digits together, and subtract that from the original number. After you do this, and you click on the crystal ball, the symbol associated with the result appears.

I think this has been answered before, but basically this is how it works:

Let's represent the two digit number as AB. The magnitude of this number is given as 10A + B. The magnitude of the sum of the digits is A + B. If we subtract the sum from the original number, we get:

10A + B - (A + B) = 9A

So the result will always be a multiple of 9. Since you can pick any two-digit number from 11-99, A can be any number from 1-9, and the result will be a multiple of 9 from 9 to 81. If you notice on the list, 99 and 90 have the wrong symbol (to throw us of the scent of multiples of 9, I suppose). However, all other multiples of 9 have the correct symbol, so when you click on the crystal ball it seems like the web just read your mind. But it's just some simple math trickery.