How do the mind reading stuff on the internet works really good?

Question

I went online on www.bored.com and I found this Mystical Ball thing. Let me tell you how this works: First, you how to pick any 2 numbers 1-99. The first number has to be bigger than the smaller than the other. Second,

Subtract the first number from the smaller. Third put the first number and the second together. Now you use the number and subtract, from the number you got when you were subtracting. Fourth, concentrate on the symbol. Sixth, click on the crystal ball. Example: 3 and 2, 3-2=1, then 32-1=31.

Answer 1

The only Mystical Ball thing I found on that site was:

Pick ONE (2-digit) number. Add the two digits together, and then subtract that from the original number. Find the symbol given for the new number.

This can be explained by:

Any 2 digit number can be represented as 10*a + b.

So 10*a + b - (a+b) = 9*a

Hence the answer will be a multiple of 9.

All multiples of 9 have the same symbol each time, so it will always choose the right symbol.

Answer 2

If I remember correctly, they change the symbols around.

Answer 3

They are invariably tricks. I found a good one, where you picked a card from four, concentrated on it, clicked on a random symbol, and saw three cards, and your was missing. Actually, all three were different from the previous four. In this case, I'd have to see the site, but maths ones rely on the fact you can work out all the answers. I.e. What's the symbol you mention? If the symbol corresponds to the answer you got, all possible answers are the same symbol (had one like that before too). The symbol would randomly change from time to time.

You can usually work it out by doing a few different possibilities at the same time.