Here is a nice trick with numbers. Ask a friend to pick a two digit number, add the digits together, and then subtract the sum of the two digits from the original number. For example, if your friend picked 85 as the original number, the sum of 8 and 5 is 13, and 85 minus 13 is 72. Now ask your friend if the number he or she is left with is a single digit. If the answer is yes, the single digit is 9. If the number has two digits, have your friend add them together, the answer will be 9. (In our example, 7 plus 2, is nine).
Before you test this out on a friend, try a few examples yourself. Let's do another one here. Say we choose 32 as the initial random two digit number. 3 plus 2 is 5, and 32 minus 5 is 27. Adding together 2 and 7 we get 9.
Here's the sequence which will baffle your friends:
Think of a random two digit number, but don't tell me what that number is.
Add the two digits together and subtract this number from your original number.
Is the resulting number a two digit number?
(If not) the number is ...let me think...it is getting clearer, it is 9.
(If yes) add those two digits together; the number is ...let me think...it is getting clearer, it is 9.
As you have read this, you will be predisposed to believe that 9 will figure every time in the answer, so this will not seem that astonishing. However, your friend who has not read this will be impressed by your powers of deduction. Just don't repeat the trick or your friend will notice the invariant pattern of nines in your predictions.
Of course, if you are creative you can take this basic concept to a more baffling level. How about if you show your victim, I mean friend, a list of numbers, each with its own symbol, and associate with the numbers that sum to 9 a special symbol. Then you can magically discern that special symbol no matter what your friend originally selected as his or her random number.
Here is a neatly presented version of this concept encoded as a flash game which plays in a browser window: http://www.milaadesign.com/wizardy.html. (I am not associated with this site in any way, other than being impressed by their game). Take a look but don't tell your friend the underlying mathematical secret. See if they can deduce it for themselves.
...and why not determine how this works?!