http://break.com/index/pick_a_number.html

Regards,

Herkdrvr

Greetings,
The puzzle works with some basic math and a little bit of trickery. 
Any number you would have picked after going through that process
would have ended up a multiple of 9.  For example the first time I did
it I picked 42 (the answer to everything of course) and ended up with
36.  The second try I made I chose 25 and ended up with 18.

The trickery is the board that they use.  The board has every number
on it however in reality very few of those numbers will ever have to
be used, only the multiples of 9.  All the multiples of 9 have the
same symbol.  That way it doesn't matter which one end up with, all
the bases are covered.

The way they get you is by switching the symbols around after every
round.  So the first time you do it the multiples of 9 will be wavy
lines.  The second time they'll be dots, etc.  The idea is that you
won't spend the time going through and noticing that they all have the
same symbol.  So when you go back and do it the second and third time
you are convinced its picking your number because you get a different
number every time.

Best,
djbaker-ga

It doesn't work for me. It just keeps blinking the icon that I hover the mouse over.

It is a real old trick. No matter which number you pick when you do
the addition and so on you will always end up with an answer that is 9
or a multiple of 9. Look at the symbols on the final page and you will
see that the symbols for 9, 18, 27 and so on are the same. That is why
the symbol "guesses" your answer

As eiffel-ga has guessed, some similar animations do indeed detect a
mouse hovering over an area or a number when you find that number and
point at it with your mouse.