this is a solution to the original ghostwhisperer puzzle.
alternatives are available under CBS, respectively Messe Ideen (a german variation).
i first found the puzzle through the Milaa-Design Wizardy-page,
which fortunately is available again (as it has a nice implementation too).

solution:

guessed two-digit number ::== z

z can be represented as:

z = 10x + y

with:

decade digit ::== x
counter digit ::== y

the puzzle rule says to subtract the sum of the digits from
the guessed number:

z' = z - q

with the definition of the sum of the digits as:

q = x + y

from this follows:

z' = z - q
   = z - ( x + y )
   = ( 10x + y ) - ( x + y )
   = 10x + y - x - y
   = 9x

which tells us:

a.) the derived number z' is completely independent of the low
    value 'counter' digit (not important)
b.) the derived number z' is always evenly dividable by 9,
    independent of the 'decade' digit (essential for the trick)

trick:
1.) create a table which has the same symbol placed on each
    position evenly dividable by 9 and on position 0
2.) fill the rest of the table with randomly selected symbols
3.) display the table in such a way, which makes it difficult
    to spot the regularity (so, no 10x10 matrix ...
4.) independent of the number the person is thinking of, the
    derived number will certainly be on a position evenly
    divisible by 9
5.) don't provide too much time for the viewer to spot the
    regularity pattern in the table
6.) show the viewer the selected symbol which stands on the
    positions divisible by 9

q.e.d.

;-)

(and yes, i sat down myself for this solution)

note: thanks to Jani Giannoudis for the hint with position 0
(for guessed numbers below 10)!