What is the largest number that can be made with 2 digits?

This trick involves a circus story and a bit of math! First view the presentation of the trick and get the story down.

This one is a favorite of mine.  Two spectators each hold out any number of fingers on one of their hands.  (E.g. one might put out 3 fingers and the other, 2.)  A third spectator tells the magician, who is looking the other way, the total (in this example, 5).  The magician immediately announces that…