If you run every acceptable number combination (i.e. 10-99) 
through the gopher’s formula, you end up with only a few possible outcomes.
 
Specifically, you always end up with a number divisible by 9 (i.e. 0, 9, 18, 27,… 
all the way up to 81). If you look at the gopher’s chart, 
you’ll notice that the same image appears on each of those numbers. 

The image is randomly generated each time to give the illusion of mind-reading. 

Likewise, the other numbers that can never be generated from the gopher’s 
formula are given random images to throw you off of the pattern. 

Like most “magic,” this trick is simply a matter of misdirection.