Magic Gopher

Piece of cake.

When you subtract the sum of the digits from any number, the difference will always be a multiple of 9 (0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 99, 108, 117, etc.).

Then if you look at the chart, all the multiples of 9 have the same symbol. So their guess will always be correct, regardless of which number you ended (or started) with.