How the hell does this work?

I’ve seen these kinds of things where you guess a number and subtract the sum of the digits and that allows you to guess the original number, but this flash app never even gets any feedback. Check it out:

Duh, never mind. I figured it out.

But, I suppose this works as a MPSIMS thread.

The formula forces the user to pick only a subset of the choices. Every one of those possible choices in a particular round have the same symbol. So matter what number you start with, you are forced to go to same symbol.

All the valid answers have the same symbol. Consider any two digit number where the digits are a and b; you have:

original number: 10a + b
then: 10a + b - (a + b) = 9a

where a can be 0…9, so only multiples of 9 are valid answers, and as you can see from the chart they all have the same symbol.