Alice: Pick a 5-digit number.
Bob: Got it.
Alice: Now reverse it and subtract the lesser from the greater.
Alice: Now pick one of the five digits of the result and circle it (but don't choose a zero). Tell me the other digits, in some random order.
Bob: Sure; they are 1, 1, 0, and 8.
Alice: Then the circled digit is....
Alice does indeed correctly give the circled digit. How did she do it?