Someone in my office asked how this worked. Below is my answer.
This works because any number minus an anagram of it is guaranteed to be a multiple of 9 (4321-3214=1107=123*9). So, if you tell me all but one digit of the result (e.g. 107), I can deduce the missing one by adding up the digits mod 9 and subtracting from 9 (9-8=1). Ive always loved number theory.