16. Rearrange the digits of any three-digit number to form the largest and smallest numbers possible, and their difference will form another three-digit number (allowing the hundreds digit to be $0$). Repeat this process. What is the number obtained after 2003 repetitions? Prove your conclusion.
16. (1) If all three digits are the same, the resulting number is 0.
(2) If the three digits are not all the same, the resulting number is 495.
(1) This is obviously true.
Below is the proof of (2).
If the three digits are not all the same, let's assume this three-digit number is $\overline{a b c}$, where $a \geqslant b \geqslant c$ and $a \geqslant c+1$.
$$
\begin{array}{l}
\overline{a b c}-\overline{c b a}=99(a-c) \\
=100(a-c-1)+10 \times 9+(10+c-a) .
\end{array}
$$

Therefore, the resulting three-digit number must have one 9, and the sum of the other two digits is 9, with a total of 5 possibilities: 990, 981, 972, 963, 954.

It is easy to verify that the above 5 numbers will result in 495 after no more than 10 operations.