For any four-digit number (digits can be the same), by changing the original order of its digits, one can always obtain the smallest four-digit number. If the difference between these two four-digit numbers is 999, find the number of such four-digit numbers.

Translate the above text into English, please keep the original text's line breaks and format, and output the translation result directly.
Solution: Let the original four-digit number be $\overline{a b c d}$ (where $a, b, c, d$ represent the digits in each place), then from the given information we have
$$
\begin{array}{l}
1000 a+100 b+10 c+d-999 \\
=1000(a-1)+100 b+10 c+(d+1) .
\end{array}
$$

Obviously, when $d \leqslant 8, a>1$, $(a-1) b c(d+1)$ is the smallest four-digit number after reordering.

When $d=9$, the unit digit of the smallest four-digit number after reordering is 0, and obviously, the tens and hundreds digits should also be 0, otherwise it would not be the smallest four-digit number. This means that three of the four digits are 0, which clearly does not meet the problem's requirements.
Therefore, $d \leqslant 8$.
Since the digits in $\overline{a b c d}$ and $\overline{(a-1) b c(d+1)}$ remain unchanged, it must be true that
$$
\left\{\begin{array}{l}
a=d+1, \\
d=a-1,
\end{array} \text { i.e., } a-d=1\right. \text {. }
$$

Thus, the reordered four-digit number is $\overline{d b c}$. Therefore, we also have $d \geqslant 1$. For any $d$ in $\{1,2,3,4,5,6,7,8\}$, the reordered four-digit numbers can be:
$$
\overline{d d d e}, \overline{d d a a}, \overline{d u a u}, \overline{d 00 a}, \overline{d 0 c a}, \overline{d 0 d u}
$$
(To ensure the minimality of the new number, since the positions of $b, c$ remain unchanged, we must have (1) $d \leqslant b \leqslant c \leqslant a$ or (2) $b=0, d \leqslant c \leqslant a$ or (3) $b=c=0$. $d<a$. — Editor's note)

Clearly, these 6 numbers are all different, so they correspond to 6 different four-digit numbers that meet the problem's conditions. Therefore, there are $6 \times 8=48$ four-digit numbers that satisfy the conditions of the problem.
(Note, the problem easily includes cases with the digit 0.)