Write the digits $1,2,3,4,5,6,7,8,9$ in some order to form a nine-digit number $\overline{\operatorname{abcdefghi}}$. If $A=\overline{a b c}+\overline{b c d}+\overline{c d e}+\overline{d e f}+\overline{e f g}+\overline{f g h}+\overline{g h i}$, find the maximum possible value of $A$.
Number Theory, Place Value Principle; Extreme Value Problem.
$$
\begin{array}{l}
A=\overline{a b c}+\overline{b c d}+\overline{c d e}+\overline{d e f}+\overline{e f g}+\overline{f g h}+\overline{g h i} \\
=a \times 100+b \times 110+(c+d+e+f+g) \times 111+h \times 11+i \times 1 ;
\end{array}
$$

To make $A$ as large as possible;
we should consider $(c, d, e, f, g), b, a, h, i$ in descending order; when $(c, d, e, f, g)=(9,8,7,6,5), b=4, a=3, h=2, i=1$, $A$ is maximized, which is $(9+8+7+6+5) \times 111+4 \times 110+3 \times 100+2 \times 11+1 \times 1=4648$.