13. Grandpa Hua Luogeng encouraged teenagers in a poem:
"Aggressive attack is the first, proficiency brings out a hundred tricks, diligence compensates for clumsiness is a good lesson, one part of hard work, one part of talent.

Now, different Chinese characters in the poem correspond to different natural numbers, the same Chinese characters correspond to the same natural numbers, and the natural numbers corresponding to different Chinese characters can be arranged into a series of consecutive natural numbers. If the average of these 28 natural numbers is 23, what is the maximum possible value of the natural number corresponding to the character "分"?

13. Solution: (1) Since $23 \times 28=644$,
(2) Let the starting number of this sequence of consecutive natural numbers be $\mathrm{m}$, and the natural numbers corresponding to different characters are:
$m, m+1, \cdots, m+23$; Let the natural number corresponding to the character “分” be $m+x$, the character “是” be $m+a$, and the character “一” be $m+b$. Since we want the natural number corresponding to “分” to be as large as possible, we can require $23 \geqslant x>a>b \geqslant 0$.

In the poem, “分” and “是” each appear 2 times, and “一” appears 3 times, while other characters appear only once. Therefore, we have
$$
\begin{array}{l}
\frac{(m+m+23) \times 24}{2}+m+x+m+a+2(m+b)=644, \\
28 \mathrm{~m}+276+(\mathrm{a}+2 \mathrm{~b})+\mathrm{x}=644,28 \mathrm{~m}=368-\mathrm{x}-(\mathrm{a}+2 \mathrm{~b}) \\
m=\frac{368-x-(a+2 b)}{28}, m+x=\frac{368+27 x-(a+2 b)}{28}, \text { but, } \mathrm{x}^{2} \\
23 \geqslant \mathrm{x}, \quad \mathrm{b} \geqslant 0, \mathrm{a}+\mathrm{b} \geqslant 1+0, \mathrm{a}+2 \mathrm{~b}=\mathrm{a}+\mathrm{b}+\mathrm{b} \geqslant 1 . \\
\text { Therefore, } m+x=\frac{368+27 x-(a+2 b)}{28} \leq \frac{368+27 \times 23-1}{28}<35.29 .
\end{array}
$$

Taking $m=12, x=23, a=9, b=0$ (or $a=5, b=2$ or $a=1, b=4$), we get a solution that satisfies the conditions, where the natural number corresponding to “分” is 35.

Answer: The maximum possible value of the natural number corresponding to “分” is 35.