9. (10 points) A three-digit number whose sum of the tens digit and the units digit equals the hundreds digit is called a "good number". How many good numbers are there?



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【Analysis】For the convenience of solving, we can classify and count by the hundreds digit. When the hundreds digit $=1$, the tens digit $=0,1$, there are 2; when the hundreds digit $=2$, the tens digit $=0,1,2$, there are 3; $\cdots$, when the hundreds digit $=k$, the tens digit $=0, \cdots, k$, there are $k+1$; based on this to solve.

【Solution】Solution. Classify and count by the hundreds digit:
When the hundreds digit $=1$, the tens digit $=0,1$, the unit digit $=1,0$, there are 2;
When the hundreds digit $=2$, the tens digit $=0,1,2$, the unit digit $=2,1,0$, there are 3;
When the hundreds digit $=3$, the tens digit $=0,1,2,3$, the unit digit $=3,2,1,0$, there are 4;

When the hundreds digit $=k$, the tens digit $=0, \cdots, k$, there are $k+1$;
Since $0<k<10$, therefore $k$ is at most 9, so $k+1=10$.
Therefore, there are $2+3+\cdots+10=54$ in total.
Answer: There are 54 good numbers.