9. A positive integer that can be written in the form $20a + 8b + 27c$ $(a, b, c \in \mathbf{N})$ is called a "good number." The number of good numbers in the set $\{1, 2, \cdots, 200\}$ is $\qquad$.
9. 153 .
First consider $20 a+8 b=4(5 a+2 b)$.
$5 a+2 b$ can take $2,4,5,6, \cdots, 50$.
Then $20 a+8 b$ can take $8,16,20,24, \cdots, 200$.
Therefore, when $c=0$, there are 48 non-zero good numbers (of the form $4 k$);
when $c=1$, there are 42 good numbers (of the form $4 k+3$), at this time the good numbers are $27,35,43,47, \cdots, 199$;
when $c=2$, there are 35 good numbers (of the form $4 k+2$), at this time the good numbers are $54,62,70,74, \cdots, 198$;
when $c=3$, there are 28 good numbers (of the form $4 k+1$), at this time the good numbers are $81,89,97,101, \cdots, 197$.

In summary, there are $48+42+35+28=153$ good numbers.