9. If a number is not a multiple of 11, but by removing any one of its digits, it becomes a multiple of 11 (for example, 111 is such a number, as removing any of its units, tens, or hundreds digit results in a multiple of 11), such a number is defined as a "Zhonghuan number". The number of four-digit "Zhonghuan numbers" is $\qquad$ (if none exist, write $\mathbf{0}$).
【Analysis】Let such a four-digit number be $\overline{a b c d}$, then according to the problem: $\left\{\begin{array}{l}\text { Move } a, \text { then } 11 \mid b+d-c \\ \text { Move } b, \text { then } 11 \mid a+d-c \\ \text { Move } c, \text { then } 11 \mid a+d-b \\ \text { Move } d, \text { then } 11 \mid a+c-b\end{array}\right.$, since $\mathrm{a}$ and $\mathrm{b}$ are both
single digits, it can only be $b=c$. Then $11|d, 11| a$, so $a=0, d=0$. Therefore, there does not exist such a four-digit number.