35. (ROM 1) Find all numbers $N=\overline{a_{1} \alpha_{2} \ldots a_{n}}$ for which $9 \times \overline{a_{1} \alpha_{2} \ldots a_{n}}=$ $\overline{a_{n} \ldots a_{2} a_{1}}$ such that at most one of the digits $a_{1}, a_{2} \ldots \ldots a_{n}$ is zero.
35. The solutions are 0 and $N_{k}=1099 \ldots 989$, where $k=0,1,2, \ldots$
Remark. If we omit the condition that at most one of the digits is zero, the solutions are numbers of the form $N_{k_{1}} N_{k_{2}} \ldots N_{k_{r}}$, where $k_{1}=k_{r}$, $k_{2}=k_{r-1}$ etc.
The more general problem $k \cdot \overline{\pi_{1} u_{2} \cdots u_{n}}=\overline{u_{m} \cdots u_{2} u_{1}}$ has solutions only for $k=9$ and for $k=4$ (namely $0,2199 \ldots 978$ and combinations as above).