10.16 There is a five-digit positive odd number $x$. In $x$, all 2s are replaced with 5s, and all 5s are replaced with 2s, while other digits remain unchanged, resulting in a new five-digit number, denoted as $y$. If $x$ and $y$ satisfy the equation $y=2(x+1)$, what is the value of $x$?
(China Junior High School Mathematics League, 1987)
[Solution 1] Since $y > 2x$, the ten-thousands digit of $y$ is greater than the ten-thousands digit of $x$, and the different digits in the same place can only be 2 and 5.
Therefore, from the fact that the ten-thousands digits of $x$ and $y$ are different, we know that the ten-thousands digit of $x$ is 2, and the ten-thousands digit of $y$ is 5.
$$
\text{Let } \begin{aligned}
x & =\overline{2 a b c d}=2 \cdot 10^{4}+10^{3} \cdot a+10^{2} \cdot b+10 \cdot c+d, \\
y & =\overline{5 a^{\prime} b^{\prime} c^{\prime} d^{\prime}}=5 \cdot 10^{4}+10^{3} \cdot a^{\prime}+10^{2} \cdot b^{\prime}+10 \cdot c^{\prime}+d^{\prime} .
\end{aligned}
$$

Here, $a$ and $a^{\prime}$, $b$ and $b^{\prime}$, $c$ and $c^{\prime}$, $d$ and $d^{\prime}$ are 2 and 5, 5 and 2, or the same digits.
Substituting $y=2(x+1)$ and rearranging, we get
$$
9998=10^{3}\left(2 a-a^{\prime}\right)+10^{2}\left(2 b-b^{\prime}\right)+10\left(2 c-c^{\prime}\right)+\left(2 d-d^{\prime}\right)
$$

When $a=a^{\prime}$, $\quad 2 a-a^{\prime}=a$;
When $a \neq a^{\prime}$, $2 a-a^{\prime}=2 \cdot 5-2=8$ or $2 \cdot 2-5=-1$.
Therefore, the thousands digit can only be $a=a^{\prime}=9$.
Similarly, we can deduce that $b=b^{\prime}=9$, $c=c^{\prime}=9$, $d=5$, $d^{\prime}=2$.
Thus, $\quad x=29995, y=59992$.
Verification: $2(x+1)=2(29995+1)=59992$.
Therefore, $\quad x=29995$.
[Solution 2] First, the ten-thousands digit of $x$ is clearly 2, so the ten-thousands digit of $y$ must be 5.
Second, the thousands digit of $x$ must be greater than 5, but the hundreds digit multiplied by 2 can at most carry 1 to the thousands place, so the thousands digit can only be 9. Similarly, we deduce that the first four digits of $x$ are $2,9,9,9$.
The units digit of $x$ can only be $1,3,5,7,9$. After inspection, the units digit of $x$ can only be 5, so $x$ is 29995.