Question 47
Find all solutions of the system of equations
$$
\left\{\begin{aligned}
s(x)+s(y) & = x \\
x+y+s(z) & = z \\
s(x)+s(y)+s(z) & = y-4
\end{aligned}\right.
$$
where $x$, $y$, and $z$ are positive integers, and $s(x)$, $s(y)$, and $s(z)$ are the numbers of digits in the decimal representations of $x$, $y$, and $z$, respectively.
$$
\left\{\begin{aligned}
s(x)+s(y) & = x \\
x+y+s(z) & = z \\
s(x)+s(y)+s(z) & = y-4
\end{aligned}\right.
$$
where $x$, $y$, and $z$ are positive integers, and $s(x)$, $s(y)$, and $s(z)$ are the numbers of digits in the decimal representations of $x$, $y$, and $z$, respectively.