\section*{Problem 5 - V01005}

When asked about his license plate number, a mathematician replies:

"It is called III Z ... You can calculate the number yourself. Of the four digits, the last 3 are the same. The cross sum is 22.

If you place the first digit at the end, the resulting number is 1998 less than the actual one.
}

Let the first digit be \(y\), and the last three digits: \(3 x\). Then the system of equations is

\[
\begin{aligned}
y+3 x & =22 \\
(1000 y+100 x+10 x+x)-1998 & =1000 x+100 x+10 x+y
\end{aligned}
\]

This system has the solution \(x=5\) and \(y=7\). Therefore, the car number is III Z 7555.

Adapted from [6]