I came across a playful problem.
On a sheet of paper it is written the number $\overline{1234xy}$, where
\begin{equation}\overline{1234xy}=1*10^5+2*10^4+3*10^3+4*10^2+x*10^1+y\end{equation}
Five students engage in the following game: each of the first four reads the number, make up a rule of transformation and writes the transformed number on the paper. The fifth, who knows only the first four digits, has to guess the rule of each student and try to find the original number, if possible.
The four numbers written by the students are
\begin{equation}123500\end{equation} \begin{equation}123470\end{equation} \begin{equation}123460\end{equation} \begin{equation}120000\end{equation}
What are the rules and can the original number be known with accuracy.
My guess is that the last digit is 0, since in all four numbers is present