\myheading{Vehicle license plate}

There was a hit and run.
And you're police officer.
And this is what your only witness can say about the 4-digit license plate of the runaway vehicle:

\begin{lstlisting}
There was 13: 1 and 3 together, I'm sure, but not sure where, 13 as first 2 digits, last 2 digits or in the middle.
And there was also 6, or maybe 8, or maybe even 9, not sure which, but one of them.
\end{lstlisting}

Combinatorics textbooks are abound with exercises like this: can you enumerate all possible 4-digit numbers constrained in this way?

\lstinputlisting{comb/plate.py}

\begin{lstlisting}
1360
1306
6130
6013

...

9139
9913
9139
9913
\end{lstlisting}

( 180 numbers )

This is something you can query registered vehicle database with...