Urban walk - Lycée Emmanuel d'Alzon (Nîmes)

In a Roman city where the streets are laid out in a grid, Numerius wants to visit his friend Gaia.
\begin{itemize}
\item How many possible paths are there for him to get to his friend?
\item What is the length of the shortest path?
\item Same question for Tiberia, who must go to Tullus’s in another neighbourhood (non-square grid).
\end{itemize}