3. (35 points) In country $B$, there are 4 southern cities and 5 northern cities. Transportation links connect each southern city with each northern city in both directions; there is no transportation link between other pairs of cities. A one-way ticket from any city $A$ to any city $B$ costs $N$ rubles. A round-trip ticket for the route $A \rightarrow B \rightarrow A$ costs $1.6 N$ rubles. A traveler starts from a southern city, plans to visit all southern cities, and return to the starting point. Determine the minimum possible amount the traveler will have to spend on tickets.
Answer: $4 \times 1.6 N$ rubles.

Solution. Since the southern cities are not connected by transportation, to visit all of them and return, it will require $2 \times 4$ trips. Any two trips cost at least $1.6 N$ rubles in total, so the total expenses will be at least $4 \times 1.6 N$ rubles.

Let's provide an example of a route where this sum is realized. Suppose the traveler starts from city $Y_{1}$, visits the other southern cities in the order $Y_{2}, Y_{3}$, and $Y_{4}$, and all transfers are made in the northern city $S_{1}$. Then the final travel route will be as follows: $Y_{1} \rightarrow S_{1} \rightarrow Y_{2} \rightarrow S_{1} \rightarrow Y_{3} \rightarrow S_{1} \rightarrow Y_{4} \rightarrow S_{1} \rightarrow Y_{1}$. The travel on this route can be carried out with the following tickets:

$$
\begin{gathered}
Y_{1} \rightarrow S_{1} \rightarrow Y_{1}-\text { this is the first and last trip of the route; } \\
S_{1} \rightarrow Y_{2} \rightarrow S_{1}-\text { the second and third trips; } \\
S_{1} \rightarrow Y_{3} \rightarrow S_{1}-\text { the fourth and fifth trips; } \\
S_{1} \rightarrow Y_{4} \rightarrow S_{1}-\text { the sixth and seventh trips. }
\end{gathered}
$$