The fourteenth question: A country has 36 cities and 5 airlines, and any two cities are connected by a bidirectional flight operated by exactly one airline. For any two flights departing from the same city and operated by the same airline, the Ministry of Transport grants a subsidy of one million lira. What is the minimum amount of money the Ministry of Transport has to subsidize?

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Note: The translation maintains the original format and line breaks as requested.
The 14th question:
Answer: Consider the 36 cities as 36 points. We need to find the minimum number of "monochromatic angles" in a 5-colored complete graph of 36 vertices.

In general, for an $n$-vertex $k$-colored complete graph $G(V, E)$, let the number of edges of the $i$-th color from a vertex $v \in V$ be $d_i(v)$. Then, $\sum_{i=1}^{k} d_i(v) = v - 1$. The number of monochromatic angles is given by:
$$
\begin{array}{l}
\sum_{v \in V} \sum_{i=1}^{k} C_{d_i(v)}^{2} = \sum_{v \in V} \frac{\sum_{i=1}^{k} d_i^2(v) - \sum_{i=1}^{k} d_i(v)}{2} \geq \sum_{v \in V} \frac{\frac{\left(\sum_{i=1}^{k} d_i(v)\right)^2}{k} - \sum_{i=1}^{k} d_i(v)}{2} \\
= \sum_{v \in V} \frac{\frac{(n-1)^2}{k} - (n-1)}{2} = \frac{(n-1)^2(n-1)}{2k} - \frac{(n-1)n}{2} = \frac{(n-1)(n-1)n}{2k}
\end{array}
$$

Specifically, when $n = 36$ and $k = 5$, the number of monochromatic angles is at least 3780.
Below is an example with exactly 3780 monochromatic angles.
Consider a complete graph $G_0$ with six vertices $A_1, A_2, \ldots, A_6$, forming the vertices of a regular hexagon, colored as follows: (1) The six edges of the hexagon are alternately colored with colors 1 and 2, and the diagonals $A_iA_{i-3}, A_{i+1}A_{i-1}, A_{i+2}A_{i-2}$ are colored with color $i$ ($i = 3, 4, 5$), where the indices are taken modulo 5.

Place a copy of $G_0$ at each vertex of $G_0$ to replace the original point, thus forming a new graph $G(V, E)$ with 36 vertices. If two vertices in $G_0$ are connected by an edge of color $t$, for the copies $G_0'$ and $G_0''$ placed at vertices $A_i$ and $A_j$, respectively, all edges between $a \in G_0'$ and $b \in G_0''$ are also colored with color $t$.

In this case, for any $v \in V$ and $i \in \{1, 2, 3, 4, 5\}$, we have $d_i(v) = 7$. Therefore, the number of monochromatic angles is $36 \times C_7^2 \times 5 = 3780$ monochromatic angles.
In conclusion, the Ministry of Transport needs to subsidize at least 3780 hundred lire.