7.3. From the highway, four roads sequentially lead to four villages A, B, C, D. It is known that the route by road/highway/road from A to B is 9 km, from A to C - 13 km, from B to C - 8 km, from B to D - 14 km. Find the length of the route by road/highway/road from A to D. Explain your answer.
Answer: 19 km.

Solution. Let's add the distances from $A$ to $C$ and from $B$ to $D$. Then the highway segment from the turn to $B$ to the turn to $C$ will be counted twice, while the highway segments from the turn to $A$ to the turn to $B$ and from the turn to $C$ to the turn to $D$, as well as the four roads from the highway to the villages, will be counted once. Therefore, if we now subtract the distance from $B$ to $C$ from the resulting sum, the difference will include each of the three highway segments and the access roads to $A$ and $D$ exactly once, which is precisely the path from $A$ to $D$. Thus, the length of this path is $13+14-8=19$ km.