Folkoro
In a certain state, the airline system is arranged in such a way that each city is connected by air routes
to no more than three other cities, and from any city, you can reach any other city with no more than one
transfer. What is the maximum number of cities that can be in this state?
Evaluation. From a fixed city $A$, one can directly reach no more than three cities, and with one transfer - no more than $3 \cdot 2=6$ additional cities. Thus, the total number of cities can be no more than ten. For an example of a network of 10 cities, see the figure below.

![](https://cdn.mathpix.com/cropped/2024_05_06_73983c7cc26f0024f238g-30.jpg?height=498&width=557&top_left_y=1746&top_left_x=745)

## Answer

10.