Question 15
In a country there are $2024$ cities, each two of which are connected bidirectionally by exactly one of three modes of transportation: rail, air, or road. A tourist arrives in this country and has the entire transportation scheme. He chooses a travel ticket for one of the modes of transportation and the city from which he starts his trip. He wants to visit as many cities as possible but using only the ticket for the specified type of transportation. How many cities is the tourist guaranteed to be able to visit? During the route, he can return to the cities he has already visited.
(Bogdan Rublov)
**Figure 20**
(Bogdan Rublov)
**Figure 20**