Question 48
In a country, there are $n$ cities, and every two of them are connected with a non-stop train operating in both directions. The ticket price for each train in both directions is the same, but for any two different trains these prices are different. Prove that a traveler may start from some city and take $n-1$ trains consecutively so that the price of every ticket will be less than the price of the previous one. (A traveler may pass through a certain city several times.)