Question 158
In a country, there are 100 cities. Each of these cities is joined to exactly three other cities by direct roads in both directions. Prove that there is a city $A$ from which one can go from city to city and return to $A$, never using the same road twice, and using a total number of roads that is not divisible by 3 (it is not required that all the cities of the country be visited during this trip).