Question 127
In a country, some pairs of cities are connected by the roads, which do not intersect outside the cities. At each city, there is a sign showing the least length of the route beginning at this city and passing through all other cities (a route can pass through some cities several times; it should not necessarily return to the original city). Prove that the ratio of any two numbers on the signs does not exceed $3/2$. (M. Murashkin)