MATH STINGER #60 
by Dr. Joel C. Fowler 
Assistant Professor of Mathematics 

For a new puzzle suppose that there are 101 cities in a country. A road in this country is 
built if and only if it joins a city to its nearest neighboring city. Suppose that no two 
distances between pairs of cities are the same and that the country is on a flat 
plane. There are several questions. 1) What is the largest number of roads 
possible in this city?; 2) What is the smallest number of roads possible 
in this city?; 3) What is the largest number of roads possible that 
meet at one city?

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