All Roads lead to Rome...
Number Theory
Level
3
In the kingdom of Anantarajya, there are 100 cities including Anantanagri, and four roads lead out of each city. How many roads are there altogether in Anantarajya?
The answer is 200.
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1 solution
This is graph theory: there are 100 vertices (cities), and 4 degrees per vertex (4 roads coming out of each city). We have 4 * 100 degrees in total. Each edge (road) counts for 2 degrees, as 1 road connects 2 cities (which is what I assumed). So the number of roads is 400/2 = 200.