SOLUTION: Let's do a Koningsberg bridge problem for the city of New York. We will ignore any tunnels and Staten Island since there is only one bridge to it which immediately makes it imposs

Question 28343: Let's do a Koningsberg bridge problem for the city of New York. We will ignore any tunnels and Staten Island since there is only one bridge to it which immediately makes it impossible. Within the city I count the following:
11 bridges between Manhattan and the Bronx
6 bridges between Manhattan and Queens/Brooklyn
4 bridges between the Bronx and Queens/Brooklyn
Is it possible to make a tour of the city crossing every bridge only once and still return to the same starting point?
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
Count the degree for each vertex:
Manhattan: 11 + 6 = 17
Bronx: 11 + 4 = 15
Queens/Brooklyn: 6+4 =10
Note that there are two odd vertices, so the only possible Euler
path is starting from Manhattan to Bronx (or reverse).
But, there is no Euler circuit which can return to the same starting point
(unless all vertices are of even degree. why ?)

Kenny
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