Is there an Euler path solution? I am solving the following problem: A city is composed of three parallel east-west streets and four parallel north-south streets: Note there are 12 intersections and 17 street segments. A policeman needs to visit every street segment, but he wants to take the shortest path. The policeman can start at any intersection, and he can only traverse streets, going from one intersection to another. How many street segments are there in the shortest path that visits each street segment at least once? I know that it cannot be an Euler circuit, however I am unsure if it can be an Euler path. I have been working on a solution, however I have found no paths yet.

I don't think there is an Euler path. The best I've been able to come up with for the moment is the following path:

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It takes all the edges exactly once, except for two of them that are taken twice.