The inspector of a certain system of tube railways inspects regularly the company's seventeen lines connecting twelve stations, as shown on the big poster plan that he is contemplating. 

He wants to arrange his route so that it shall take him over all the lines with as little travelling as possible. 
He may begin where he likes and end where he likes. 

What is his shortest route?

Hint:
If the stations are a mile apart, he will have to travel more than seventeen miles to inspect every line.
How far is he compelled to travel, and which route do you recommend?