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THE TUBE INSPECTOR'S PUZZLE.

(Unicursal and Route Problems)
The man in our illustration is in a little dilemma. He has just been
appointed inspector of a certain system of tube railways, and it is his
duty to inspect regularly, within a stated period, all the company's
seventeen lines connecting twelve stations, as shown on the big poster
plan that he is contemplating. Now 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?
Could anything be simpler? But the reader will soon find that, however
he decides to proceed, the inspector must go over some of the lines more
than once. In other words, if we say that the stations are a mile apart,
he will have to travel more than seventeen miles to inspect every line.
There is the little difficulty. How far is he compelled to travel, and
which route do you recommend?


Answer:

The inspector need only travel nineteen miles if he starts at B and
takes the following route: BADGDEFIFCBEHKLIHGJK. Thus the only portions
of line travelled over twice are the two sections D to G and F to I. Of
course, the route may be varied, but it cannot be shortened.










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