INSPECTING A MINE.
(Unicursal and Route Problems
The diagram is supposed to represent the passages or galleries in a
mine. We will assume that every passage, A to B, B to C, C to H, H to I,
and so on, is one furlong in length. It will be seen that there are
thirty-one of these passages. Now, an official has to inspect all of
them, and he descends by the shaft to the point A. How far must he
travel, and what route do you recommend? The reader may at first say,
"As there are thirty-one passages, each a furlong in length, he will
have to travel just thirty-one furlongs." But this is assuming that he
need never go along a passage more than once, which is not the case.
Take your pencil and try to find the shortest route. You will soon
discover that there is room for considerable judgment. In fact, it is a
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