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THE GRAND TOUR.





(Unicursal and Route Problems)
One of the everyday puzzles of life is the working out of routes. If you
are taking a holiday on your bicycle, or a motor tour, there always
arises the question of how you are to make the best of your time and
other resources. You have determined to get as far as some particular
place, to include visits to such-and-such a town, to try to see
something of special interest elsewhere, and perhaps to try to look up
an old friend at a spot that will not take you much out of your way.
Then you have to plan your route so as to avoid bad roads, uninteresting
country, and, if possible, the necessity of a return by the same way
that you went. With a map before you, the interesting puzzle is attacked
and solved. I will present a little poser based on these lines.
I give a rough map of a country--it is not necessary to say what
particular country--the circles representing towns and the dotted lines
the railways connecting them. Now there lived in the town marked A a man
who was born there, and during the whole of his life had never once left
his native place. From his youth upwards he had been very industrious,
sticking incessantly to his trade, and had no desire whatever to roam
abroad. However, on attaining his fiftieth birthday he decided to see
something of his country, and especially to pay a visit to a very old
friend living at the town marked Z. What he proposed was this: that he
would start from his home, enter every town once and only once, and
finish his journey at Z. As he made up his mind to perform this grand
tour by rail only, he found it rather a puzzle to work out his route,
but he at length succeeded in doing so. How did he manage it? Do not
forget that every town has to be visited once, and not more than once.


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