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THE SAILOR'S PUZZLE.

(Unicursal and Route Problems)
The sailor depicted in the illustration stated that he had since his
boyhood been engaged in trading with a small vessel among some twenty
little islands in the Pacific. He supplied the rough chart of which I
have given a copy, and explained that the lines from island to island
represented the only routes that he ever adopted. He always started from
island A at the beginning of the season, and then visited every island
once, and once only, finishing up his tour at the starting-point A. But
he always put off his visit to C as long as possible, for trade reasons
that I need not enter into. The puzzle is to discover his exact route,
and this can be done with certainty. Take your pencil and, starting at
A, try to trace it out. If you write down the islands in the order in
which you visit them--thus, for example, A, I, O, L, G, etc.--you can at
once see if you have visited an island twice or omitted any. Of course,
the crossings of the lines must be ignored--that is, you must continue
your route direct, and you are not allowed to switch off at a crossing
and proceed in another direction. There is no trick of this kind in the
puzzle. The sailor knew the best route. Can you find it?


Answer:

There are only four different routes (or eight, if we count the reverse
ways) by which the sailor can start at the island marked A, visit all
the islands once, and once only, and return again to A. Here they are:--
A I P T L O E H R Q D C F U G N S K M B A A I P T S N G L O E U F C D K
M B Q R H A A B M K S N G L T P I O E U F C D Q R H A A I P T L O E U G
N S K M B Q D C F R H A
Now, if the sailor takes the first route he will make C his 12th island
(counting A as 1); by the second route he will make C his 13th island;
by the third route, his 16th island; and by the fourth route, his 17th
island. If he goes the reverse way, C will be respectively his 10th,
9th, 6th, and 5th island. As these are the only possible routes, it is
evident that if the sailor puts off his visit to C as long as possible,
he must take the last route reading from left to right. This route I
show by the dark lines in the diagram, and it is the correct answer to
the puzzle.
The map may be greatly simplified by the "buttons and string" method,
explained in the solution to No. 341, "The Four Frogs."










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