Help a Traveling Salesman Find Every Route in this Math Puzzle

Math Puzzle: How Several Routes Can You Come across?

By Heinrich Hemme

Henry Ernest Dudeney may be between the most sizeable puzzle inventors who ever lived. He was born in Mayfield, England, in 1857, the son of a village schoolteacher, and he died in 1930. Dudeney built brainteasers for newspapers and publications frequently for many years, and he later on compiled most of his puzzles into guides. This head-scratcher comes from his 1917 e book Amusements in Mathematics.

A traveling salesman who lives in city A would like to stop by all cities from B to P about the study course of a week, however not essentially in alphabetical get, and return to A at the stop. He strategies to enter just about every city just after. The blue strains are the only roadways connecting the 16 metropolitan areas. The traveling salesman may well use only a straight route among any two cities he is not permitted to switch at the intersection of two streets. How many diverse routes are probable?

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If the touring salesman enters a town on a single street, he will have to depart it again on an additional. In order for a spherical journey to be feasible at all, at minimum two roadways need to direct to every town. There are specifically two streets primary to towns A, B, E, F, G and H. The touring salesman have to thus travel on these streets no make a difference what. This also decides which roadways he will use to access and leave cities I, J, M and N. The remaining connections are then also apparent. There is consequently only one doable spherical trip for the touring salesman—AIENHDOFJBMGCKPLA—but he can travel it in two distinct instructions.

Editor’s Note: The model of the puzzle that appeared in the print version of the July/August 2024 difficulty improperly integrated connections involving C and I and amongst I and M. The mistake did not impact the resolution.