Math Puzzle: How Many Routes Can You Discover?
Attempt to resolve a touring salesman’s directional dilemma
Henry Ernest Dudeney could also be among the many most important 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 designed brainteasers for newspapers and magazines usually for many years, and he later compiled most of his puzzles into books. This head-scratcher comes from his 1917 e-book Amusements in Arithmetic.
A touring salesman who lives in metropolis A needs to go to all cities from B to P over the course of per week, although not essentially in alphabetical order, and return to A on the finish. He plans to enter every metropolis precisely as soon as. The blue traces are the one roads connecting the 16 cities. The touring salesman could use solely a straight route between any two cities; he isn’t allowed to show on the intersection of two streets. What number of totally different routes are doable?
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If the touring salesman enters a metropolis on one highway, he should depart it once more on one other. To ensure that a spherical journey to be doable in any respect, a minimum of two roads should result in every metropolis. There are precisely two roads resulting in cities A, B, E, F, G and H. The touring salesman should subsequently journey on these roads it doesn’t matter what. This additionally determines which roads he’ll use to achieve and depart cities I, J, M and N. The remaining connections are then additionally clear. There may be subsequently just one doable spherical journey for the touring salesman—AIENHDOFJBMGCKPLA—however he can journey it in two totally different instructions.
Editor’s Observe: The model of the puzzle that appeared within the print version of the July/August 2024 concern incorrectly included connections between C and I and between I and M. The error didn’t affect the answer.
