Henry Ernest Dudeney/Puzzles and Curious Problems/269 - Sixteen Straight Runs/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $269$
- Sixteen Straight Runs
- A commercial traveller started in his car from the point $A$ shown,
- and wished to go $76$ miles in $16$ straight runs, never going along the same road twice.
- The dots represent the towns and villages, and these are one mile apart.
- The lines show the route he selected.
- It will be seen that he carried out his plan correctly, but $6$ towns or villages were unvisited.
- Can you show a better route by which he could have gone $76$ miles in $16$ straight runs, and left only $3$ towns unvisited?
Solution
Solution $1$
Solution $2$
Here is a solution which leaves just one town unvisited:
Also see
- $161$ - A Motor-Car Puzzle from his Modern Puzzles collection, which is a similar problem.
Historical Note
The solution leaving $3$ towns unvisited was the one provided by Dudeney.
The improved solution leaving just $1$ town unvisited was discovered by Victor Meally.
Martin Gardner presented it in his Mathematical Games column in Scientific American, later republished in his $1975$ collection Mathematical Carnival.
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solution: $269$. -- Sixteen Straight Runs
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $427$. Sixteen Straight Runs