Henry Ernest Dudeney/Puzzles and Curious Problems/269 - Sixteen Straight Runs/Solution

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