Henry Ernest Dudeney/Puzzles and Curious Problems/267 - A Motor-Car Tour/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $267$

A Motor-Car Tour

A man started in a motor-car from town $A$, and wished to make a complete tour of these roads,

going along every one of them once, and once only.

How many different routes are there from which he can select?

Every route must end at the town $A$, from which you start,

and you must go straight from town to town -- never turning off at crossroads.

Solution

$264$.

Proof

This theorem requires a proof. In particular: According to Dudeney, "it is quite a difficult puzzle." You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solution: $267$. -- A Motor-Car Tour
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $425$. A Car Tour