Henry Ernest Dudeney/Puzzles and Curious Problems/268 - Mrs. Simper's Holiday Tour/Solution

by : $268$

 * Mrs. Simper's Holiday Tour
 * The diagram shows a plan, very much simplified, of a tour that Mrs. Simper proposes to take next autumn.
 * It will be seen that there are $20$ towns, all connected by railway lines.
 * Mrs. Simper lives at $H$, and wants to visit every other town once and once only, ending her tour at home.


 * Dudeney-Puzzles-and-Curious-Problems-268.png


 * There are in fact $60$ possible routes she can select from, counting the reverse of a route as different.
 * There is a tunnel between $N$ and $O$, and one between $R$ and $S$, but Mrs. Simper does not want to go through these.
 * ''She also wants to delay her visit to $D$ as long as possible so as to meet a friend who lives there.


 * The puzzle is to show Mrs. Simper the best route under these circumstances.

Solution
Although there are $60$ routes altogether, only $8$ of them avoid both tunnels.

The route that complies with the conditions, avoids both tunnels, and delays the visit to $D$ till as late as possible, is:


 * $HISTLKBCMNUQRGFPODEAH$


 * Dudeney-Puzzles-and-Curious-Problems-268-solution.png