Henry Ernest Dudeney/Modern Puzzles/158 - The Nine Bridges/Solution

by : $158$

 * The Nine Bridges

Solution
Tompkins, and likewise Johnson, lives at either $B$ or $D$.

He has $132$ routes to choose from.

Proof
First we transform the map into a graph, by representing each island by a vertex and each bridge by an edge.

The outer mainland is represented by $E$.

The resulting graph is shown below.


 * Dudeney-Modern-Puzzles-158-solution.png

It remains to count the number of different Eulerian trails.