Route & Network Puzzles 155the same diagram and asked to start where you like and try to pass through
every short line comprising the figure, once and once only, without crossing
your own path. Figure 3 will make quite clear what is meant. It is an
attempted solution, but it fails because the line from K to L has not been
crossed. We might have crossed it instead ofKM, but that would be no better.
Is it possible? Many who write to me about the puzzle say that though they
have satisfied themselves as a "pious opinion" that it cannot be done,
yet they see no way whatever of proving the impossibility, which is quite an-
other matter. I will show my way of settling the question.
- THE NINE BRIDGES
The illustration represents the map of a district with a peculiar system of
irrigation. The lines are waterways enclosing the four islands, A, B, C, and D,
each with its house, and it will be seen that there are nine bridges available.Whenever Tompkins leaves his house to visit his friend Johnson, who lives in
one of the others, he always carries out the eccentric rule of crossing every
one of the bridges once, and once only, before arriving at his destination.
How many different routes has he to select from? You may choose any house
you like as the residence of Tompkins.