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

Modern Puzzles by Henry Ernest Dudeney: $158$

The Nine Bridges

The diagram 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.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Unicursal and Route Problems: $158$. -- The Nine Bridges
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Route & Network Puzzles: $415$. The Nine Bridges