Taxi Cab Routing

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Olympic Victory Stand
Trip to the Zoo
Lunch Box Mix-Up
Nine Letters
Sporting Friends
Party Girls
The Dog Show
TV Shuffle
On The Train
Who Owns The Zebra?
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What Do You Do?
The Homesick Stars
Cousins & Aunts
Shopping Syndrome
Tennis Match
Baseball Logic Problem
Olympic Dating
The Bachelors
Santa's Pack
Harry's Seven Bottles
The Ship
Taxi Cab Routing
Crossing The Ravine
Logic Problem Answers

TAXI CAB ROUTING

A taxi cab driver is experimenting in how many different routes he may take in getting from point A to point J. A map of his area is shown below.

The streets are all one-way, with the arrows indicating the direction. One pathway would be ABCDEFGHIJ. A shorter route would be ACEGIJ.

How many different routes can be taken before the driver must repeat a particular pathway?