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The map below displays the train network of Beastville, including the stations X and Y, and the lines a, b, c, d, e, and f.  There is a station where any two lines intersect, and on every line, trains stop at each station.

 

Grogg wants to travel from station X to station Y, with the following conditions:
* Once Grogg leaves station X, he never returns to station X.

* Once Grogg arrives at station Y, he never leaves station Y.
* Grogg travels along each line at most once.
 

How many different routes can Grogg take?

 
 Oct 30, 2024

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