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A bug travels from $A$ to $B$ along the segments in the hexagonal lattice pictured below. The segments marked with an arrow can be traveled only in the direction of the arrow, and the bug never travels the same segment more than once. How many different paths are there?

enter image description here

The answer is 2400

What is a way to do this combinatorics problem that could generalize to do any of problems similar to this but with more path?

i have limited terminology knowlegde, i would like a technical solution but please explain

No answer for a week already, Can anybody gave some clues?

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What's your question? –  Alex Becker Feb 25 '12 at 2:29
    
@Alex: I believe that Victor is looking for a general solution for digraphs of this type. –  Brian M. Scott Feb 25 '12 at 2:35
    
@BrianM.Scott The last sentence was not present when I inquired. It clears things up nicely. –  Alex Becker Feb 25 '12 at 2:37
    
@BrianM.Scott - exactly, however i have limited terminology knowlegde, i would like a technical solution but please explain –  Victor Feb 25 '12 at 2:40
    
How do you know the answer is 2400? Do you have a worked-out solution of this problem? Does it come from some source that might give some general ideas? –  Gerry Myerson Feb 27 '12 at 23:51

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