Looping Train Tracks Our son just received some train tracks for his second birthday. We've been experimenting with various layouts.
The one below has remained assembled for (almost) half and hour now, and I began to notice that, when going past any point, the train is always heading in the same direction (it seems the train cannot be made to turn around via a loop and return in the opposite direction).
Are there any possible configurations so the train can be made to pass a given point in the A-to-B direction, and later on, the B-to-A direction?

 A: By now, all that remains of the given layout is the photograph.
However, after further reflection on the individual track pieces, there is a rather simple proof that reversal is not possible:


*

*All straight tracks connect A-to-B

*All Y-switches connect A-to-BB or B-to-AA

*Without any B-to-B or A-to-A connection in either straight tracks or Y-switches, direction cannot be reversed; QED
A: You can prove it by using a state graph $G=(X,U)$ where $X$={(0,*,*), (*,0,*), (*,*,0), (1,*,*), (*,1,*), (*,*,1)}. Each state indicates both the position of the train (you have 3: (Upper, bottom left, bottom right)) and its direction (by the value of 0 or 1 for left-to-right and vice versa respectively). For example (1,*,*) means the train is in the upper edge heading right to left. For your photo the state is (*,*,0).  
The graph associated to your photo 
The arcs of $G$ indicate if two states are consecutive. For example, from (*,0,*) you can only reach (1,*,*). To be able to pass a given point in a direction, and later on, on the opposite, you must have a path between two vertices with the same position of the two asteriscs and an inverted bit (for example from (*,*,0) to (*,*,1)).
In your situation, this is impossible because all such couple of vertices are in different connected components. 
