New Addtion to the family

Here's a video of our new daughter getting ready to come home from the hospital.

Train Topology Anyone?

I have been playing with my sons Geotrax system of late. When he wants to play trains it means he sits on the bed and daddy puts the trains together so that he can break them apart.

So naturally, being the nurd that I am, was wondering if there was a mathematical way to determine the number of layouts that used every piece of a given set of pieces. I have recently managed to create a layout that uses every piece:


The question is. How many are there like this? Also, how do you determine what their basic topological properties are such as how the points relate to each other and what the symmetric must look like.

Any ideas?