PPT Slide
Once TailWagger found all of the snakes (up through 6-space) all of the duplicate snakes had to be thrown out in order to determine the number of unique snakes and their composition.
The matter required a bit of careful thought.
Notes:
Most of the snakes are merely transformations of each other. It is an interesting exercise to determine the set of snakes that cannot be transformed into each other. Here are some examples.