TITLE: Forms of a Rubik's Snake
QUESTION [6 upvotes]: A Rubik's Snake is a game made by Rubik Erno. It is a rod with 24 triangular prisms fixed together on 23 pivots. Each pivot can be twisted with 4 x 90 degree turns to create different shapes.  I know I can find the number of forms it can take, provided that it only makes 90 degree turns at each pivot and there is no 'lack' of space (can be easily found out by taking the figures 4 twists available, and 23 pivots for each twist. $4^{23} = 70368744177664$. 
How would I incorporate the fact that there is limited space available, and that not all moves would be accepted? I don't mind whether they are sensitive to orientations, or not. Therefore, go for the easier option.

REPLY [2 votes]: As ofthis article on Wikipedia:

The number of different shapes of the Rubik's Snake is at most 423 = 70 368 744 177 664 (≈ 7×1013), i.e. 23 turning areas with 4 positions each. The real number of different shapes is lower since some configurations are spatially impossible (because they would require multiple prisms to occupy the same region of space). Peter Aylett computed via an exhaustive search that 13 535 886 319 159 (≈ 1×1013) positions are possible when prohibiting prism collisions, or passing through a collision to reach another position; or 6 770 518 220 623 (≈ 7×1012) when mirror images (defined as the same sequence of turns, but from the other end of the snake) are counted as the one position.