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.
Forms of a Rubik's Snake
6
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combinatorics
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0Would it be $4^{23}$ not $22$ ? ... This is a hard problem to discount all the self intersecting configurations ... – 2017-02-24
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0I know! And yes, you are right. Just a simple error! Thanks – 2017-02-24
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0Maybe there exist two configurations with no self intersections such that the first cannot be re-twisted into the second without collisions. I'm not sure there is only one equivalence class. Does the question regard only the equivalence class represented by the picture? Also, whether simultaneously twisting multiple pivots is allowed or not may affect the number of equivalence classes. Is simultaneously twisting multiple pivots allowed, or is it one at a time? – 2017-02-24
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0Doesn't matter. This is only about the form of the snake. Not the movement. – 2017-02-24
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0@Coolwater, the picture of the rubiks snake only shows what the snake looks like in a single form. – 2017-02-25
1 Answers
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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.