I don't have a clue about the equation to solve this but I managed to do it brute force with Python.

Code:

`>>> import itertools`

>>> couples = {0:1, 2:3, 4:5, 6:7}

>>> for k,v in couples.items():

couples[v] = k

>>> all_positions = list(itertools.permutations(range(8)))

>>> def is_valid(position):

if position[0] == couples[position[-1]]:

return False

for p in range(len(position) - 1):

if position[p] == couples[position[p+1]]:

return False

return True

>>> all_positions = [p for p in all_positions if is_valid(p)]

>>> len(all_positions)

11904>>>

seems to be 11904