15 different balls are kept in a straight line.
Then their order is changed such that no ball is adjacent to a ball which it was adjacent to earlier. In how many ways can this task be achieved?
I thought of the negation approach, which would lead us to $15!-(\text{no of ways in which at least 1 ball is adjacent to one of its previous partners})$
But that's not too useful either, as the number of cases (and subcases) is still far too high..
$\textbf{Source:}$ My friend gave this problem to me as a challenge about 2 weeks ago.
