Question 6
We consider permutations $(x_1,\ldots,x_{2n})$ of the set $\{1,\ldots,2n\}$ such that $|x_i-x_{i+1}|=n$ for at least one $i\in\{1,\ldots,2n-1\}$. For every natural number $n$, find out whether permutations with this property are more or less numerous than the remaining permutations of $\{1,\ldots,2n\}$.