Question 5
Given a permutation $(a_0,a_1,\ldots,a_n)$ of $0,1,\ldots,n$, a transposition of $a_i$ with $a_j$ is called legal if $a_i=0$ for $i\gt 0$ and $a_{i-1}+1=a_j$. The permutation is called regular if after a number of legal transpositions it becomes $(1,2,\ldots,n,0)$. For which $n$ is $(1,n,n-1,\ldots,3,2,0)$ regular?