Problem- Let $n\geq$ and let $T$ be the set of all permutations in $S_n$ of the form
$t_k=\prod_{1\leq i\leq k/2}(i,k-i)$ for $k=2,3,4.....(n+1)$.
Then find the least integer $f_n$ such that every $x \in S_n$ can be written as a product of at most $f_n$ elements from $T$.
I saw this problem in first chapter of Permutation groups by Dixon($1996$). It has been 18 years since it published (I guess there hasn't been any furthuer edition yet), so I was wondering whether is it solved or not, if it is can somebody give me Hints. It looks very tough. I have shown that $T$ generates $S_n$, and still working on showing $2n-3$ is always and upper bound.