12.23 (1992)

The index of permutability of a group $G$ is defined to be the minimal integer $k \geqslant 2$ such that for each $k$-tuple $x_1, \dots, x_k$ of elements in $G$ there is a non-identity permutation $\sigma$ on $k$ symbols such that $x_1 \cdots x_k = x_{\sigma(1)} \cdots x_{\sigma(k)}$. Determine the index of permutability of the symmetric group $S_n$.