I need help with d) here.

> 
> Let $2 \le r \le n$ be two natural numbers. Assume that $\rho \in S\_n$
>  is a permutation of the set $I\_n=\{1,2,...,n\}$. Let $x\_i \in I\_n$ for
>  $1 \le i\le r$ be $r$ different numbers.
> 
> 
> a) Show that
>  $\rho(x\_1,...,x\_i,...,x\_r)\rho^{-1}=(\rho(x\_1),...,\rho(x\_i),\rho(x\_{i+1}),...,\rho(x\_r))$.
>  HINT: For $i < r$ feed the left side with $\rho(x\_i)$ and check that
>  you get $\rho(x\_{i+1})$.
> 
> 
> b) Show that: $(2, 4)(1 ,5)(1, 2 ,3 ,4, 5)(2, 4)(1, 5)=(5,4,3,2,1)$.
> 
> 
> c) Let $\sigma$ be the $r$-cycle $(1,2,3,...,r)$ in $S\_n$. Show that
>  $\sigma$ is conjugate to its own inverse; that is, there is a
>  permutation such that $\rho\sigma\rho^{-1}=\sigma^{-1}$.
> 
> 
> d) Show that in c) one may take for $\rho$ a permutation that fixes
>  any of the numbers that $\sigma$ moves. (This means: Pick one
>  $1 \le i\le r$, then one may find a $\rho$ with $\rho(i)=i$).
> 
> 
> 

If $r$ is odd I can just generalize b), but what if $r$ is **even**? I don't see how to solve the exercise then.